Keywords: bleu de prusse analogues, photomagnetism, Fe, Co, XAS, XMCD, seuils L 2, 3, seuils K Prussian Blue Analgues, Photomagnetism, Fe, Co, XAS, XMCD, L 2, 3 edges, K edges

Les analogues du bleu de Prusse contenant du Fe et du Co (Fe/Co PBA) sont des complexes moléculaires qui présentent des propriétés physiques bistables. Par conséquent, ils sont considérés comme des candidats potentiels pour le stockage d'informations à base de molécules. Cette thèse vise à étudier la structure électronique et magnétique de Fe/Co PBA en utilisant des techniques expérimentales et théoriques avancées. Les techniques X-ray Absorption Spectroscopy (XAS) et X-ray magnetic circular dichroism (XMCD) combinées avec la théorie des multiplets en champ de ligands (LFM) sonde le changement dans les propriétés magnétiques macroscopiques de Fe/Co PBA et peuvent donner des informations locales sur les centres métalliques des complexes. Les spectres XAS et XMCD aux seuils L 2,3 du Fe et du Co sont simulés en utilisant la LFM. Le composé tridimensionnel RbCoFe PBA, deux complexes de dinucléaire photomagnétiques et les précurseurs de Fe sont étudiés. L'étude de XMCD combinée avec la LFM a révélé une grande valeur du moment magnétique d'orbite du précurseur FeTp. Une étude détaillée a été effectuée pour vérifier les règles de somme d'orbite et de spin dans le cas des ions de Fe III bas spin et il a été constaté que la règle spin somme n'était pas valide à cause de l'entremélange des seuils L 2 et L 3 . L'enquête XMCD des complexes dinucléaires photomagnétiques a confirmé le transfert d'électrons métal-métal. Cette enquête XMCD de la plus petite unité de la famille Fe / Co PBA est utile pour comprendre les propriétés magnétiques de la famille de Fe / Co PBA. L'étude XMCD sur aux seuils K du Fe et du Co d'un composé tridimensionnel RbCoFe PBA a prouvé l'existence d'une interaction antiferromagnétique entre les ions métalliques de Fe et de Co dans l'état photoinduit.

Paris was a foreign land to me when I first arrived here four years ago to pursue my higher education, and now it has become a home away from home which has made me understand the true meaning of the quote by Victor Hugo: "To study in Paris is to be born in Paris!" Undoubtedly, Paris with its great art history, picturesque landmarks and mesmerizing scenic beauty, cross-cultural ambiance on one hand and being the hub of cutting-edge scientific research on the other hand is an ideal place for anyone who seeks Eudaimonia (human flourishing). I admit that living and studying at Paris will always be a wonderful experience of my life which I can never forget.

The quality years of my life that I devoted to my doctoral research were full of adventures and if I put it another way more precisely it is correct to say my PhD was never less than a roller coaster ride. Performing experiments, handling the pressure to get the good results, group meetings, presentations, time management, meeting the deadlines and sleepless nights at synchrotron during beamtimes are few things to mention in the long list of my journey as a PhD researcher. First of all, I am thankful to my PhD advisor Philippe SAINCTAVIT who had been a great mentor throughout my PhD project. I was privileged to work under his supervision and to learn from him. He always encouraged me to present my research work in many conferences. It was his support due to which I presented my work in several conferences, summer school and synchrotron users' meetings in France, Russia, Germany and Brazil. Despite being the head of the team MIMABADI at IMPMC and the director of research CNRS, his undivided attention towards my PhD project was commendable. I really appreciate his guidance and dedication! I look forward to learn more from him if I get any opportunity in my future research projects to collaborate. Besides, I would like to thank my other team members, Marie-Anne ARRIO and Amélie JUHIN for their encouragement and support during my PhD. I would like to thank for the help they provided me for Ligand Field Multiplet Calculations. I would like to thank Prof. Eric COLLET and Prof. Cyrille TRAIN for their valuable time they dedicated to review my PhD manuscript. I am very thankful Prof. Talal MALLAH, Prof. Corine MATHONIERE and Prof Rodrigue LESCOUEZEC for their participation in the PhD defense jury.

My special thanks to my collaborators Corine MATHONIERE (ICMCB), Rodolphe CLERAC (CRPP) and Evangelia S. KOUMOUSI (ICMCB, CRPP) from University of Bordeaux on the project of dinuclear Prussian Blue Analogues. Our meetings and discussions at the beamtimes were very fruitful and helped me learn from your experiences. I would like to thank Eva for her help during the beamtimes. Eva, a brilliant chemist trained under Corine and Rodolphe, who synthesized the beautiful samples of photomagnetic dinuclear complexes and their precursors for the XMCD measurements at synchrotron. When a physicist meets a chemist wonderful things happen. This is true in fact! And I am looking forward to our publications together on two dinuclear complexes in near future.

My deepest thanks to my collaborators from ICMMO on the project of tridimensional Prussian Blue Analogues: Anne BLEUZEN, Amélie BORDAGE and Robinson MOULIN.

My sincere thanks to Christophe CARTIER DIT MOULIN and Loïc JOLY. Finally, I thank my dear family for their love and support. Thanks to my siblings who always cheered me up which helped me to accomplish my projects in time. I owe a lot to my lovely sisters Batool and Andaleeb who always believed in me. Thank you for your unconditional love! Thank you my dear sister Batool for being always there for me. You never got tired listening to my stories, daily struggles and achievements. I will never forget our "special" sarcastic jokes and laughter moments. I am confident to say that there is a great part of yours in the success of this doctoral thesis. My special thanks is for my loving parents whose love and care made me who I am today. You have always given me freedom to discover my true potential. I love you papa and mama and I dedicate my doctoral thesis to both of you. P.S: A huge thanks to all the wonderful people I have met so far, the great scientists, friends and mentors who have inspired me! Sadaf Fatima Jafri Paris, September 2016. Dedicated to my loving parents... "I have discovered the secret that after climbing a great hill, one only finds that there are many more hills to climb. I have taken a moment here to rest, to steal a view of the glorious vista that surrounds me, to look back on the distance I have come. But I can only rest for a moment, for with freedom come responsibilities, and I dare not linger, for my long walk is not ended."

Nelson Mandela, Long Walk to Freedom

Table of contents Introduction

The family of the Fe/Co Prussian Blue Analogues (PBA) is well known for their bistable physical properties that are triggered and tuned by external stimuli such as light, temperature or pressure. The reversibility of the photo-induced and thermal-induced magnetization makes Fe/Co Prussian Blue Analogues a potential candidate for high density information storage devices. Since the discovery of photomagnetism in Fe/Co PBA, many efforts have been devoted towards the understanding of their interesting bistable properties. Among others, one of the important step in this direction is to study the electronic and magnetic structures of the corresponding precursors. This thesis aims to investigate the electronic and magnetic structure of two different photomagnetic Fe/Co dinuclear complexes, of a tridimensional RbCoFe PBA and of the corresponding Fe-bearing precursors. The manuscript is structured as follows:

Chapter 1 is a brief introduction to photomagnetic Fe/Co Prussian Blue Analogues.

Chapter 2 is dedicated to the experimental and theoretical techniques that were employed for the investigation of the Fe/Co PBA systems. X-ray Absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) are combined with Ligand Field Multiplet (LFM) theory to get information about the electronic and magnetic structures of the absorbing atoms.

Chapter 3 deals with the study of Fe-bearing precursors of Fe/Co PBA which includes the Potassium Ferricyanide precursor for tridimensional PBA crystals and FepzTp, FeTp*, FeTp that are the precursors for the cube, the square and the dinuclear molecular complexes respectively. A detailed XMCD investigation on Fe L 2,3 edges of FeTp precursor is presented.

Ligand Field Multiplet calculations have been performed to extract orbit and spin magnetic moments and a value of the orbit magnetic moment larger than the spin magnetic moment is measured along the C 3 axis. Magneto-optical sum rules were applied and tested on Fe III LS bearing FeTp precursor. A thorough examination of the LFM results showed that the spin sum rule fails and a systematic study is performed to find out the origin of the failure for Fe III LS system. The results are published in a recently accepted paper. Chapter 4 is dedicated to the XMCD investigations of two photomagnetic dinuclear Fe/Co PBA complexes, which are the smallest building block of the Fe/Co PBA family.

The first dinuclear complex exhibits magnetic and optical bistability in solid state when solvent molecules are evaporated. The metal-to-metal electron transfer (ET) is confirmed by K and L 2,3 edges XMCD. Most of the results concerning this dinuclear complex are gathered in a paper to be submitted soon. The second dinuclear complex requires its solvent molecules to display the ET properties. Hence, it is investigated at Fe and Co K edges in an experimental cell preserving from evaporation and the ET is also observed with temperature and light irradiation. The field of molecular magnetism offers a dynamic range of molecular magnetic materials which are designed from pre-defined molecular precursors using a rational building block approach. The current challenge is to tailor properties of molecular complexes using state-of-the-art techniques to build smart materials. The manipulation of properties of magnetic materials at the nanoscale is an interdisciplinary research field at the crossroad of chemistry, physics and material science. In the last two decades, this field has grown regarding the design and the characterization of materials with novel functionalities. These molecular clusters which have been widely studied include spin cross over (SCO), [START_REF] Decurtins | Light-Induced Excited Spin State Trapping in a Transition-Metal Complex: The hexa-1-propyltetrazole-iron (II) tetrafluoroborate spin-crossover system[END_REF]2] single molecule magnets (SMM) [3][START_REF] Sessoli | High-Spin Molecules:[Mn 12 O 12 (O 2 CR) 16 (H 2 O) 4[END_REF][START_REF] Codreanu | Functionalization of Molecular Magnetic Materials: Towards the Soluble Systems and Liquid Crystal[END_REF] and photomagnetic systems. [START_REF] Decurtins | Light-Induced Excited Spin State Trapping in a Transition-Metal Complex: The hexa-1-propyltetrazole-iron (II) tetrafluoroborate spin-crossover system[END_REF][START_REF] Sato | Photoinduced Magnetization of a Cobalt-Iron Cyanide[END_REF][START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF][START_REF] Koumousi | Synthesis and Characterization of Dinuclear Fe/Co Complexes Exhibiting Metal-to-Metal Electron Transfer Properties[END_REF] These molecular magnetic systems offer promising applications based on their multiple bistabilities and structure-based multifunctionalities. [START_REF] Codreanu | Functionalization of Molecular Magnetic Materials: Towards the Soluble Systems and Liquid Crystal[END_REF][START_REF] Koumousi | Synthesis and Characterization of Dinuclear Fe/Co Complexes Exhibiting Metal-to-Metal Electron Transfer Properties[END_REF][START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Tokoro | Novel Magnetic Functionalities of prussian Blue Analogs[END_REF] The study of photomagnetism and related phenomena in molecular systems is appealing because of their technological applications related to externally controlled magnetization. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Tokoro | Novel Magnetic Functionalities of prussian Blue Analogs[END_REF] Magnetic molecules can act as switches and thus can be used as molecular bits. [START_REF] Mondal | On/Off Photoswitching in a Cyanide-Bridged {Fe 2 Co 2 } Magnetic Molecular Square[END_REF] In this regard, the first example of photo-induced switching of magnetization in molecular species was reported in a Fe II spin-crossover system by the Mainz group in 1984. [START_REF] Decurtins | Light-Induced Excited Spin State Trapping in a Transition-Metal Complex: The hexa-1-propyltetrazole-iron (II) tetrafluoroborate spin-crossover system[END_REF] Spin-crossover is the spin state switching mechanism from low spin (LS) to high spin (HS) triggered by external parameters such as temperature, pressure, light irradiation and magnetic field. [2] In consequence, light-induced excited spin state trapping (LIESST) effect can be observed. An excited HS state is trapped when the energy barrier between the ground state and the excited state prevents the system to go back to the ground state.

In the following a brief overview of photomagnetic Fe/Co Prussian blue analogues is presented to help readers to understand the results described in the next chapters.

Chapter 1

Photomagnetism in metal-to-metal electron transfer systems: Fe/Co Prussian Blue Analogues

Prussian Blue Analogues (PBA) are a prominent class of transition metal cyanide-based systems where the functionality of cyanido ligand is used to build molecular complexes. The cyanido ligand is a non-symmetric bridging molecule, and gives molecular complexes with strong metal-carbon bonds. [START_REF] Juan M Herrera | Mixed Valency and Magnetism in Cyanometallates and Prussian Blue Analogues[END_REF] They are probably the oldest studied family of coordination compounds that has gained recognition for being the prototype of molecular magnets.

The Prussian Blue family is widely known for its electronic and magnetic properties. The Prussian Blue can be identified as Fe 4 [Fe(CN) 6 ] 3 . The intense and characteristic blue color of the Prussian Blue pigment is attributed to the metal-to-metal electron transfer band around 700 nm due to the weak electron delocalization between metallic centres through the cyanide bridge. [START_REF] Melvin B Robin | The Color and Electronic Configurations of prussian Blue[END_REF] The general formula of PBA can be written as

A x M y [M'(CN) 6 ]•nH 2 O
where M and M' are transition metal ions, for instance, M = Co, M' = Fe, and A is an alkali metal cation (K + , Rb + , Na + , Cs + ) randomly located in the structure. This coordination network has a face-centered cubic (fcc) structure with F m 3m space group and a cell parameter close to 10 Å. [START_REF] Sato | Photoinduced Magnetization of a Cobalt-Iron Cyanide[END_REF][START_REF] Bleuzen | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 1. Conditions to Observe the Phenomenon[END_REF][START_REF] Escax | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 3. Control of the Photo-and Thermally Induced Electron Transfer by the [Fe(CN) 6 ] Vacancies in Cesium Derivatives[END_REF] In the schematic representation of tridimensional PBA in Figure 1.1, the metallic centres are connected by cyanide bridges, where Fe III and Co II are bonded to carbon and nitrogen respectively. In 1996, reversible photo-induced magnetism was discovered in K 0.2 Co 1. 4 [Fe(CN) 6 ]•6.9H 2 O PBA by Sato et al. [START_REF] Sato | Photoinduced Magnetization of a Cobalt-Iron Cyanide[END_REF][START_REF] Sato | Cation-Driven Electron Transfer Involving a Spin Transition at Room Temperature in a Cobalt Iron Cyanide Thin Film[END_REF] Upon light irradiation at low temperature, diamagnetic Fe II LS (t 6 2g e 0 g , S=0)-CN-Co III LS (t 6 2g e 0 g , S=0) state is transformed into paramagnetic Fe III LS (t 5 2g e 0 g , S=1/2)-CN-Co II HS (t 5 2g e 2 g , S=3/2) state. The family of Prussian Blue Analogues offers multi-functional applications based on tunable physical properties. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Tokoro | Novel Magnetic Functionalities of prussian Blue Analogs[END_REF] These bistable physical properties are triggered and tuned by an external stimuli like light, [START_REF] Sato | Photoinduced Magnetization of a Cobalt-Iron Cyanide[END_REF][START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF][START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Sato | Optically Switchable Molecular Solids: Photoinduced Spin-Crossover, Photochromism, and Photoinduced Magnetization[END_REF] temperature, [START_REF] Shimamoto | Control of Charge-Transfer-Induced Spin Transition Temperature on Cobalt-Iron Prussian Blue Analogues[END_REF] electric field, [START_REF] Sato | Electric-Field-Induced Conductance Switching in FeCo Prussian Blue Analogues[END_REF] and pressure. [START_REF] Ksenofontov | Pressure-Induced Electron Transfer in Ferrimagnetic Prussian Blue Analogs[END_REF] The metal-to-metal electron transfer (Figure 1.2) accompanies modification in the electronic structure of the Co centre (HS or LS) also referred as charge-transfer-induced spin transition (CTIST). [START_REF] Shimamoto | Control of Charge-Transfer-Induced Spin Transition Temperature on Cobalt-Iron Prussian Blue Analogues[END_REF] This metal-to-metal electron transfer is confirmed by infrared (IR), [START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF] Mössbauer [START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF] and X-ray absorption near edge structure (XANES) spectroscopies. [START_REF] Yokoyama | Local Structure of a Trapped Photoexcited State of a Fe-Co cyanide studied by X-ray-Absorption Fine-Structure Spectroscopy[END_REF] A systematic study has been carried out by Sato et al. [START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF] and Verdaguer and co-workers [START_REF] Bleuzen | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 1. Conditions to Observe the Phenomenon[END_REF][START_REF] Bleuzen | Photomagnetism in C x Co 4 [Fe(CN) 6 ] (8+x)/3 •nH 2 O Prussian Blue Analogues: Looking for the Maximum Photo-Efficiency[END_REF][START_REF] Escax | Nature of the Long-Range Structural Changes Induced by the Molecular Photoexcitation and by the Relaxation in the Prussian Blue Analogue Rb 1[END_REF][START_REF] Bleuzen | Thermally Induced Electron Transfer in a CsCoFe Prussian Blue Derivative: The Specific Role of the Alkali-Metal Ion[END_REF][START_REF] Escax | The Co Ligand Field: A Key Parameter in Photomagnetic CoFe Prussian Blue Derivatives[END_REF] to investigate the driving factors of photo-induced magnetization in tridimensional Fe/Co PBA. Sato et al. [START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF] performed a study where potassium was replaced by rubidium to have Rb 0.66 Co 1.25 [Fe(CN) 6 ]•4.3H 2 O. This compound was characterized by infrared and Mössbauer spectroscopies to understand the photo-induced long-range magnetic order and results were compared with the alkali free PBA. Co [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF] The ligand field of nitrogen atoms from cyanido ligand is higher than for an oxygen atom in water molecule. Since, nitrogen atoms from cyanide bond are missing to make Co-NC bond, the ligand field around Co is modified. The ligand field around the Co ions plays a key role in stabilizing the Fe II LS -CN-Co III LS configuration or the other Fe III LS -CN-Co II HS . A series of Na + based Fe/Co PBA has also been synthesized where the CTIST temperature was found to vary by controlling the composition Co/Fe ratio. The Co/Fe ratio thus determines the strength of ligand field around Co II ions. [START_REF] Shimamoto | Control of Charge-Transfer-Induced Spin Transition Temperature on Cobalt-Iron Prussian Blue Analogues[END_REF] Sato et al. [START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF] and Verdaguer et al. [START_REF] Bleuzen | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 1. Conditions to Observe the Phenomenon[END_REF][START_REF] Cartier Dit Moulin | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 2. X-ray Absorption Spectroscopy of the Metastable State[END_REF][START_REF] Bleuzen | Photo-Induced Electron Transfer and Magnetic Switching in CoFe Cyanides: Study of the Metastable State[END_REF][START_REF] Goujon | Photo-Excitation from Dia-to Ferri-Magnetism in a Rb-Co-Hexacyanoferrate Prussian Blue Analogue[END_REF][START_REF] Goujon | Thermo-Chromism and Photo-Chromism in a Prussian Blue Analogue[END_REF] reported that the ground state of the Fe/Co Prussian Blue analogues depends on the type of the interstitial alkali cation. They also studied the effect of different Co environments on the photomagnetic properties. The different environments correspond to different amount of vacancies introduced in the structure.

In conclusion, the photomagnetic properties are affected by the chemical composition such as the nature and the amount of alkali metal ion (0 to 4) per unit cell, the [Fe(CN) 6 ] 3- vacancies and the zeolitic water molecules. In the metastable state (i.e. Fe III LS -CN-Co II HS ), the framework is stabilized by strong cooperativity effects of the extended lattice as well as structural defects, features that are considered to be prerequisite for trapping the photo-induced species.

In addition, the structural information is significant to understand the fascinating photomagnetic properties in PBA. Extended X-ray absorption fine structure (EXAFS) results have shown that the major structural modifications occur in the vicinity of the Co ion: the Co-N bond length increases by 0.18 Å during the Co III LS to Co II HS spin transition. [START_REF] Yokoyama | Characterization of magnetic CoFe cyanides by x-ray-absorption fine-structure spectroscopy[END_REF] This transition is isostructural with a change in the unit cell volume. [START_REF] Hanawa | Coherent Domain Growth Under Photo-excitation in a prussian Blue Analogue[END_REF] The structural changes were further investigated and characterized by X-ray absorption spectroscopy (XAS) at the metal L 2,3 edges combined with Ligand Field Multiplet Theory. [START_REF] Escax | The Co Ligand Field: A Key Parameter in Photomagnetic CoFe Prussian Blue Derivatives[END_REF][START_REF] Cartier Dit Moulin | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 2. X-ray Absorption Spectroscopy of the Metastable State[END_REF][START_REF] Cartier Dit Moulin | Structural Rearrangements Induced by Photoexcitation in a RbCoFe Prussian Blue Derivative[END_REF][START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF] Thanks to the chemical selectivity of XAS, valuable information on each of the two metallic ions in cyanide based systems (A-CN-B) can be extracted such as oxidation LS ) electronic configurations due to thermally and photo-induced metal-to-metal electron transfer processes. This figure is taken from the review by Aguilà et al. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF] state, spin state, local site symmetry. XAS and XMCD spectra can be simulated using Ligand Field Multiplet calculations to obtain the crystal field parameters. Arrio et al. [START_REF] Anne Arrio | Characterization of Chemical Bonds in Bimetallic Cyanides using X-ray Absorption Spectroscopy at L 2,3 edges[END_REF] characterized the chemical bonds in hexacyanochromate(III) based system of Prussian Blue Analogues having Cr III -CN-A II units (A II = V II , Mn II , Fe II , Co II , or Ni II ). The ferro-or ferrimagnetic ordering occurs below critical temperatures that ranges from 66 to 315 K. [START_REF] Ferlay | A Room-Temperature Organometallic Magnet Based on Prussian Blue[END_REF] The comparison of A II -NC and Cr III -CN bonds gives that the A II -NC bond experiences small ligand-metal charge transfer. The LFM calculations show similar results for all four divalent A II ions. In addition, by simulating the XAS and XMCD signals by LFM the orbit and spin magnetic moments of the ground state can be extracted. [START_REF] Anne Arrio | Measurement of Magnetic Moment at the Atomic Scale in a High Tc Molecular Based Magnet[END_REF] The first experimental determination of the Co crystal field parameters in a photomagnetic PBA was reported by Escax et al. [START_REF] Escax | The Co Ligand Field: A Key Parameter in Photomagnetic CoFe Prussian Blue Derivatives[END_REF] The spectral signatures for Co III LS and Co II HS ions were found to be characteristic of Co ion in octahedral symmetry. In 2006, Hocking et al. [37] performed a detailed investigation of K 3 [Fe III (CN) 6 ] and K 4 [Fe II (CN) 6 ] by LFM calculations. This study helped to understand the role of Potassium Ferricyanide as a percursor and to explain the origin of various features on Fe III LS L 2,3 edges XAS spectrum. Moreover, LFM calculations performed with configuration interaction confirm that X-ray absorption spectroscopy is a direct probe of metal-to-ligand back-bonding. Cafun et al. [START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF] performed the LFM calculations of the Co L 2,3 edges XAS spectra for the low temperature diamagnetic state and the photo-induced state in three different systems with Na, Rb and Cs alkali ions. They extracted the crystal field value for Co. The 10Dq(Co) was found to be 2.4 eV before irradiation (Fe II HS -CN-Co III LS ) and 1.1 eV after irradiation (Fe III LS -CN-Co II HS ).

Towards molecular analogues of Fe/Co PBA

In tridimensional PBA, the quantity and amount of alkali metal ions modify the amount of vacancies. The vacancies influence the environment around the Co ions and the coordination sphere that is completed by water molecules, hence altering the electron transfer properties. structure. This results in the presence of inactive diamagnetic or paramagnetic pairs. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF] For technological applications, the electron transfer properties of tridimensional PBA systems must be transferred to their low-dimensional analogues. Some attempts have been made

to develop Fe/Co cyanide complexes but thermal-and/or photo-induced electron transfer properties could not be observed. [START_REF] Shu-Zhong | Synthesis, Characterization and Electrochemical Properties of Cyanide-Bridged Cobalt (III)/iron(II) Complexes[END_REF][START_REF] Bernhardt | The First Structurally Characterized Discrete Dinuclear µ-Cyano Hexacyanoferrate Complex[END_REF][START_REF] Paul | Discrete Dinuclear Cyano-Bridged Complexes[END_REF] The first evidence of thermally induced metalto-metal electron transfer was reported in cyanido-bridged Fe/Co pentanuclear [Fe 2 Co 3 ] molecule by Dunbar and co-workers in 2004. [START_REF] Curtis P Berlinguette | A Charge-Transfer-Induced Spin Transition in the Discrete Cyanide-Bridged Complex[END_REF][START_REF] Funck | Light-Induced Excited Spin State Trapping and Charge Transfer in Trigonal Bipyramidal Cyanide-Bridged Complexes[END_REF] Fe 4 ] before (black dots), after irradiation (red dots); and after thermal quenching (blue dots). This figure is taken from the review by Aguilà et al. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Li | Magnetic and Optical Bistability Driven by Thermally and Photoinduced Intramolecular Electron Transfer in a Molecular Cobalt-Iron Prussian Blue Analogue[END_REF] The group of chemists, C. Mathonière, R. Clérac and co-workers at Bordeaux succeeded in synthesizing the molecular cube and square analogues of tridimensional PBAs with electron transfer properties. The reversible photo-induced electron transfer in molecular cube [Fe 4 Co 4 ] was reported by Li et al. [START_REF] Li | Magnetic and Optical Bistability Driven by Thermally and Photoinduced Intramolecular Electron Transfer in a Molecular Cobalt-Iron Prussian Blue Analogue[END_REF] This complex is the first molecular system that mimics the optical and magnetic bistability in Co/Fe Prussian Blue complexes. The molecular structure of the cube analogue is presented in Figure 1.3. In this molecular system the photo-induced state obtained by light irradiation or rapid cooling was found to have higher lifetime compared to the tridimensional networks. For Na + based PBA the metastable life time was 3 hours at 120 K [START_REF] Rémy | Optical and Magnetic Properties of the Photo-induced State in the Coordination Network Na 2 Co 4[END_REF] whereas it was 10 years at 120 K for the molecular cube. [START_REF] Zhang | Reversible Thermally Photoinduced Electron Transfer in a Cyano-Bridged {Fe 2 Co 2 } Square Complex[END_REF] In 2010, another discrete molecular system, a cyano-bridged [Fe 2 Co 2 ] square complex (Figure 1.4) was synthesized and characterized by Zhang et al. [START_REF] Zhang | Reversible Thermally Photoinduced Electron Transfer in a Cyano-Bridged {Fe 2 Co 2 } Square Complex[END_REF][START_REF] Zhang | Thermochromic and Photoresponsive Cyanometalate Fe/Co Squares: Toward Control of the Electron Transfer Temperature[END_REF] In addition, Siretanu et al. [START_REF] Siretanu | Controlling Thermally Induced Electron Transfer in Cyano-Bridged Molecular Squares: From Solid State to Solution[END_REF] showed that the magnetic properties of molecular square complexes in solutions and particularly the electron-transfer temperature can be modulated by the nature of the solvent. The thermally induced switchable behavior, as was observed in the solid state for square molecules, had been transferred to diluted solutions. Later in 2012, Hashino et al. reported electron transfer properties in [CoFe] chain induced by light or temperature. [START_REF] Hoshino | Three-Way Switching in a Cyanide-Bridged [CoFe] chain[END_REF] Recently, thermal-and photo-induced electron transfer have been demonstrated in the smallest unit of the Fe/Co PBA family by Koumousi et al. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] The molecular structure of the dinuclear complex is presented in Figure 4.1. In this dinuclear complex, the thermalinduced electron transfer is observed at 170 K with a thermal hysteresis of 5 K. At 10 K ) and temperature before (black dots) and after (red dots) white light irradiation with a sweep rate of 0.4 K/min (right). This figure is taken from the review by Aguilà et al. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] under white light irradiation photoconversion occurs. The metastable state of this complex relaxes to the diamagnetic state around 45 K. The miniaturization of molecular species tends to decrease the relaxation temperature which is particularly low in this complex. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF]

Summary of Chapter 1

It is desirable to understand the physical properties of nanostructures of Fe/Co PBA using XAS and XMCD techniques. The XMCD technique is proved to be essential for characterization and determination of the electronic and magnetic structures of molecule based magnets. [START_REF] Anne Arrio | Characterization of Chemical Bonds in Bimetallic Cyanides using X-ray Absorption Spectroscopy at L 2,3 edges[END_REF][START_REF] Dujardin | Synthesis and Magnetization of New Room-Temperature Molecule-Based Magnets: Effects of Stoichiometry on Local Magnetic Structure by X-ray Magnetic Circular Dichroism[END_REF][START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF][START_REF] Mannini | X-Ray Magnetic Circular Dichroism Picks out Single-Molecule Magnets Suitable for Nanodevices[END_REF][START_REF] Cornia | Chemical Strategies and Characterization tools for the Organization of Single Molecule Magnets on Surfaces[END_REF][START_REF] Letard | Remnant Magnetization of Fe8 High-Spin Molecules: X-ray Magnetic Circular Dichroism at 300 mK[END_REF][START_REF] Ghigna | X-ray Magnetic-Circular-Dichroism Spectra on the Superparamagnetic Transition-Metal ion Clusters Mn12 and Fe8[END_REF][START_REF] Prado | Magnetic 127 Anisotropy of Cyanide-Bridged Core and Core-Shell Coordination Nanoparticles Probed by X-ray Magnetic Circular Dichroism[END_REF] Some XAS and/or XMCD measurements have been reported on Fe/Co chain [START_REF] Michael | X-ray Magnetic Circular Dichroism Investigation of the Electron Transfer Phenomena Responsible for Magnetic Switching in a cyanidebridged [CoFe] Chain[END_REF] and Fe/Co molecular square. [START_REF] Sekine | X-ray-Induced Phase Transitions by Selective excitation of Heterometal ions in a Cyanide-bridged Fe-Co Molecular Square[END_REF][START_REF] Sekine | Investigation of the Light-Induced Electron-Transfer-Coupled Spin Transition in a Cyanide-bridged [Co 2 Fe 2 ] omplex by X-ray Diffraction and Absorption Measurements[END_REF] In collaboration with Prof. Corine Mathonière and Dr. Rodolph Clérac and their teams, the XAS and XMCD experiments have been performed on two dinuclear complexes and Fe-bearing precursors. In case of the dinuclear complexes, the switching mechanism of the local magnetization is observed.

The XMCD results on Fe-bearing precursors and dinuclear complexes are presented in have already confirmed the antiferromagnetic coupling in photo-induced state of this PBA system. [START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF] In the present study, this antiferromagnetic interaction between Fe and Co is observed by recording XMCD signals at L 2,3 edges. The results are detailed in Chapter 5.

Chapter 2

Experimental Methods to study Fe/Co Prussian Analogues

Introduction

This chapter is a brief introduction to the experimental techniques which are employed to study the electronic and magnetic structure of the FeCo Prussian Blue systems in this work. The X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) are element specific techniques to study the local structure, spin, oxidation state and site-symmetry. In the case of coordination complexes, XAS and XMCD have been valuable in determining the details of the electronic and magnetic structures in nanoparticles, molecular materials and single molecule magnets. [START_REF] Dujardin | Synthesis and Magnetization of New Room-Temperature Molecule-Based Magnets: Effects of Stoichiometry on Local Magnetic Structure by X-ray Magnetic Circular Dichroism[END_REF][START_REF] Mannini | X-Ray Magnetic Circular Dichroism Picks out Single-Molecule Magnets Suitable for Nanodevices[END_REF][START_REF] Cornia | Chemical Strategies and Characterization tools for the Organization of Single Molecule Magnets on Surfaces[END_REF][START_REF] Prado | Magnetic 127 Anisotropy of Cyanide-Bridged Core and Core-Shell Coordination Nanoparticles Probed by X-ray Magnetic Circular Dichroism[END_REF] The XMCD is the difference of two X-ray absorption spectra recorded with left and right circular polarized X-rays. XMCD probes the magnetic moment of individual atoms thanks to the chemical and orbital selectivity of X-ray absorption and can separate the orbit and spin contributions to the total magnetic moment of the absorbing atom.

XAS and XMCD

X-ray absorption spectroscopy

The X-ray sources from synchrotron radiation are highly intense, tunable and with well defined polarization state. The energy of X-ray photons ranges from few hundreds eV to several tens keV. XAS is a core level spectroscopy that is element specific and is considered as surface sensitive technique in the soft X-ray range (300 to 3000 eV) due to the detection mode that is usually the Total Electron Yield. The chemical sensitivity of XAS is obtained by tuning the incident X-ray photon energy to the core to valence transition energy of a specific element. When the electromagnetic radiation with photon energy E interacts with matter its intensity I as a function of penetration depth d is reduced in result of interaction with matter. The Beer-Lambert law is given as:

I(E, d) = I 0 (E) exp -µ(E)d
Chapter 2

where µ(E) is the linear photoabsorption coefficient of the sample, I 0 (E) is the incident intensity and I is the intensity measured after absorption, behind the sample. At low energy of X-rays, the media are generally not transparent so that the absorption coefficient is not directly measured in the transmission mode and one has to detect a phenomenon that is expected to be proportional to the absorption coefficient. For energies below 20 keV, photoelectric effect is the dominant process compared to both elastic Rayleigh scattering and inelastic Compton scattering. [START_REF] Beaurepaire | Magnetism and synchrotron radiation[END_REF] When a X-ray photon with energy E = ω is absorbed, a core-level electron with E i binding energy in the initial state |i is excited to an empty level |f above the Fermi level with energy

E f = E i + E. Therefore, XAS
probes the empty states of the absorbing atom. The X-ray absorption cross-section is defined as the number of photons absorbed per atom divided by the number of incident photons per unit area and hence the dimension [length 2 /atom]. [START_REF] Stöhr | Interactions of Polarized Photons with Matter[END_REF] The photoabsorption coefficient is proportional to absorption cross section.

In the electric dipole approximation the interaction Hamiltonian writes ε • r and the transition probability per unit time is given by the Fermi Golden rule:

σ( ω) = 4π 2 α ω i,f 1 d i | f |ε • r|i | 2 δ(E f -E i -ω). (2.1)
In Equation 1.1, α is the fine structure constant, ω is the photon energy, |i and |f are multielectronic wavefunctions for the initial and the final configurations, d i is the degeneracy of the multielectronic ground state, ε is the photon polarization vector, r is the integration variable, E i and E f are the energies associated to wavefunctions,

δ(E f -E i -ω)
is the Dirac distribution that ensures energy conservation and the sum i,f extends over all the populated terms of the initial state and all the terms of the final state configuration.

The set-up for XAS experiments is illustrated in Figure 2.1.

Selection rules

In XAS, the electric dipole selection rules only permit transitions where the angular momentum quantum number l changes by unity ∆l = ±1 and conserve the spin ∆s = 0.

In addition to the selection rules involving l, other selection rules involve the magnetic quantum number m. For linear polarized light the selection rule is ∆m l = 0, for left circularly polarized light it is ∆m l = +1, and for right circularly polarized light it is

∆m l = -1.
In addition for the electric quadrupole transitions, the selection rules writes ∆l = ±2 or ∆l = 0. For 3d transition elements, the electric quadrupole transitions are negligible at L 2,3 edges and often detectable at K edges although they are found between 10 and 100 times weaker than the electric dipole transitions. [START_REF] Stöhr | Interactions of Polarized Photons with Matter[END_REF] In the electric dipole approximation, the isotropic absorption is the average of absorption measured for the three directions perpendicular to the polarization. The polarization vectors ε-, ε+ and ε|| are orthogonal and defined as (to some phase conventions),

ε-= - 1 √ 2 êx -iê y ε+ = - 1 √ 2 êx + iê y ε|| = êz
Then:

σ iso = 1 3 σ + + σ -+ σ ||

X-ray magnetic circular dichroism (XMCD)

Dichroism refers to the polarization dependent absorption of a material and is the manifestation that the optical response of a material depends upon the relative orientation of the polarization direction of light with respect to the symmetry axes of the material.

It arises due to the charge or spin anisotropy in the system. The charge anisotropy (crystal field) causes the 'natural dichroism' like X-ray natural linear dichroism (XNLD) and X-ray natural circular dichroism (XNCD) whereas, X-ray magnetic linear dichroism (XMLD) and X-ray magnetic circular dichroism (XMCD) occur due to the anisotropy of Chapter 2 spin distribution. [START_REF] Beaurepaire | Magnetism and synchrotron radiation[END_REF] When a sample carries a net magnetic moment, the system is no more invariant by time reversal so that the absorption with left polarized X-rays is no more equal to the absorption with right polarized X-rays: this is the origin of XMCD. XMCD effect was predicted theoretically in 1975 by Erskin and Stern and observed experimentally at Fe K edge in a Fe foil by Schütz et al. [START_REF] Schütz | Absorption of Circularly Polarized X-rays in Iron[END_REF] At L 2,3 edges, a strong XMCD effect was first reported in ferromagnetic nickel by Chen et al., [START_REF] Chien-T Chen | Soft-X-ray Magnetic Circular Dichroism at the L 2,3 edges of Nickel[END_REF] . The effect was ≈2 orders of magnitude larger than those at the K edges of transition metals. [START_REF] Schütz | Absorption of Circularly Polarized X-rays in Iron[END_REF] The principle of XMCD measurements is illustrated in Figure 2.2. The quantization axis is defined in the ẑ direction that is usually the direction of the wave vector of the incident beam. When necessary, a magnetic induction is applied along ẑ to induce a net magnetic moment in the sample. The XMCD signal is the difference ∆σ between the two absorption cross sections for left and right polarized X-ray beam defined as,

∆σ = σ -(B) -σ + (B) = σ right (B) -σ lef t (B),
when B is parallel to the propagation vector k.

The signs "+" or "-" in σ + and σ -refer to X-ray helicity with "+" for left and "-" for right polarized X-rays. . With these definitions, a negative XMCD signal at the L 3 edge of 3d transition elements corresponds to a magnetic moment pointing in the same direction as the external magnetic induction. For powder samples with negligible XMLD, the equation σ + + σ -= 2σ || holds and then the absorption cross section can be written as σ iso = σ + +σ -

2

. The XAS and XMCD spectra at Fe L 2,3 edges are presented in Figure 2.3.

One of the important aspect of XMCD is the ability of measuring the element-specific magnetization curves. In this method, the intensity of dichroic signal is recorded by setting the monochromator at a given energy and the external magnetic induction is varied. When the XMCD signal is proportional to the magnetization of the absorbing atom, the XMCD detected magnetization curve is specific of the magnetization of the absorbing atom and can be compared to conventional magnetization curves such as those measured by SQUID or VSM magnetometers.

The review by Van der Laan et al. [START_REF] Van Der Laan | Applications of Soft X-ray Magnetic Dichroism[END_REF][START_REF] Van Der Laan | X-ray Magnetic Circular Dichroism-A Versatile Tool to Study Magnetism[END_REF] summarizes the main applications in a variety of fields. XMCD is an excellent local probe which has been used to understand the switching mechanism, magnetic interactions and electronic structure of the metal in complexes. [START_REF] Dujardin | Synthesis and Magnetization of New Room-Temperature Molecule-Based Magnets: Effects of Stoichiometry on Local Magnetic Structure by X-ray Magnetic Circular Dichroism[END_REF][START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF][START_REF] Kuepper | Electronic Structure and Soft-X-ray-Induced Photoreduction Studies of Iron-Based Magnetic Polyoxometalates of Type {(M)M 5 } 12 Fe iii 30[END_REF][START_REF] Bunau | Understanding the Photomagnetic Behavior in Copper Octacyanomolybdates[END_REF] Moreover, XMCD measurements under pressure have also been reported to study the structural distortions in these complexes. [START_REF] Cafun | XMCD at the Transition Metal K-Edges as a Probe of Small Pressure-Induced Structural Distortions in Prussian Blue Analogues[END_REF] Thanks to the magnetooptical sum rules applied to the XMCD spectra, spin and orbit contribution to the total magnetic moment can be separated and thus orbit and spin magnetic moments can be extracted. The sum rules were developed by B.T Thole, G. Van der Laan and P. Carra et al. [START_REF] Thole | X-ray Circular Dichroism as a Probe of Orbital Magnetization[END_REF][START_REF] Paum Carra | X-ray Circular Dichroism and Local Magnetic fields[END_REF] With

p = L 3 (σ --σ + )dE, q = L 3 +L 2 (σ --σ + )dE, and r = 1 2 L 3 +L 2 (σ + + Chapter 2
σ -)dE, the sum rules can be written as L z = 2 3 q r n h and S z + 7 2 T z = 3p-2q 2r n h where T z is the magnetic dipole operator [START_REF] Paum Carra | X-ray Circular Dichroism and Local Magnetic fields[END_REF] along the ẑ axis and n h is the number of holes on the 3d shell. The integrals of XAS (r) and XMCD (p and q) are presented in figure 2.4. These sum rules relates the integral of XMCD at a specific edge to the ground state expectation values of orbit and spin magnetic moments. The sum rules are derived after several approximations. The energy dependency of the wave function in the matrix elements is not taken into account. Moreover, the L 3 and L 2 edges should be well separated to ensure correct integration on each edge. Hence, applicability of the sum rules on various systems requires great care. Some d states are present in the continuum and may also complicate the interpretation of the sum rules. The applicability of the magneto-optical sum rules is extensively addressed in the study of Fe III LS ion in FeTp in the next chapter.

Detection Methods

In the soft X-ray range the detection mode is the Total Electron Yield (TEY). TEY refers to the current of secondary electrons emitted as a consequence of the absorption of an X-ray photon. In this work absorption spectra are recorded with TEY by means of sample current measurements. The total electron yield is proportional to the absorption coefficient as long as the escape depth λ e -of the electron is much smaller compared to absorption length 1/µ(E). [START_REF] Vogel | Polarization and Angular Dependence of the L 2,3 Absorption edges in Ni (110)[END_REF][START_REF] Yüksel Ufuktepe | Thickness and Angular Dependence of the L-edge X-ray Absorption of Nickel Thin Films[END_REF] In the soft X-ray range, one can safely say that λ e -≤ 5 nm whereas 1/µ(E) ≥ 500 nm.

For hard X-rays (i.e. Fe and Co K edges), the XAS spectra have been recorded by Total Fluorescence Yield (TFY). TFY is easier to measure than the transmitted flux that relies mainly on the sample thickness and homogeneity of the sample. Unfortunately, TFY is often damaged by the so-called reabsorption effects that have then to be corrected. In the present case of FeCo PBA, the Fe and Co concentrations are low enough to reduce the reabsorption effects to a minimum and it was found that it was not necessary to apply any correction.

Program TT-Multiplet

The details of the Ligand Field Multiplet calculations are given in next chapter. For in-depth understanding of the theoretical concepts of multiplet calculations, readers can consult The hitchhiker's guide to multiplet calculations by Gerrit van der Laan. [START_REF] Van Der Laan | Hitchhiker's guide to multiplet calculations[END_REF] The program RCN was written by Cowan. [START_REF] Robert D Cowan | The theory of atomic structure and spectra[END_REF]75] Fe-bearing Precursors of Photomagnetic FeCo Prussian Blue Complexes

Introduction

In cyanometalate TM (TM : transition metal) complexes, cyanido ligand acts as strong mediator of magnetic coupling between the transition metal ions. These complexes are synthesized by pre-formed precursors using a building block approach. Cyanometalate precursors being the smallest units are likely to influence the magnetic, electronic and optical properties of cyanido-based molecular magnets such as Prussian Blue Analogues.

In this chapter we present the study of the electronic structure of four Fe III LS bearing cyanometalate precursors that are used to synthesize the Fe/Co based PBA molecules. FeTp * [START_REF] Li | Single-Molecule Magnets Constructed from Cyanometalates:{[Tp* Fe III (CN) 3 M II (DMF)[END_REF][START_REF] Li | Synthesis and Spectroscopic and Magnetic Characterization of Tris(3,5dimethylpyrazol-1-yl)borate Iron Tricyanide Building Blocks, a Cluster, and a One-Dimensional Chain of Squares[END_REF] is the precursor for the square molecule, [START_REF] Zhang | Reversible Thermally Photoinduced Electron Transfer in a Cyano-Bridged {Fe 2 Co 2 } Square Complex[END_REF][START_REF] Zhang | Thermochromic and Photoresponsive Cyanometalate Fe/Co Squares: Toward Control of the Electron Transfer Temperature[END_REF] FepzTp [START_REF] Li | An S= 2 Cyanide-Cridged Trinuclear Fe iii 2 Ni ii Single-Molecule Magnet[END_REF] is the precursor for the cube [START_REF] Li | Magnetic and Optical Bistability Driven by Thermally and Photoinduced Intramolecular Electron Transfer in a Molecular Cobalt-Iron Prussian Blue Analogue[END_REF] and FeTp is the precursor used in the synthesis of the dinuclear Fe/Co PBA. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] These samples were synthesized following the procedure developed by Li et al., [START_REF] Li | Magnetic and Optical Bistability Driven by Thermally and Photoinduced Intramolecular Electron Transfer in a Molecular Cobalt-Iron Prussian Blue Analogue[END_REF][START_REF] Li | Synthesis and Spectroscopic and Magnetic Characterization of Tris(3,5dimethylpyrazol-1-yl)borate Iron Tricyanide Building Blocks, a Cluster, and a One-Dimensional Chain of Squares[END_REF] Lescouëzec et al. [START_REF] Lescouëzec | Ferromagnetic Coupling between Low-and High-Spin Iron(III) Ions in the Tetranuclear Complexf ac[END_REF] and Koumousi et al. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] Potassium hexacyanidoferrate(III) [START_REF] Figgis | The Crystallography and Paramagnetic Anisotropy of Potassium Ferricyanide[END_REF][START_REF] Figgis | Crystal tructures of the Simple Monoclinic and Orthorhombic Polytypes of Tripotassium hexacyanoferrate (III)[END_REF] is the precursor for 3-dimensional bulk PBA systems discussed in the review by Aguilà et al. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF] The structures of the four precursors are presented in Figure 3.1 and crystallographic data are presented in Table 3.1, as reported by Li et al., [START_REF] Li | Synthesis and Spectroscopic and Magnetic Characterization of Tris(3,5dimethylpyrazol-1-yl)borate Iron Tricyanide Building Blocks, a Cluster, and a One-Dimensional Chain of Squares[END_REF][START_REF] Li | An S= 2 Cyanide-Cridged Trinuclear Fe iii 2 Ni ii Single-Molecule Magnet[END_REF] Jafri et al. [START_REF] Sadaf | Large Orbital Magnetic Moment Measured in [T P Fe III (CN) 6 ]the Precursor of Photomagnetic Molecular Prussian Blue Analogues[END_REF] and Figgis. [START_REF] Figgis | Crystal tructures of the Simple Monoclinic and Orthorhombic Polytypes of Tripotassium hexacyanoferrate (III)[END_REF] In FeTp, FeTp* and FepzTp, Fe III ions are connected to 3 cyanido ligands on one side and three Nitrogen atoms on the other side as shown in Figure 3.1. In these precursors the local point group symmetry around Fe ions is close to C 3v . [START_REF] Li | Synthesis and Spectroscopic and Magnetic Characterization of Tris(3,5dimethylpyrazol-1-yl)borate Iron Tricyanide Building Blocks, a Cluster, and a One-Dimensional Chain of Squares[END_REF][START_REF] Lescouëzec | Ferromagnetic Coupling between Low-and High-Spin Iron(III) Ions in the Tetranuclear Complexf ac[END_REF] In Potassium hexacyanidoferrate(III), Fe III ions are connected to the six cyanides forming a distorted octahedral coordination sphere. [START_REF] Day | Polarized Neutron Diffraction from Cs 2 KFe(CN) 6 : The Orbital Moment and its Anisotropy[END_REF] When Fe III ion is bonded to carbon atoms of the cyanido ligand this imposes a large π-back bonding in addition to σ bonding. [37] In case of

Z 3 4 2 2
Table 3.1 -Crystallographic data of FeTp*, [START_REF] Li | Synthesis and Spectroscopic and Magnetic Characterization of Tris(3,5dimethylpyrazol-1-yl)borate Iron Tricyanide Building Blocks, a Cluster, and a One-Dimensional Chain of Squares[END_REF] FepzTp, [START_REF] Li | An S= 2 Cyanide-Cridged Trinuclear Fe iii 2 Ni ii Single-Molecule Magnet[END_REF] FeTp [START_REF] Sadaf | Large Orbital Magnetic Moment Measured in [T P Fe III (CN) 6 ]the Precursor of Photomagnetic Molecular Prussian Blue Analogues[END_REF] and Potassium hexacyanidoferrate(III). [START_REF] Figgis | Crystal tructures of the Simple Monoclinic and Orthorhombic Polytypes of Tripotassium hexacyanoferrate (III)[END_REF] The study of the precursors (which are non-photomagnetic systems) follows a methodological approach where the experimental spectra at the Fe L 2,3 edges are analyzed in order to yield valuable information concerning their impact on the properties exhibited by various photomagnetic Prussian Blue molecular magnets.

Paper I: Magnetic properties of the FeTp precursor

The precursor FeTp has been studied extensively. Theoretical and experimental details with the presentation of results on FeTp precursor can be found in the following paper that is printed in Section 3.2 with Supporting Information in Section 3.3. The paper has been accepted for publication in Inorganic Chemistry in June 2016. [START_REF] Sadaf | Large Orbital Magnetic Moment Measured in [T P Fe III (CN) 6 ]the Precursor of Photomagnetic Molecular Prussian Blue Analogues[END_REF] (DOI:

10.1021/acs.inorgchem.6b00664)

Introduction

Molecule-based magnets, derived from three-dimensional (3D) Prussian Blue Analogues (PBA), are the topic of intensive research [START_REF] Ferlay | A Room-Temperature Organometallic Magnet Based on Prussian Blue[END_REF][START_REF] Verdaguer | Room-Temperature Molecule-Based Magnets[END_REF][START_REF] Sato | Photoinduced Magnetization in Molecular Compounds[END_REF][START_REF] Sato | Control of magnetic properties through external stimuli[END_REF] since they are potential candidates for future molecular electronic devices [START_REF] Tokoro | Novel Magnetic Functionalities of prussian Blue Analogs[END_REF][START_REF] Verdaguer | Molecular Electronics Emerges from Molecular Magnetism[END_REF][START_REF] Camarero | Molecular vs. Inorganic Spintronics: The Role of Molecular Materials and Single Molecules[END_REF][START_REF] Gatteschi | Molecular Nanomagnets: The First 10 Years[END_REF] due to their tunable physical properties as a function of external stimuli such as magnetic field, light, pressure or temperature. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Sato | Photoinduced Magnetization in Molecular Compounds[END_REF][START_REF] Sato | Control of magnetic properties through external stimuli[END_REF] In this class of materials, cobalt ferricyanides are among the most well-known compounds exhibiting electron transfer switching induced by temperature and light. One of the most important aspects is their capability to act as photoswitches. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Sato | Photoinduced Magnetization in Molecular Compounds[END_REF][START_REF] Sato | Control of magnetic properties through external stimuli[END_REF] In 1996, the first evidence of photo-induced ferrimagnetism was reported by Hashimoto et al. [START_REF] Sato | Photoinduced Magnetization of a Cobalt-Iron Cyanide[END_REF] in a 3D , high spin, S = 3/2) units. In these systems, the photoinduced paramagnetic units in the 3D network after light irradiation led to the stabilization of a ferrimagnetic ground state with a Curie temperature of about 19 K. [START_REF] Sato | Photoinduced Magnetization of a Cobalt-Iron Cyanide[END_REF] Similar behavior has been also evidenced in other Co/Fe PBAs where the alkali metal ion has been substituted. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF] In one of these systems, Rb state. [START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF] Whereas these tridimensional systems exhibit very interesting properties for technological applications, they contain many structural defects and are not soluble in common solvents.

Consequently, they are difficult to manipulate and to shape for the future use. This drawback oriented research efforts to the synthesis of Prussian Blue molecular fragments that can be easily manipulated and studied. The design of soluble molecules that possess tunable magnetic, electrical and optical properties is based on the building block approach. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Zhang | Thermochromic and Photoresponsive Cyanometalate Fe/Co Squares: Toward Control of the Electron Transfer Temperature[END_REF] This synthetic path uses preformed precursors of the desired metal centers (Fe or Co) that are bearing at least one cyanido group and organic capping ligands. Indeed the redox properties of these precursors control the electron transfer behavior of the Prussian Blue molecules as recently demonstrated. [START_REF] Li | Magnetic and Optical Bistability Driven by Thermally and Photoinduced Intramolecular Electron Transfer in a Molecular Cobalt-Iron Prussian Blue Analogue[END_REF] Therefore, a careful study of the precursors is required in order to design the electron transfer properties of the molecules. Recently, complexes with either a cubic octanuclear, a square tetranuclear, or a linear dinuclear shape have been synthesized, [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Mondal | On/Off Photoswitching in a Cyanide-Bridged {Fe 2 Co 2 } Magnetic Molecular Square[END_REF][START_REF] Li | Magnetic and Optical Bistability Driven by Thermally and Photoinduced Intramolecular Electron Transfer in a Molecular Cobalt-Iron Prussian Blue Analogue[END_REF][START_REF] Zhang | Reversible Thermally Photoinduced Electron Transfer in a Cyano-Bridged {Fe 2 Co 2 } Square Complex[END_REF][START_REF] Zhang | Thermochromic and Photoresponsive Cyanometalate Fe/Co Squares: Toward Control of the Electron Transfer Temperature[END_REF][START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF][START_REF] Li | Synthesis and Spectroscopic and Magnetic Characterization of Tris(3,5dimethylpyrazol-1-yl)borate Iron Tricyanide Building Blocks, a Cluster, and a One-Dimensional Chain of Squares[END_REF] and they have been found to exhibit thermallyand light-induced electron transfer at the molecular scale. This prompted us to carry out a detailed investigation of the Fe III precursor used in the synthesis of the linear dinuclear Co ferricyanide PBA. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] More precisely, this paper describes the mononuclear

(N(C 4 H 9 ) 4 [TpFe III (CN) 3 ]
) complex, (Tp being tris-pyrazolyl borate; named hereafter FeTp). The molecular structure of this complex was determined by single-crystal X-ray crystallography (see Figure 3.2 and Supporting Information). Combined experimental and theoretical studies based on X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) were performed and allowed us to describe in detail the magnetic and electronic structures of the iron metal ion in this complex.

Experimental section

Sample was synthesized following the procedure described in work by Koumousi et al. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] The crystal structure of FeTp at 120 K revealed an anionic mononuclear complex, where the Fe III metal ion is in a meridional octahedral geometry formed by the tripodal Tp ligand and completed by three cyanido groups linked to the ion center by the C atoms (Figure 3.2).

The negative charge of the complex is compensated by the [N(C 4 H 9 ) 4 ] + cation (Supprting Information: Figure 3.6). The magnetic properties were investigated as a microcrystalline powder using a SQUID magnetometer with the field dependence of the magnetization (M ) at different temperatures (from 1.85 to 8 K) and the thermal dependence of the χT XAS and XMCD spectra were recorded at the Fe L 2,3 edges on the soft X-ray beamline DEIMOS at SOLEIL synchrotron (France). [START_REF] Ohresser | DEIMOS: A Beamline Dedicated to Dichroism Measurements in the 350-2500 eV Energy Range[END_REF] Circularly polarized photons delivered by an Apple II undulator were monochromatized by a plane grating monochromator working in the Petersen geometry. Samples were prepared by drop-casting on silicon wafers. All spectra were measured in total electron yield mode at T = 2 K and under ultra high vacuum (UHV) in the 1×10 -10 mbar range.

The XMCD signal is defined as the difference between the XAS spectra measured with right and left circularly polarized X-rays. The XMCD signals were recorded by flipping both the circular polarization (either left or right helicity) and the external magnetic field (either B + = +6.5 T or B -= -6.5 T). This method minimizes most of the spurious residual signals that might pollute the XMCD signal. The XMCD signal is obtained as the difference

σ XM CD = σ --σ + where σ -= (σ L (B -) + σ R (B + ))/2, σ + = (σ L (B + ) + σ R (B -))/2, σ L (σ R )
is the cross-section with left (right) polarized X-rays, and B + (B -) the magnetic field parallel (antiparallel) to the X-ray propagation vector. With these definitions, a negative XMCD signal at the L 3 edge of 3d metals corresponds to a magnetic moment pointing in the same direction as the external magnetic field. The background is subtracted using two arctangent functions that model the 2p 3/2 → continuum and 2p 1/2 → continuum transitions following the method described by Chen et al. [START_REF] Chen | Experimental Confirmation of the X-ray Magnetic Circular Dichroism Sum rules for Iron and Cobalt[END_REF] The isotropic spectra are then normalized to 1 at the maximum of the L 3 edge so that comparison between experimental Chapter 3. Fe-bearing Precursors of Photomagnetic FeCo Prussian Blue Complexes 41 and calculated spectra is straightforward.

The analysis of XAS and XMCD signals can either make use of the magneto-optical sum-rules developed by Thole and Carra [START_REF] Thole | X-ray Circular Dichroism as a Probe of Orbital Magnetization[END_REF][START_REF] Paum Carra | X-ray Circular Dichroism and Local Magnetic fields[END_REF] or be performed using Ligand Field Multiplet (LFM) calculations. For a magnetic field B along the ẑ axis, the orbit and spin magnetic moments along ẑ are related to the orbit and spin kinetic momentum operators by

m orbit = -L z µ B and m spin = -g o S z µ B = -2 S z µ B ,
L 3 (σ --σ + )/( ω)dE, q = L 3 +L 2 (σ --σ + )/( ω)dE, and r = 1 2 L 3 +L 2 (σ + + σ -)/( ω)
dE, the sum rules can be written as L z = 2 3 q r n h and S z + [START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF] 2 T z = 3p-2q 2r n h where T z is the magnetic dipole operator [START_REF] Paum Carra | X-ray Circular Dichroism and Local Magnetic fields[END_REF] along the ẑ axis and n h is the number of holes on the 3d shell.

The effective spin kinetic momentum value is defined by

S eff z = S z + 7 2 T z . [92]

Ligand Field Multiplet (LFM) calculations

The detailed interpretation of XAS and XMCD spectra was achieved within the LFM theory, which is known to describe well the atomic-like ground and excited states, such as those involved in the XAS L 2,3 edges of 3d transition elements in iono-covalent compounds.

LFM theory and its practical implementation for the calculation of XAS spectra are due to the pioneering work by Theo Thole, [START_REF] Frank | 2p X-ray Absorption of 3d Transition-Metal Compounds: An Atomic Multiplet Description Including the Crystal Field[END_REF] based on atomic theory developed by Cowan [START_REF] Robert D Cowan | The theory of atomic structure and spectra[END_REF] and the crystal field interactions (i.e., symmetry) described by Butler. [START_REF] Butler | Point group symmetry applications: methods and tables[END_REF] In the electric dipole approximation, the absorption cross section is calculated according to the Fermi golden rule at 0 K:

σ( ω) = 4π 2 α ω i,f 1 d i | f |ε • r|i | 2 δ(E f -E i -ω), ( 3.1)
where |i and |f are the many-body eigenfunctions associated to the ground state (with no core-hole) and to the final state (with a 2p core-hole in the present case), respectively.

Many-body eigenfunctions |i and |f , as well as the corresponding eigenvalues E i and E f , are determined from the exact diagonalization of an atomic, multielectronic, semi-empirical

Hamiltonian. In the absence of magnetic field, the multielectronic ground state |i is possibly degenerate (with d i the degeneracy). The Hamiltonian describing the interaction between light and matter, ε • r, is expressed in the electric dipole approximation, with ε being the polarization vector, r the position vector, ω the photon energy, and α the fine structure constant. The Dirac distribution δ(E f -E i -ω) ensures the conservation of energy.

In the LFM approach, the spherical part of the atomic Hamiltonian takes into account the electron kinetic energy, the electron-nucleus Coulomb attractions, all the many-body electron-electron Coulomb repulsions between open shells, and the spin-orbit interaction on every shell of the absorbing ion. The geometrical environment of the absorbing atom is taken into account through the crystal field potential, i.e. an electrostatic field that obeys Chapter 3

the point group site symmetry of the absorbing atom. [START_REF] Butler | Point group symmetry applications: methods and tables[END_REF][START_REF] Beverley | Inorganic electronic spectroscopy[END_REF] Inter-electronic repulsions are taken into account by Slater integrals, F 2 dd and F 4 dd in the ground state, and

F 2 dd , F 4 dd , F 2 pd , G 1
pd , and G 3 pd in the final state. Slater integrals are calculated in an atomic Hartree-Fock model and are scaled down by a reduction factor κ that reflects the electronic delocalization of the 3d electrons. The κ parameter follows the trends of the nephelauxetic series. [START_REF] Beverley | Inorganic electronic spectroscopy[END_REF] The atomic spin-orbit coupling parameters on the open shells are calculated through a spherical monoelectronic potential around the free ion. The symmetry for Fe III metal ion in FeTp is very close to C 3v [START_REF] Lescouëzec | Ferromagnetic Coupling between Low-and High-Spin Iron(III) Ions in the Tetranuclear Complexf ac[END_REF] so that the strength of the crystal field potential is parametrized by three independent parameters 10Dq, Dσ and Dτ . [START_REF] Juhin | X-ray Linear Dichroism in Cubic Compounds: The Case of Cr 3+ in MgAl 2 O 4[END_REF] In the case of weakly covalent bond, the Fe III ground state is described by only one configuration, |i = |2p 6 3d 5 , and the corresponding excited state by |f = |2p 5 3d 6 . [START_REF] Anne Arrio | Characterization of Chemical Bonds in Bimetallic Cyanides using X-ray Absorption Spectroscopy at L 2,3 edges[END_REF] The chemical bond between a transition metal and a CN -ligand is generally described in terms of σ donation between the occupied orbitals of the ligand and the unoccupied and partially occupied orbitals of the metal, and π back bonding between the occupied orbitals of the metal ion and the unoccupied orbitals of the ligand. [START_REF] Anne Arrio | Characterization of Chemical Bonds in Bimetallic Cyanides using X-ray Absorption Spectroscopy at L 2,3 edges[END_REF]37] In the LFM model, several configurations are needed to account for these charge-transfers. The σ donation is modeled by the reduction in electron repulsion (κ) known as the nephelauxetic effect and by the ligand-to-metal charge transfer (LMCT)

through the configuration interaction between |2p 6 3d 5 and |2p 6 3d 6 L , where L stands for one hole in a ligand orbital. The π back bonding is modeled by the metal-to-ligand charge transfer (MLCT) through the configuration interaction between |2p 6 3d 5 and |2p 6 3d 4 L -, where L -stands for one additional electron on a ligand orbital. In Hocking et al. [37] ,

the ground state of the 3d 5 Fe III ion was alternatively taken as a linear combination of the three configurations |2p 6 3d 5 , |2p 6 3d 4 L -and |2p 6 3d 6 L , while the final state was expressed as the linear combination of |2p 5 3d 6 , |2p 5 3d 5 L -and |2p 5 3d 7 L . Their results are excellent although not much better than ours (see Section Results), so that we preferred to stick to two configurations, which model only MLCT, therefore using a reduced number of parameters. In the present work, the ground state is expressed as a combination of

Results

The XAS and XMCD spectra measured for the FeTp complex are shown in Figure 3.3.

The spectral shape is characteristic of low spin Fe III ion and is similar to K 3 Fe(CN) 6 . [37,[START_REF] Michael | X-ray Magnetic Circular Dichroism Investigation of the Electron Transfer Phenomena Responsible for Magnetic Switching in a cyanidebridged [CoFe] Chain[END_REF] In particular, the peak a in the XAS spectrum is the electronic signature of a Fe III ion surrounded by cyanido ligands. In a very simple purely atomic picture with no spin-orbit coupling and no distortion (O h symmetry), peak a is attributed to the transition 2p 6 t 5 2g → 2p 5 t 6 2g . Differences in the XAS intensity can be noticed for the two peaks (b,c) around 708.5eV and the big charge transfer feature (e) at 712.3 eV which could be related to the structural environment of Fe that is bound to three cyanido ligands in FeTp at the difference of K 3 Fe(CN) 6 where Fe is surrounded by six cyanido ligands. [37] The intensity of the XMCD signal α for FeTp is close to 100 % of the normalized isotropic XAS, which is a strong indication that this sample has not suffered from the UHV conditions and that it contains only low spin Fe III sites. This assumption is strongly supported by our LFM calculations, which are described in the next paragraph.

In order to extract electronic and magnetic information from the XAS and XMCD spectra, LFM calculations were performed for FeTp. As shown in Figure 3.4, the model, that provides the best agreement between the theoretical and experimental XAS and XMCD spectra (top panel), includes three theoretical key ingredients: the trigonal distortion of the Fe site (C 3v point group symmetry), the σ donation with 70 % of nephelauxetic reduction and the π back bonding (MLCT). The parameters used in the best simulation are given in Table 3.2. Parameters for all the calculations are given in Supporting Information (Table 3.5).

When the three ingredients are properly taken into account, the main features of the so that the constant Lorentzian broadening used at the L 3 edge is overestimated. The XMCD simulation is also quite good since all the experimental features are present in the calculation, with intensities that are fairly reproduced. The only slight discrepancy is found for the negative feature γ followed by the positive peak .

∆ i ∆ f V eg V t 2 g
2.8 0.07 0.12 0.7 3.0 3.4 -0.8 1.8

Discussion

Since LFM simulations of the isotropic XAS and XMCD spectra yield a good agreement with the experiment, it is now possible to identify the role played by the various ingredients of the calculations, such as π back donation of the chemical bond around the Fe III metal ion, and its local symmetry including possible distortions.

Chapter 3. Fe-bearing Precursors of Photomagnetic FeCo Prussian Blue Complexes 45

Influence of bond covalency and site symmetry

The lower panel of It is clear that the peak e cannot be properly reproduced unless π back bonding (MLCT) is taken into account using a configuration interaction. Also, the XMCD intensity is strongly reduced when the π back bonding is not taken into account. The energy difference between |2p 6 3d 5 and |2p 6 3d 4 L -configurations (∆ i ) used for MLCT was estimated from the energy difference measured on the experimental XAS spectrum between the main features c at the L 3 edge and the satellite peak e (∆ i ≈ 3.0 eV). Note that in our calculation, LMCT was mimicked by simply using a nephelauxetic parameter κ = 0.7. Charge transfer parameters V eg and V t2g change only the shape of the peak e. It is well known that there is a large π back bonding between the iron metal ion and cyanido ligands [37] , which implies that the π overlap integral has to be increased relative to the σ one in the model. Thus, the |V t2g /V eg | ratio is larger than 2, like in K 3 Fe(CN) 6 . [37] For the calculations performed in the O h symmetry with MLCT, the peak e is well reproduced and small discrepancies in intensities are observed for the different peaks. The main missing feature is a small peak f, which is absent in both XAS and XMCD spectra.

When the calculation is performed in C 3v symmetry (upper panel), the peak f is present in both XAS and XMCD signals. One can also notice that the intensity of the XMCD signal is reproduced at best for the calculation in C 3v symmetry with the external magnetic field set along the C 3 axis. From the previous discussion, we conclude that both π back bonding and C 3v symmetry are mandatory ingredients in the calculation to obtain a fair agreement with experiment.

Determination of expectation values from LFM calculations

From the LFM calculations, ground state expectation values O = i|O|i can be directly computed for the orbital angular kinetic momentum L z , the spin kinetic momentum S z , the magnetic dipole T z and n h the number of holes on the 3d shell. The L z , S z , T z expectation values for the different set of parameters (O h , O h with LMCT, C 3v and C 3v with LMCT) are given in Supporting Information (Table 3.6). Using the parameter set yielding the best agreement to experiment (Table 3. The main new information is that the orbital magnetic moment is thus quite large with Chapter 3

m orbit = -L z µ B = 1.24µ B .
The LFM calculated ground state writes α|3d 5 +β|3d 4 L -, with α 2 = 0.73 and β 2 = 0.27 so that the effective electron number on the 3d shell is 4.73 and then n h = 10 -4.73 = 5.27 for the number of holes on the 3d shell. Thus, the π back bonding induces a strong reduction of the local electronic density (4.73 compared to 5 for a free Fe III ion).

Application of magneto-optical sum rules to the LFM calculated spectra

The values of orbital and spin magnetic moments can also be determined by application of the magneto-optical sum rules. [START_REF] Thole | X-ray Circular Dichroism as a Probe of Orbital Magnetization[END_REF][START_REF] Paum Carra | X-ray Circular Dichroism and Local Magnetic fields[END_REF] In the case of highly covalent high spin Fe III center, Piamonteze et. al. showed that the sum rule for the orbital magnetic moment is expected to be followed, but a systematic underestimation of S z by 30% is expected from the spin sum rule. [START_REF] Piamonteze | Accuracy of the Spin Sum Rule in XMCD for the Transition-Metal L edges from Manganese to Copper[END_REF] However, Piamonteze and coworkers did not include neither the case of a low spin Fe III center nor the case of a covalent Fe III metal ion. The LFM calculations suppose that the radial integrals of the 3d orbitals and other radial integrals are energy independent.

Several papers questionned whether this approximation might impair the application of the orbit sum rule to the K edges or L 2,3 edges of 3d transitions elements. [START_REF] Strange | Interpretation of X-ray-Absorption Dichroism Experiments[END_REF][START_REF] Wu | Limitation of the Magnetic-Circular-Dichroism Spin Sum Rule for Transition Metals and Importance of the Magnetic Dipole Term[END_REF][START_REF] Wu | First Principles Investigation of the Validity and Range of Applicability of the X-ray Magnetic Circular Dichroism Sum Rule[END_REF] The generally excellent agreement observed between the experimental L 2,3 edges spectra for 3d transition metal ion and the spectra calculated in the LFM framework tend to indicate that the energy dependence of the radial integrals is expected to be highly negligible, at least for L 2,3 edges. The values extracted from the sum rules are reported in Table 3.3. The sum rule for the orbital magnetic moment yields L z = -1.2357, which is very close to the value computed for the Fe III ground state ( L LFM z = -1.2361), with a difference less than 0.02%. This confirms the fact that the orbital sum rule is valid even when configuration interaction is needed to give a proper description of the ground state. [START_REF] Altarelli | Orbital-Magnetization Sum Rule for X-ray Circular Dichroism: A Simple Proof[END_REF] On the contrary, the sum rule for the spin magnetic moment yields S eff The error on the estimation of the spin magnetic moment calculated from the spin sum rule is found to be close to 60%. In the next section, we investigate the origin of the spin sum rule breakdown.

Chapter 3. Fe-bearing Precursors of Photomagnetic FeCo Prussian Blue Complexes 47

Origin of the failure of the spin sum rule

The application of the spin sum rule requires a separated integration of the XMCD data at the L 3 edge on one hand, and at the L 2 edge on the other hand. Three main reasons could make such integrations unreliable: (i) the instrumental and intrinsic resolutions might broaden the L 3 or L 2 edges, (ii) the determination of the cutoff energy separating the L 3 edge from the L 2 edge might be not straightforward, and (iii) a large component of the 2p 1/2 core-hole might be present in the L 3 edge as well as a large component of the 2p 3/2 core-hole in the L 2 edge (i.e., the so-called intermixing).

The influence of spectral resolution on the spin sum rule is detailed in the Supporting Information (Section 3.3.5) . It is found to be small. The error coming from the choice of the cutoff energy separating the L 3 edge from the L 2 edge is also small (see Supporting Information Section 3.3.5) and can not explain the inaccuracy of the spin sum rule.

Influence of 2p spin-orbit coupling

Finally, we questioned the possible intermixing of L 3 and L 2 edges. By definition, the a low spin configuration for the Fe III metal ion combined with the large crystal field and the large π back bonding of the cyanido ligands. This conclusion is also valid at finite temperatures. Indeed, by performing LFM calculations and applying the sum rules, we checked that whatever the temperature, the orbital sum rule is obeyed whereas the spin sum rule is not. The results are summarized in Table 3.7 of Supporting Information.

L
S LFM z -S eff z (ζ 2p ) S eff,LFM

Application of the sum rule to the experimental spectra and comparison to the experimental magnetization data

As discussed previously, we can expect the orbital sum rule applied to the experimental spectra to yield a good estimate of the orbital magnetic moment. To do so, LFM calculations are essential since they provide the value of the effective number of holes (n h ) on the metal 3d shell. On the contrary, the spin sum rule can not provide a reliable value since it already fails when applied to the theoretical spectra. In addition, the determination of m spin from the experimental spectra would require the knowledge of T z , which is unknown and very likely different from zero, as it found from the expectation value determined by LFM ( T z LFM = -0.115). One can then conclude that it is impossible to extract the spin magnetic moment from the spin sum rule applied to the experimental spectra for low spin Fe III L 2,3 edges. Nevertheless, results of its application are presented in Table 3.3 for completeness.

Application of the orbital sum rule to the experimental spectra yields L z = -0.88 (m orbit = 0.88µ B ) with an usual estimated error of approximately 10%. The spin sum rule does not hold and we used the following strategy to determine the spin magnetic moment.

We suppose that the ratio between the LFM values for L z LFM and S z LFM is the same Chapter 3. Fe-bearing Precursors of Photomagnetic FeCo Prussian Blue Complexes 49 as the ratio of the experimental values for L z Exp and S z Exp . Considering that L z LFM and S z LFM are given by the LFM calculation, and L z Exp is determined by the sum rule for the orbital magnetic moment, S z Exp is simply determined by Equation 3.2.

S z Exp = S z LFM × L z Exp L z LFM (3.2)
Application of Eq. 3.2 yields S z = -0.35 (m spin = 0.70µ B ) and a total magnetic moment m total = 1.58µ B . For the FeTp complex, the value of the orbital magnetic moment m orbit is thus very large and slightly larger than m spin (m orbit /m spin > 1). This is a quite unique situation, because the orbital magnetic moment is usually quenched for 3d transition ions and smaller than the spin magnetic moment. Our findings are in line with previous reports [START_REF] Ohresser | Magnetism of Small Fe Clusters on Au(111) Studied by X-ray Magnetic Circular Dichroism[END_REF][START_REF] Gambardella | Ferromagnetism in One-Dimensional Monatomic Metal Chains[END_REF][START_REF] Bansmann | Magnetism of 3d Transition Metal Nanoparticles on Surfaces Probed with Synchrotron Radiation -From Ensembles Towards Individual Objects[END_REF][START_REF] Peredkov | Spin and Orbital Magnetic Moments of Free Nanoparticles[END_REF] that stated that the value of the orbital magnetic moment increases as the dimensionality of the system decreases, although the m orbit values were always less than the m spin values. Nevertheless Figgis predicted a high value of orbital magnetic moment for a low spin Fe III ion in the K 3 Fe(CN) 6 compound. [START_REF] Brian | Ligand field theory and its applications[END_REF] Moreover, Day and coworkers predicted that the orbital magnetic moment is 60% of the total magnetic moment in Cs 2 KFe(CN) 6 . [START_REF] Day | Polarized Neutron Diffraction from Cs 2 KFe(CN) 6 : The Orbital Moment and its Anisotropy[END_REF] However, no direct measurement of m orbit has been reported yet. In addition, magnetic measurements show that the value of the g factor deviates significantly from 2 which is consistent with a large value of the orbital magnetic moment.

The XAS and XMCD measurements performed in this work give for the first time a direct measurement of m orbit for a low spin Fe III center and corroborate previous findings.

Nevertheless, the total magnetic moment deduced from the present XMCD investigation (≈ 1.6 µ B ) exceeds significantly the one deduced from the magnetization measurements (0.86 µ B ). In order to solve this apparent discrepancy, we investigated the theoretical angular dependence of the XMCD spectra and of the orbital and spin magnetic moments.

Indeed, the magnetization data (Figure 3 ) and [111] (α = 54.7 • ). We found that L z (α) ≈ cos(α) × L z (0) and S z (α) ≈ cos(α) × S z (0) (see Table Table 3.8 in Supporting Information; note that z is the direction of B and O z is the projection of the operator Ô on the z direction). Interestingly the averaged value for T z (α) does not follow the cos(α) law as can be seen from Table 3.8. This is very likely because T z (α) is quadratic in the orbit kinetic momentum and linear in the spin kinetic momentum so that the angular dependence is more involved. One can notice that T z remains small for all the calculated angles. The angular dependence for L z and Chapter 3

S z supports the fact that the C 3 axis is an easy axis of magnetization. The theoretical LFM values of L z LFM and S z LFM that would be expected for a fully disordered sample are therefore obtained by the angular spherical average, yielding respective values of 1 2 L z LFM (0) = 0.618 µ B and 1 2 S z LFM (0) = 0.244 µ B (see supporting information Section 3.3.6) and a total theoretical magnetic moment of 1.106 µ B at 0 K. Remarkably, this value is fully compatible with the magnetization data (Figure 3.7). As mentioned previously, the XMCD measurements were performed on a dropcasted sample. The crystals show a needle-shaped morphology with the C 3 axis almost perpendicular to the needle axis. [START_REF] Ridier | Polarized Neutron Diffraction to Probe Local Magnetic Anisotropy of a Low-Spin Fe III Complex[END_REF] When the ±6.5 T magnetic field is applied on such a sample, the crystallites for which the C 3 axis makes a large angle with respect to the B direction experience a torque, rotate along the needle axis and tend to orientate along the magnetic field direction so that the measured sample can be considered as partially oriented with the C 3 axis along the B direction. A simple analysis of the intensity of the experimental XMCD signal compared to its maximum calculated value along the ternary axis indicates that the C 3 axis of the measured crystallites are distributed inside a cone centered along the B direction and with a half angle at the summit of 65 • . Hence the XMCD measurements were obviously performed on an oriented sample and this explains the larger experimental orbital and spin magnetic moments determined from XMCD with respect to the SQUID magnetization data.

Conclusion

The ground state electronic and magnetic properties of the Fe III metal ion in the FeTp building block of the molecular Prussian Blue Analogues have been determined by measuring low temperature XAS and XMCD spectra at the Fe III L 2,3 edges. As expected, it is found that the electronic structure is in agreement with a low spin Fe III state and an effective electron number of 4.73 due to the π back bonding of the cyanido ligands. The inaccuracy of the spin sum rule has been demonstrated and its origin is found in the intermixing between L 3 and L 2 edges. This result completes the previous work from Piamonteze [START_REF] Piamonteze | Accuracy of the Spin Sum Rule in XMCD for the Transition-Metal L edges from Manganese to Copper[END_REF] and leads to the conclusion that the spin sum rule is inaccurate in the general case of Fe III ion.

In its ground state, the Fe III ion carries an exceptionnally large orbital magnetic moment where m orbit /m spin is slightly larger than 1. Along the magnetic easy axis, the orbital moment can be as large as 1.2 µ B . Such a strong orbital moment is expected to significantly influence the magnetic properties of the compound. Indeed, spin-orbit coupling links the spin magnetic moment to the orbital part, which depends on the spatial organization around the ion. When the precursors are engaged in building Prussian Blue Analogues, the orbital magnetic moment couples efficiently to the crystallographic structure. Therefore, a change of valency and magnetism, such as observed for Fe III (S = 1/2) to Fe II (S = 0) transformation in Fe/Co cyanido bridged complexes exhibiting electron transfer, shall be accompanied by crystallographic relaxations, and therefore, the large orbital magnetic moment is likely to play a major role in the photoconversion mechanism.

In a next future, we will report the X-ray absorption and XMCD studies of Fe/Co photomagnetic molecular PBAs involving the FeTp precursor. Chapter 3

Supporting Information of Paper I

This section contains some technical information that we have been using for the understanding of the electronic and magnetic properties of FeTp. These are the crystallographic data of the FeTp complex, the magnetic susceptibility and magnetization measured by SQUID, the parameters used for the Ligand Field Multiplet calculations, a review of the validity of the spin sum rule and the analysis of the angular dependence of the orbit and spin magnetic moments extracted from LFM calculations.

Crystallographic data of the FeTp complex

Single crystal of (N(C 4 H 9 ) 4 [(Tp)Fe III (CN) 3 ]•3H 2 O) (FeTp)

was mounted in Cargille TM

NHV immersion oil on a 50 mm MicroMountsTM rod at 120 K. The crystallographic data were collected with Bruker APEX II Quasar diffractometers, housed at the Institut de Chimie de la Matière Condensée de Bordeaux, and equipped with a graphite monochromator centered on the MoKα path. The program SAINT was used to integrate the data, which was thereafter corrected for absorption using SADABS. [START_REF] Michael | Bruker analytical x-ray systems[END_REF] The structure was solved by direct methods and refined by a full-matrix least-squares method on F 2 using SHELXL-2013. [START_REF] Michael | [END_REF] All non-hydrogen atoms were refined anisotropically. Hydrogen atoms were assigned to ideal positions and refined isotropically using suitable riding models. Reflections were merged by SHELXL according to the crystal class for the calculation of statistics and refinement. Figures 3.6 was generated using CrystalMaker R (CrystalMaker Software Ltd, www.crystalmaker.com).

Magnetic data of the FeTp complex

Magnetic susceptibility measurements were performed on a Quantum Design SQUID magnetometer MPMS-XL housed at the Centre de Recherche Paul Pascal (Pessac) at temperatures between 1.85 and 300 K and dc magnetic fields ranging from -7 to 7 T.

Microcrystalline powder of FeTp (13.24 mg) introduced in sealed polyethylene bag, which was containing 10.88 mg of paraton oil. Prior to the experiments, the field-dependent magnetization was measured at 100 K in order to detect the presence of any bulk ferromagnetic impurities. In fact, paramagnetic or diamagnetic materials should exhibit a perfectly linear dependence of the magnetization that extrapolates to zero at zero dc field. The sample appeared to be free of any significant ferromagnetic impurities. The magnetic data were corrected for the sample holder, paratone oil and the intrinsic diamagnetic contributions. spectrum is divided by the same value.

Experimental XAS : raw data and background subtraction

Parameters used for Ligand Field Multiplet calculations and L z , S z , T z expectation values

The parameters used for Figure 3.4 are given in Table 3.5 and L z , S z , T z expectation values for the three previous set of parameters are given in Another important aspect for the application of the spin sum rule is the choice of the cutoff energy that separates the XMCD signal into its contribution to the L 3 edge and to the L 2 edge. The value chosen here was 716.8 eV, although this choice is not straightforward because there are many transitions with non-zero amplitudes close to this energy (i.e., 1000 times smaller than the largest transitions, see Figure 3.9). If the cutoff energy is varied between 715.8 and 717.8 eV, one finds that the effective spin S eff z changes by ≈ 1%.

Z 2 a R 1 (I > 2σ(I)) 0.0630 b wR 2 (all data) 0.1801 R int 0.0277 CCDC 1451192 a R 1 = ||F 0 | -|F c ||/ |F 0 | , b wR 2 = [ (F 2 0 -F 2 c ) 2 / (F 2 0 ) 2 ] 1/2
Hence, we can conclude that the cutoff energy cannot be the cause for the failure of the spin sum rule.

Influence of temperature

The calculation for L z , S z and T z have been performed at 0 K. For finite temperatures, we first calculated the thermal average values for L z , S z and T z which are given by the Boltzmann distribution at temperature T. For L z it reads

L z (T ) = n i=0 i|L z |i exp[-( E i -Eo kT )] n i=0 exp[-( E i -Eo kT )] (3.3)
Chapter 3. Fe-bearing Precursors of Photomagnetic FeCo Prussian Blue Complexes 57

where i is the index running on the initial states, E i is the energy of the initial state i and the Boltzmann constant k = 8.617 × 10 -5 eV.K -1 . For S z and T z , similar formula are applied. The values obtained from the calculations at 0 K, 2 K and 4 K are reported in Table 3.7. Whatever the temperature, the orbit sum rule is obeyed whereas the spin sum rule is not.

LFM calculations Sum rules: calculated Spectra Sum rules: calculated sticks axis of the molecule and α is the angle between the C 3 axis and the z axis that is the direction of the X-ray propagation vector k (i.e. the direction of B in the present XMCD experiments). S z (0) and L z (0) are the values of S z and L z at α = 0.

0 K 2 K 4 K 0 K 2 K 4 K 0 K 2 K 4 K L z -1.

Average values

From LFM calculations, we obtained L z (α) ≈ cos(α) × L z (0). In the present case, α is obviously the acute angle between the C 3 axis and the B direction so that 0 α π 2 (this is equivalent to say that, for a paramagnetic ion, the magnetization is never antiparallel to the external magnetic field). Then the k propagation vector only maps the half sphere along the [001] direction of the C 3 axis. The average value of a f (α, φ) function (α, φ are Chapter 3 the angular spherical coordinates) on the half sphere is given by:

f average = 1 2π α=π/2 α=0 φ=2π φ=0 sin(α)f (α, φ)dαdφ (3.4) If f (α, φ) = L z (α) = cos(α). L z (0) then L z average = 1 2π π/2 0 2π 0 sin(α) L z (α)dαdφ (3.5) = 1 2π L z (0) π/2 0 2π 0 cos(α) sin(α)dαdφ (3.6) = 1 2 L z (0) (3.7)
Similarly one obtains: S z average = 1 2 S z (0). If the C 3 axes are uniformly distributed in a cone of half angle at maximum of Θ then the angular average for the orbital magnetic moment yields L z average = 1 2 [1 + cos(Θ) L z (0)] and a similar expression for the spin magnetic moment. From the ratio between the measured and the calculated magnetic moments, one deduces that Θ = 65˚. XAS spectra are plotted separately in Figure 3.11. The features on XAS spectra look rather similar for all precursors and are signature of Fe III LS . However, slight differences can be seen, which will provide a deeper understanding of their electronic structure. The the cyanido ligands that is larger than for the other three precursors. The intensity of peak e is then simply a sign of π-back bonding and MLCT. [START_REF] Anne Arrio | Characterization of Chemical Bonds in Bimetallic Cyanides using X-ray Absorption Spectroscopy at L 2,3 edges[END_REF] Chapter 3 dependence that has been found for the magnetic moments in FeTp (see Section 3.3.6).

We did not perform X-ray Natural (or Magnetic) Linear Dichroism so that this assertion is sensible but highly speculative. The difference in the relative intensities of α and γ is larger in Potassium hexacyanidoferrate(III) (1.4) The intensity and shape of XAS spectrum at L 2,3 edges are a probe of the electronic and magnetic structure of the absorbing atom. In addition to the total nuclear charge (Z ef f ), the effective chemical valence and the ligand field around the absorbing ion also contribute to the precise energy of the edge, the so-called chemical shifts. From the work by Hocking et al., the energy position of the multiplet features (Figure 3.13) can be affected by the 10D q value for crystal field and the Coulomb repulsions between the open shells. [37] The total integrated intensity of XAS L 2,3 edges spectra for the four precursors are roughly the same, indicating that the number of holes on the 3d shell is a constant for the four precursors.

Influence of crystal field on the XAS spectral shape

Chapter 3. Fe-bearing Precursors of Photomagnetic FeCo Prussian Blue Complexes 63

This is best seen by comparison of the energy difference between peak a and peak c. The difference is roughly 4.0 eV for Potassium hexacyanidoferrate(III) and 3.5 eV for the three other precursors. From Ligand Field Multiplet, the energy difference between a and c scales with the 10D q value around the absorbing ion so that it can be deduced from the XAS spectra that the crystal field around the Potassium hexacyanidoferrate(III) is 0.5 eV larger than around the three other precursors. Hocking et al. [37] found 10Dq = 3.8 -4.0 eV for Potassium hexacyanidoferrate(III) and we found 10Dq = 2.8 eV for FeTp (see Table 3

Comparison of SQUID with XMCD detected magnetization curves

We have shown in the preceding paper that FeTp entities are highly anisotropic. [START_REF] Sadaf | Large Orbital Magnetic Moment Measured in [T P Fe III (CN) 6 ]the Precursor of Photomagnetic Molecular Prussian Blue Analogues[END_REF] Recently, Ridier et al. [START_REF] Ridier | Polarized Neutron Diffraction to Probe Local Magnetic Anisotropy of a Low-Spin Fe III Complex[END_REF] confirmed this finding with polarized neutron diffraction. We guess that the situation is quite similar for FeTp* and FepzTp. As for Potassium hexacyanidoferrate(III), the situation is not so clear. Its space group is monoclinic so that one can suppose that the expected large orbital magnetic moment for Fe is coupled to the low symmetry of the space group to yield a substantial magnetic anisotropy.

Polarized neutron diffraction on Cs 2 K[Fe(CN) 6 ] by Day et al. [START_REF] Day | Polarized Neutron Diffraction from Cs 2 KFe(CN) 6 : The Orbital Moment and its Anisotropy[END_REF] evidenced strong anisotropy dominated by the orbital magnetic moment.

The magnetization curves measured by SQUID for three of the four Fe precursors are reported in Figure 3.14. The magnetization curves are compared to XMCD detected magnetization curves. They have been measured by setting the energy of the monochromator at the energy of peak α where the XMCD is large. The magnetization curve is then simply the variation of the intensity of peak α as a function of the external magnetic induction.

The intensity of the XMCD detected magnetization curves have been rescaled arbitrarily to fit at best the SQUID measurements. The general shape of the magnetization curves measured by either SQUID or XMCD have roughly the same shape so that there is no apparent deviation between the bulk and surface sensitive measurements of magnetization as shown in Figure 3.14.

Application of Sum Rules

We have shown that the spin sum rule does not hold for Fe III LS ions. [START_REF] Sadaf | Large Orbital Magnetic Moment Measured in [T P Fe III (CN) 6 ]the Precursor of Photomagnetic Molecular Prussian Blue Analogues[END_REF] Therefore, we have applied only the orbital magnetic sum rule on the experimental Fe III LS XAS spectra and extracted the expectation value of orbit magnetic moment L z for each precursor. We find that the average value is very close to 0.

Summary of Chapter 3

In this chapter, I have presented four different precursors with low spin Fe III ions. The environment of Fe ion in the precursors remains almost unchanged when they enter the Chapter 3. Fe-bearing Precursors of Photomagnetic FeCo Prussian Blue Complexes 65 associated PBA so that understanding the electronic and magnetic structures of Fe in the precursors can be highly enlightening for the understanding of the electronic and magnetic properties of the PBA.

The main outcome of this chapter concerns the high orbital magnetic moment that low spin Fe III ions possess. The orbital magnetic moment is as large as 1.2 µ B (along the C 3 axis) that is even larger than the spin magnetic moment that equals ≈ 1µ B . This high orbital magnetic moment is accompanied by a very large magnetic anisotropy such that the easy axis of magnetization is along the trigonal (or almost trigonal) axis of the Fe ions.

The anisotropy is so strong that the orbital and spin magnetic moments are almost zero when external magnetic field is applied perpendicular to the trigonal axis. In our desire to understand the XMCD of Fe L 2,3 edges, I examined very carefully the reason why the spin sum rule does not hold for low spin Fe III . I showed that among the many possible sources of breakdown, the intermixing was the most important one and it could not be safely overcome to yield values for the spin magnetic moment. Although my findings are essentially applicable to low spin Fe III , the type of analysis that I have developed can be extended to other ions for which the validity of the spin sum rule is under question.

We have performed Ligand Field Multiplet calculations for Fe with special emphasis for the XAS and XMCD signal of FeTp. The calculations helped us understand the magnetic anisotropy and the angular dependence of the orbit and spin magnetic moment. A rather large X-ray Natural Linear Dichroism (XNLD) has been predicted in our calculations (see

Introduction

The detailed experimental and theoretical studies of Fe bearing precursors, including the FeTp precursor for dinuclear PBA have been presented in the previous chapter. We showed that the FeTp precursor carried a large orbital magnetic moment equal to 0.9 µ B at 2 K and with 6.5 T. This large orbital moment might play a role in the magnetic transition by linking the magnetic properties to the structure. The present chapter is dedicated to the XMCD investigations on two recently reported photomagnetic [Fe-CN-Co] PBA dinuclear complexes synthesized by Koumousi et al. [49] [8] Both dinuclear complexes have FeTp as Fe bearing precursor and have the following chemical formula :

[(Tp)Fe III (CN) 3 Co II PY5Me 2 ](CF 3 SO 3 ) (labeled 1) [(Tp)Fe III (CN) 3 Co II PY5Me 2 ](PF 6 )•2DMF (labeled 2•2DMF)
The dinuclear complex 1 displays thermal-and light-induced electron transfer properties after desolvation (when it is dried in oven under vacuum) whereas 2•2DMF needs to be kept in its mother solution to preserve its electron transfer properties. These dinuclear complexes were synthesized by Dr. Evangelia S. Koumousi The photomagnetic measurements on 1 (see Fig. 4 in the study by Koumousi et al. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] )

demonstrates the first dinuclear PBA with thermal-and photo-induced reversible electron transfer. The paramagnetic state is reached by white light irradiation at 10 K. Upon heating above 45 K, the metastable state thermodynamically relaxes back to the diamagnetic state. This is by far the lowest relaxation temperature reported for any PBA molecular systems.

Measurements of the macroscopic magnetic susceptibility and the X-ray diffraction patterns confirmed the complete and reversible electron transfer in 1. This is the first dinuclear complex to exhibit both thermal and photomagnetic bistability in solid state and mimics the properties of the 3-dimensional network of PBAs. Hence, it serves as a model system with a simple structure to study the electron transfer mechanism at low temperature by XAS and XMCD which are element specific techniques. Since Complex 1 preserves its properties under vacuum, it is possible to record XAS and XMCD spectra in the Total Electron Yield mode that is the preferred mode in the soft X-ray range of Fe and Co L 2,3

edges.

The next part of the present chapter concerns the XMCD results at Fe and Co K edges for 2•2DMF. Complex 1 is obtained by desolvation of the complex with the chemical formula [(Tp)Fe III (CN) 3 Co II PY5Me 2 ](CF 3 SO 3 )•2DMF (labelled 1•2DMF) [START_REF] Koumousi | Synthesis and Characterization of Dinuclear Fe/Co Complexes Exhibiting Metal-to-Metal Electron Transfer Properties[END_REF][START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] . In her Ph.D. manuscript, E.S. Koumousi detailed the magnetic and photomagnetic studies on 1•2DMF that reveal a partial electron transfer. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] Moreover, single crystal analysis suggests that van der Waals interactions between the solvent molecules and the [Fe-CN-Co] complex influence the electron transfer process. Therefore, by slight modifications in the environment of these molecular complexes, E.S. Koumousi has been able to obtain new systems showing interesting thermal-and/or light-induced intramolecular electron transfer.

Indeed, Koumousi found that different counter ions (CF 3 SO - 3 vs PF - 6 ) induce different temperatures of thermal conversion and different relaxation temperature of the metastable state. Thus, Koumousi obtained another dinuclear complex 2•2DMF for which macroscopic magnetic studies evidenced a complete thermal-induced electron transfer in presence of solvent molecules. The electron transfer takes place at 100 K with 20 K wide thermal hysteresis. The transition temperature is ≈70 K lower than the transition temperature for complex 1. In addition, the photo-induced paramagnetic state Fe III LS -Co II HS fully relaxes into the diamagnetic state Fe II LS -Co III LS at 53 K compared to 45 K for complex 1. [START_REF] Koumousi | Synthesis and Characterization of Dinuclear Fe/Co Complexes Exhibiting Metal-to-Metal Electron Transfer Properties[END_REF] Complex 2•2DMF can only be measured with its solvent, therefore, XAS and XMCD spectra at L 2,3 edges are almost impossible to record. This prompted us to record the XMCD signals at Fe K edge. Another related complex, the [Fe 2 Co 2 ] square, has already been studied by XAS where the thermal and X-ray induced electron transfer have been followed at Fe and Co K edges. [START_REF] Sekine | X-ray-Induced Phase Transitions by Selective excitation of Heterometal ions in a Cyanide-bridged Fe-Co Molecular Square[END_REF][START_REF] Sekine | Investigation of the Light-Induced Electron-Transfer-Coupled Spin Transition in a Cyanide-bridged [Co 2 Fe 2 ] omplex by X-ray Diffraction and Absorption Measurements[END_REF] XAS and XMCD are excellent probes to follow the change in oxidation state, the spin state and the local magnetic moments during thermal-or photo-induced electron transfer.

We succeeded to draw a nice picture of the electronic structure of complex 1. For complex Chapter 4. Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 69 2•2DMF, the situation is not as satisfying because the analysis of Fe and Co K edges mainly rests on a finger print approach and performing XMCD calculations within the DFT approximation is well beyond the scope of my thesis.

Introduction

With growing technological interests, smart molecular materials with reduced dimensions [START_REF] Camarero | Molecular vs. Inorganic Spintronics: The Role of Molecular Materials and Single Molecules[END_REF][START_REF] Gatteschi | Molecular Nanomagnets: The First 10 Years[END_REF][START_REF] Sanvito | Molecular Spintronics[END_REF][START_REF] Joachim | Electronics using Hybrid-Molecular and Mono-Molecular Devices[END_REF] are being designed, synthesized and investigated for quantum computing applications, [START_REF] Michael | Quantum Computing in Molecular Magnets[END_REF] which include, for instance, switching devices, [START_REF] Miyamachi | Robust Spin Crossover and Memristance Across a Single Molecule[END_REF] data storage and processing, [START_REF] Ludwig | A Molecular Logic Gate[END_REF] and logic gates [START_REF] Andréasson | All-Photonic Multifunctional Molecular Logic Device[END_REF] where a single molecular specie is employed to perform numerous binary operations based on logic. Molecular complexes exhibiting externallycontrolled bistable physical properties are well-suited for these applications because of their flexible and versatile chemistry. The ON-OFF switching capability between two molecular states, for example, magnetic (ON or 1) and diamagnetic (OFF or 0) states is termed as bi-stability. This switching phenomenon can be used to store data as binary units "0" and "1" if the molecules possess a memory effect after the triggering source (light, temperature, magnetic field, pressure etc) has been switched off. To develop such smart materials using state-of-the-art techniques, careful manipulation and tailoring of molecular properties, with control down to a single spin, is a current challenge. [START_REF] Sato | Optically Switchable Molecular Solids: Photoinduced Spin-Crossover, Photochromism, and Photoinduced Magnetization[END_REF][START_REF] Sato | Photoinduced Magnetization in Molecular Compounds[END_REF][START_REF] Camarero | Molecular vs. Inorganic Spintronics: The Role of Molecular Materials and Single Molecules[END_REF][START_REF] Bonhommeau | One Shot Laser Pulse Induced Reversible Spin Transition in the Spin-Crossover Complex [Fe(C 4 H 4 N 2 )Pt(CN) 4 ] at Room Temperature[END_REF] In this regard, the versatile molecular chemistry of mixed valence cyanido-bridged Prussian Blue (Fe II -CN-Fe III ) and its derivatives (A II -CN-B III , where A and B are 3d transition metal ions) referred to as Prussian Blue analogues (PBA) has been exploited to engineer bi-stable systems. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF] The first evidence of light-induced magnetism in 3-dimensional network of Fe/Co PBA by Hashimoto and co-workers [START_REF] Sato | Photoinduced Magnetization of a Cobalt-Iron Cyanide[END_REF] fuelled the quest of designing molecular magnets with novel functionalities in this family. Fe/Co PBA molecular magnets are unique systems exhibiting bi-stability where electron transfer transforms Fe II LS (S=0)-CN-Co III LS (S=0) diamagnetic entities into Fe III LS (S=1/2)-CN-Co II HS (S=3/2) paramagnetic ones (LS = low spin; HS = high spin).

The presence of the bi-stability is attributed to this metal-to-metal electron transfer via cyanido bridge which is tuned by external parameters like light, temperature and pressure. [START_REF] Sato | Photoinduced Magnetization of a Cobalt-Iron Cyanide[END_REF][START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF][START_REF] Ksenofontov | Pressure-Induced Electron Transfer in Ferrimagnetic Prussian Blue Analogs[END_REF][START_REF] Sato | Photoinduced Magnetization in Molecular Compounds[END_REF][START_REF] Sato | Control of magnetic properties through external stimuli[END_REF][START_REF] Verdaguer | Molecular Electronics Emerges from Molecular Magnetism[END_REF][START_REF] Sato | Switchable Molecular Magnets[END_REF] Reducing the dimensionality of molecular complexes allows miniaturisation of devices, which is the ultimate goal. The first step is to develop Fe/Co nanostructures of PBA with desired thermal and photo-induced electron transfer properties. Some attempts have been made to develop Fe/Co cyanide complexes but thermaland/or photo-induced electron transfer properties could not be observed. [START_REF] Shu-Zhong | Synthesis, Characterization and Electrochemical Properties of Cyanide-Bridged Cobalt (III)/iron(II) Complexes[END_REF][START_REF] Bernhardt | The First Structurally Characterized Discrete Dinuclear µ-Cyano Hexacyanoferrate Complex[END_REF][START_REF] Paul | Discrete Dinuclear Cyano-Bridged Complexes[END_REF] The first evidence of thermally induced metal-to-metal electron transfer is reported in cyanido-bridged Fe/Co pentanuclear [Fe 2 Co 3 ] molecule by Dunbar and co-workers in 2004. [START_REF] Curtis P Berlinguette | A Charge-Transfer-Induced Spin Transition in the Discrete Cyanide-Bridged Complex[END_REF][START_REF] Funck | Light-Induced Excited Spin State Trapping and Charge Transfer in Trigonal Bipyramidal Cyanide-Bridged Complexes[END_REF] PBA based [Fe n Co n ] nanostructures such as 1-dimensional chain, [START_REF] Hoshino | Three-Way Switching in a Cyanide-Bridged [CoFe] chain[END_REF][START_REF] Michael | X-ray Magnetic Circular Dichroism Investigation of the Electron Transfer Phenomena Responsible for Magnetic Switching in a cyanidebridged [CoFe] Chain[END_REF][START_REF] Li | Synthesis and Spectroscopic and Magnetic Characterization of Tris(3,5dimethylpyrazol-1-yl)borate Iron Tricyanide Building Blocks, a Cluster, and a One-Dimensional Chain of Squares[END_REF][START_REF] Liu | Photoinduced Metal-to-Metal Charge Transfer toward Single-Chain Magnet[END_REF] and 0-dimensional molecular cube, [START_REF] Li | Magnetic and Optical Bistability Driven by Thermally and Photoinduced Intramolecular Electron Transfer in a Molecular Cobalt-Iron Prussian Blue Analogue[END_REF] square, [START_REF] Mondal | On/Off Photoswitching in a Cyanide-Bridged {Fe 2 Co 2 } Magnetic Molecular Square[END_REF][START_REF] Zhang | Reversible Thermally Photoinduced Electron Transfer in a Cyano-Bridged {Fe 2 Co 2 } Square Complex[END_REF][START_REF] Zhang | Thermochromic and Photoresponsive Cyanometalate Fe/Co Squares: Toward Control of the Electron Transfer Temperature[END_REF][START_REF] Mercurol | Fe II LS Co III LS[END_REF] and dinuclear complex [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF][START_REF] Jeon | Spin Crossover or Intra-Molecular Electron Transfer in a Cyanido-Bridged Fe/Co Dinuclear Dumbbell: A Matter of State[END_REF] have been synthesized. However, few are supported by structurally characterized light-induced metastable state. [START_REF] Mondal | On/Off Photoswitching in a Cyanide-Bridged {Fe 2 Co 2 } Magnetic Molecular Square[END_REF][START_REF] Nihei | Thermally Two-stepped Spin Transitions Induced by Intramolecular Electron Transfers in a Cyanide-bridged Molecular Square[END_REF] Furthermore, there are not many examples where the light-induced electron transfer is observed at the atomic scale using XAS/XMCD techniques. [START_REF] Sekine | Investigation of the Light-Induced Electron-Transfer-Coupled Spin Transition in a Cyanide-bridged [Co 2 Fe 2 ] omplex by X-ray Diffraction and Absorption Measurements[END_REF] Recently, Koumousi et al. succeeded in synthesizing the first dinuclear complex which exhibits both thermal and photomagnetic bistablility in solid state. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] It is a dinuclear complex which is built from Fe III cyanides and Co II ions that can be seen as the elementary motif of Fe/Co PBA (see Figure 4 A quick increase in χT product is observed at 10 K and within 4 hours of irradiation it reached at the maximum value of 2.77 cm 3 K mol -1 . The electron transfer process is complete and reversible, which is for the first time observed in a dinuclear system. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] The thermal-and optical bistability of the this dinuclear complex can be used to design new multifunctional materials. All the above mentioned phase transitions driven by electron transfer have been proposed to explain the variation of the magnetic susceptibility measured by SQUID magnetometry. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] However, there has been so far no direct confirmation at the atomic scale of Fe and Co ions that such a electron transfer does indeed take place. Therefore, we have investigated the modification of the electronic and magnetic structure by temperature and light irradiation using X-ray Absorption Spectroscopy (XAS) and X-ray Magnetic Circular Dichroism (XMCD), which are element-specific synchrotron based techniques. The goal is to determine the electronic and magnetic structures of Fe and Co ions in the three phases involved in the photomagnetic mechanism: the 300 K paramagnetic phase, the 100 K diamagnetic phase and the 4 K photo-induced paramagnetic phase. The analysis of the XAS and XMCD experimental data is supported by Ligand Field Multiplet (LFM) calculations [START_REF] Frank | 2p X-ray Absorption of 3d Transition-Metal Compounds: An Atomic Multiplet Description Including the Crystal Field[END_REF] developed by Theo Thole and application of magneto-optical sum rules [START_REF] Thole | X-ray Circular Dichroism as a Probe of Orbital Magnetization[END_REF][START_REF] Paum Carra | X-ray Circular Dichroism and Local Magnetic fields[END_REF] in order to yield the orbit and spin magnetic moments of Fe and Co in the 4 K photo-induced paramagnetic phase. The nature of the magnetic coupling between Fe and Co ions in the dinuclear complex was investigated using element specific magnetization curves measured by XMCD.

Previously, element specific and surface sensitive XAS has been successfully employed to understand bistability in other molecular systems such as spin cross over (SCO) systems, [START_REF] Warner | Temperature-and Light-Induced Spin Crossover Observed by X-ray Spectroscopy on Isolated Fe(II) Complexes on Gold[END_REF][START_REF] Vincent Davesne | First Glimpse of the Soft X-ray Induced Excited Spin-State Trapping Effect Dynamics on Spin Cross-Over Molecules[END_REF][START_REF] Briois | Full Multiple Scattering and Crystal Field Multiplet Calculations Performed on the Spin Transition Fe II (phen) 2 (NCS) 2 Complex at the Iron K and L 2,3 X-ray Absorption Edges[END_REF] or Cobalt-dioxolene Valence tautomers. [START_REF] Dapporto | Complete Direct and Reverse Optically Induced Valence Tautomeric Interconversion in a Cobalt-Dioxolene Complex[END_REF][START_REF] Poneti | X-ray Absorption Spectroscopy as a Probe of Photo-and Thermally Induced Valence Tautomeric Transition in a 1:1 Cobalt-Dioxolene Complex[END_REF][START_REF] Poneti | Soft-X-ray-Induced Redox Isomerism in a Cobalt Dioxolene Complex[END_REF][START_REF] Poneti | Magnetic and Spectroscopic Investigation of Thermally and Optically Driven Valence Tautomerism in Thioether-Bridged Dinuclear Cobalt-Dioxolene Complexes[END_REF] In SCO compounds, one follows a high spin (HS) to low spin (LS) transition in the absence of electron transfer while in Cobalt-dioxolene Valence tautomers, an electron transfer takes place between a Cobalt ion and the dioxolene ligand. In PBAs, the situation is quite different from both previous ones because one observes a metal-to-metal electron electron transfer via cyanido ligands. [START_REF] Bleuzen | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 1. Conditions to Observe the Phenomenon[END_REF][START_REF] Escax | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 3. Control of the Photo-and Thermally Induced Electron Transfer by the [Fe(CN) 6 ] Vacancies in Cesium Derivatives[END_REF][START_REF] Yokoyama | Local Structure of a Trapped Photoexcited State of a Fe-Co cyanide studied by X-ray-Absorption Fine-Structure Spectroscopy[END_REF][START_REF] Cartier Dit Moulin | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 2. X-ray Absorption Spectroscopy of the Metastable State[END_REF][START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF][START_REF] Sekine | X-ray-Induced Phase Transitions by Selective excitation of Heterometal ions in a Cyanide-bridged Fe-Co Molecular Square[END_REF][START_REF] Sekine | Investigation of the Light-Induced Electron-Transfer-Coupled Spin Transition in a Cyanide-bridged [Co 2 Fe 2 ] omplex by X-ray Diffraction and Absorption Measurements[END_REF] The metal-to-metal electron transfer is accompanied by a HS to et al. at K edges. [START_REF] Sekine | X-ray-Induced Phase Transitions by Selective excitation of Heterometal ions in a Cyanide-bridged Fe-Co Molecular Square[END_REF][START_REF] Sekine | Investigation of the Light-Induced Electron-Transfer-Coupled Spin Transition in a Cyanide-bridged [Co 2 Fe 2 ] omplex by X-ray Diffraction and Absorption Measurements[END_REF] The originality of the results shown in the present work stems from the possibility to record XAS and XMCD spectra independently for both metallic ions involved in the electron transfer, thus providing an atomic scale picture of the switching mechanism and to check possible antiferromagnetic coupling as suggested by Koumousi et al. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF]

Experimental Section

Sample Preparation

The FeCo dinuclear complex referred to as sample 1 with the with stoichiometric for-

mula [(Tp)Fe III (CN) 3 Co II (PY5Me 2 )](OTf) (OTf : CF 3 SO 3 , Trifluoromethanesulfonate)
and the corresponding Fe and Co precursors (referred to as 2 and 3 respectively) were synthesized following the procedure used by Koumousi et al. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] The chemical formulae for For sample 1 the metal-to-metal electron transfer in solid state was studied using standard magnetometric techniques, single crystal diffraction and optical reflectivity methods (Reference by Koumousi et al. and Supporting Information). [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] The crystals of 1 were then deposited on doubly coated conductive carbon tape suitable for cryogenic temperatures and mounted on a copper sample holder.

XAS and XMCD measurements

XAS and XMCD measurements were performed at both K and L 2,3 edges of Fe and Co.

Spectra at the L 2,3 edges were recorded on the soft X-ray beamline DEIMOS at SOLEIL synchrotron (France) [START_REF] Ohresser | DEIMOS: A Beamline Dedicated to Dichroism Measurements in the 350-2500 eV Energy Range[END_REF] and at SIM beamline in SLS (Paul Scherrer Institute, Switzerland). [START_REF] Letard | Remnant Magnetization of Fe8 High-Spin Molecules: X-ray Magnetic Circular Dichroism at 300 mK[END_REF][START_REF] Mannini | X-Ray Magnetic Circular Dichroism Picks out Single-Molecule Magnets Suitable for Nanodevices[END_REF] All spectra at L 2,3 edges were measured by recording the total electron yield (TEY) under UHV conditions. K edge XAS spectra were recorded at ID12 beamline [START_REF] Goulon | Optical Activity Probed with X-rays[END_REF][START_REF] Goulon | Instrumentation Developments for X-ray Linear and Circular Dichroism at the ESRF Beamline ID12a[END_REF] of the ESRF (France) by measuring the total fluorescence yield.

The DEIMOS beamline is equipped with a 7 T cryo-magnet that has a variable temperature insert. To avoid any spurious signals, XMCD signal was measured by taking the difference of two XAS spectra recorded for left and right polarized X-rays with propagation vector parallel or antiparallel to the direction of external magnetic induction B. By definition, the XMCD signal is obtained by [START_REF] Brouder | Prolegomena to Magnetic Circular Dichroism in X-ray Absorption Spectroscopy[END_REF] XAS and XMCD spectra for sample 1 were first recorded at 300 K, 100 K and 4 K to check for thermal-induced conversion. At 4 K, the sample was irradiated with a laser (λ = 660 nm) for 2 hours and the the photo-converted state was studied. We also followed the relaxation of the light-induced excited state when the temperature was raised up to 50 K. The reversibility of the thermal-and photo-induced conversion has been checked by recording XAS spectra for temperatures between 100 K and 300 K.

σ XMCD = σ --σ + where σ -= [σ L (B -) + σ R (B + )]/2 and σ + = [σ L (B + ) + σ R (B -)]/2.
To check for the nature of the magnetic coupling between the Fe and Co ions in the photo-induced state, XMCD signals should be measured in sub-kelvin temperature because Chapter 4

the Fe-Co exchange coupling is expected to be small. On the SIM beamline, the French TBT-mK cryomagnet is a unique tool to perform XMCD measurements in the sub-kelvin range down to 300 mK. [START_REF] Letard | Remnant Magnetization of Fe8 High-Spin Molecules: X-ray Magnetic Circular Dichroism at 300 mK[END_REF] However, due to technical issues, the measurements could only be performed at 2 K. At 2 K, the sample was irradiated using the 660 nm laser and the XMCD signal of the photo-excited paramagnetic state was measured. Thanks to XMCD, it is possible to record magnetization curves that are specific of the absorbing ion. One sets the energy of the monochromator at the maximum (in absolute value) of the XMCD signals and then sweeps the intensity of the magnetic induction. As can be seen from the magneto-optical sum rules, the variation of the intensity of the XMCD signal at L 2,3 edges is a measure of the magnetization of the absorbing atom.

At ID12 beamline, Fe and Co K edge XAS were measured at 300 K and at 2 K. At 2 K, sample 1 was irradiated for 3 hours by the white light delivered by a tungsten halogen lamp and then Fe and Co K edge spectra were measured in the photoexcited state.

Ligand Field Multiplet calculations

The quantitative information from the XAS/XMCD spectra can be extracted by using Ligand Field Multiplet (LFM) calculations. [START_REF] Frank | 2p X-ray Absorption of 3d Transition-Metal Compounds: An Atomic Multiplet Description Including the Crystal Field[END_REF][START_REF] De | Multiplet Effects in X-ray Spectroscopy[END_REF][START_REF] De | Core level spectroscopy of solids[END_REF] These calculations are performed employing LFM theory which is developed by Theo Thole [START_REF] Frank | 2p X-ray Absorption of 3d Transition-Metal Compounds: An Atomic Multiplet Description Including the Crystal Field[END_REF] , based on atomic theory developed by Cowan [START_REF] Robert D Cowan | The theory of atomic structure and spectra[END_REF] and the crystal field interactions (i.e., symmetry) described by

Butler. [START_REF] Butler | Point group symmetry applications: methods and tables[END_REF] We have performed LFM calculations to simulate the Co L 3 edge spectra. The LFM calculations on Co are done in distorted octahedral environment. The parameters of calculations are presented in the supporting information in Table 4.1. In addition, application of magneto-optical sum rules [START_REF] Thole | X-ray Circular Dichroism as a Probe of Orbital Magnetization[END_REF][START_REF] Paum Carra | X-ray Circular Dichroism and Local Magnetic fields[END_REF][START_REF] Chen | Experimental Confirmation of the X-ray Magnetic Circular Dichroism Sum rules for Iron and Cobalt[END_REF] are applied on the experimental spectrum to obtain orbit magnetic moments for Fe and Co ions in photo-induced state.

Results

Thermal-and light-induced metal-to-metal electron transfer process

In Figure 4.2 are shown the XAS experimental spectra at Fe and Co L 3 edges for sample 1 at 300 K, 100 K before laser irradiation and at 4 K after laser irradiation (λ = 660 nm). At 300 K before irradiation, the spectral shape is characteristic of Fe III LS [37] and Co II HS ions. [START_REF] Escax | The Co Ligand Field: A Key Parameter in Photomagnetic CoFe Prussian Blue Derivatives[END_REF][START_REF] Cartier Dit Moulin | Structural Rearrangements Induced by Photoexcitation in a RbCoFe Prussian Blue Derivative[END_REF] Peak a on the Fe L 3 XAS is the electronic signature of Fe III LS ions surrounded by cyanido ligands, and peaks a' to d' on the Co L 3 XAS are mainly the contribution from Co II HS . [37] After sample 1 is cooled down to 100 K, peak b at the Fe L 3 edge and peak e' at the Co L 3 edge become the main features. Both b and e' can be respectively associated to Fe III LS and Co III LS ions, thus confirming the temperature-induced switching mechanism proposed from SQUID measurements. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] Nevertheless, at 100 K peaks a, a', b' and c' have not completely disappeared, which implies that conversion is not complete for both Fe and Co ions. One can estimate that around 22 % of the high temperature phase is still present at 100 K. This percentage is determined by linear combinations of LFM reference spectra calculated for Co II HS , Co III LS , Fe II LS and Fe III LS ions. Then, sample 1 is further cooled down to 4 K and irradiated by a laser (λ = 660 nm). From a straightforward comparison with the XAS signature at 300 K and with literature [37] , it is clear that the light-induced state is

Thermal Relaxation of the photo-induced excited state

We have recorded the relaxation of the photoexcited state to the thermodynamically stable diamagnetic state when the temperature is increased. After sample 1 is cooled to 4 K and irradiated with the 660 nm laser, the temperature is raised from 4 K to 10 K and For comparison the variation of the magnetic susceptibility χT that was measured by SQUID magnetometer is reported in Figure 4.4. The normalized product χT is almost independent of temperature: it is zero for a diamagnetic pair and equals 3 cm 3 .K.mol -1

for a Fe III LS -Co II HS paramagnetic pair.

Reversibility of the electron transfer process

One major point is to check whether the spectral modifications observed with temperature and light irradiation are fully reversible, in order to discard any degradation of the sample that could explain these changes. Starting from the light-induced spin state at 4 K, we have warmed up sample 1 and recorded XAS spectra at 100 K and at 300 K. By doing so, sample 1 has followed a complete temperature cycle: 300 K, 100 K, 4 K and irradiation by a 660 nm laser, 100 K, 300 K. Spectra recorded at 100 K before and after the photomagnetic conversion are almost identical at both the Fe and Co L 3 edges (Supporting Information: LS and Co II HS ions. At 300 K, the two spectra recorded at the beginning of the temperature cycle and at the very end bear the clear signature of Fe III LS and Co II HS ions (Supporting Information: Figure 4.9). This confirms the complete reversibility of the electron transfer process for both the temperature-induced and the light-induced conversion. In other words, there is no sign of any sample degradation under the action of X-rays or the 660 nm laser.

For completeness, the Fe and Co K edges XAS spectra were recorded for sample 1 at 300 K, at 4 K before light irradiation and at 4 K after light irradiation. Since the escape depth for hard x-ray photons at the Fe and Co K edges is larger than 10 µm, the obtained information relates to the bulk of the sample while at the Fe and Co L 2,3 edges, the escape edges.

Magnetic properties of the light-induced excited state

XMCD spectra have been recorded at the Fe and Co L 2,3 edges at 4 K after photoexcitation, in an external magnetic induction of 6.5 T (Figure 4.5). The large intensity of the Fe L 2 edge on the XAS signal is a clear indication that Fe is in a low spin state, [START_REF] Thole | Linear relation between x-ray absorption branching ratio and valence-band spin-orbit expectation value[END_REF][START_REF] Thole | Branching ratio in x-ray absorption spectroscopy[END_REF] while the relatively small Co L 2 edge is a sign that Co ions are in a high spin state. XMCD signals at the Fe L 3 and the Co L 3 edges are both negative, which evidences that Fe and Co total magnetic moments point in the same direction at T = 4 K and B = 6.5 T. In such conditions, there is no indication of an antiferromagnetic coupling between Fe and Co ions.

The XMCD signal at the Fe L 2,3 edges has three main negative features α, γ, ζ and a moderate positive one, β. Its intensity is not small since the γ feature amounts to 57 % of the maximum of the L 3 edge. Thus, from the shape and intensity of XMCD, one expects a moderate total magnetization where a rather large orbital magnetic moment is likely to overcome the spin magnetic moment. This is confirmed by application of the orbital magneto-optical sum rule, which yields 0.31 µ B ± 0.1 for the orbital magnetic moment.

The XMCD signal at the Co L 2,3 edges is characterized by a large negative contribution γ accompanied by two smaller negative ones α and δ , while the XMCD signal at the L 2 edge gives a small positive contribution. The intensity of the γ' peak is rather large and amounts to 83 % of the maximum of the Co L 3 edge spectrum. One thus expects a rather large magnetic moment carried by the Co ions with a large contribution from the orbital magnetic moment. Application of the orbital magneto-optical sum rule yields 0.32 µ B ± 0.1. No detectable opening of the magnetization curves is observed. In addition, the shape of the magnetization curves are very similar for both Fe and Co, so that there is no sign of any antiferromagnetic coupling between both ions at T = 2 K. It is not possible from the present set of magnetization curves to determine if the Fe and Co ions are ferromagnetically coupled or if they simply experience a similar magnetization under the action of the external magnetic induction.

Discussion

The present experimental results clearly evidence that the temperature-induced conversion between 300 K and 100 K corresponds to a electron transfer transition between the Fe III LS -Co II HS paramagnetic pair into the Fe II LS -Co III LS diamagnetic pair. At lower temperature, around 4 K, the Fe II LS -Co III LS diamagnetic pair transforms almost completely into the Fe III LS -Co II HS paramagnetic one upon light irradiation. This result is obviously in line with what had been claimed by Koumousi et al. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] on the same system based on SQUID magnetometry data. Nevertheless, we want to stress that the present work reports the first direct evidence of the electronic state of Fe and Co ions at the atomic scale, and this for the different phases involved in the switching mechanism. This conclusion is absolutely unambiguous since the spectral features associated to the L 2,3 edges XAS spectra of Fe II LS , Fe III LS , Co II HS and Co III LS are well documented in the literature for the experimental spectra as well as for the theoretical spectra calculated in the Ligand Field Multiplet approach. [START_REF] Escax | The Co Ligand Field: A Key Parameter in Photomagnetic CoFe Prussian Blue Derivatives[END_REF][START_REF] Cartier Dit Moulin | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 2. X-ray Absorption Spectroscopy of the Metastable State[END_REF][START_REF] Cartier Dit Moulin | Structural Rearrangements Induced by Photoexcitation in a RbCoFe Prussian Blue Derivative[END_REF][START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF]37,[START_REF] Poneti | Soft-X-ray-Induced Redox Isomerism in a Cobalt Dioxolene Complex[END_REF][START_REF] Bonhommeau | Metal-to-Ligand and Ligand-to-Metal Charge Transfer in Thin Films of Prussian Blue Analogues Investigated by X-ray Absorption Spectroscopy[END_REF] In addition, the features at the K edges support this conclusion although quantitative results are more difficult to extract.

At T = 100 K, it has been found that the temperature-induced conversion was not complete. This is regularly observed when temperature-or light-induced conversions are Chapter 4. Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 79

followed by XAS at L 2,3 edges. Indeed, depending on the samples Poneti et al. observed between 50 % and 60 % of residual high temperature phase at 100 K, [START_REF] Poneti | Soft-X-ray-Induced Redox Isomerism in a Cobalt Dioxolene Complex[END_REF][START_REF] Poneti | Magnetic and Spectroscopic Investigation of Thermally and Optically Driven Valence Tautomerism in Thioether-Bridged Dinuclear Cobalt-Dioxolene Complexes[END_REF][START_REF] Poneti | Thermal and Optical Control of Electronic States in a Single Layer of Switchable Paramagnetic Molecules[END_REF] and Warner et al. observed between 10 % and 55 % of residual depending on the sample thickness. [START_REF] Warner | Temperature-and Light-Induced Spin Crossover Observed by X-ray Spectroscopy on Isolated Fe(II) Complexes on Gold[END_REF] The temperature induced conversion is possible when the environement of the Co ions allows enough flexibility so that the site can accommodate a Co II HS to Co III LS transition. [START_REF] Bleuzen | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 1. Conditions to Observe the Phenomenon[END_REF][START_REF] Cartier Dit Moulin | Structural Rearrangements Induced by Photoexcitation in a RbCoFe Prussian Blue Derivative[END_REF][START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF] At the very surface of complex 1 it is likely that the Co coordination sphere undergoes a partial reorganisation that might prevent the temperature-induced electron transfer.

At 300 K and at 4 K after irradiation, sample 1 is built from Fe III LS -Co II HS paramagnetic pairs. From the comparison of both XAS spectra at the Fe L 2,3 edges, one can conclude that the electronic and local structure of Fe at 300 K is very similar to that at 4 K after irradiation (Figure 4.7). On the contrary, the same comparison for the Co L 2,3 edges clearly indicates that the two spectra at 300 K and at 4 K are quite different: for the latter, feature a' is sharper, the intensities of features b' and c' are reversed and feature e' is larger. These differences cannot originate from an incomplete photomagnetic conversion as can be deduced from the more intense feature a'. They might arise either from a temperature dependence of the Co L 2,3 edges spectra, or from local rearrangements around the Co ions similar to the ones observed for 3-dimensional PBA molecule based magnets. [START_REF] Escax | The Co Ligand Field: A Key Parameter in Photomagnetic CoFe Prussian Blue Derivatives[END_REF][START_REF] Cartier Dit Moulin | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 2. X-ray Absorption Spectroscopy of the Metastable State[END_REF][START_REF] Cartier Dit Moulin | Structural Rearrangements Induced by Photoexcitation in a RbCoFe Prussian Blue Derivative[END_REF][START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF] Therefore, XAS spectra were calculated in the Ligand Field Multiplet approach for a Co II ion in the same environment at 4 K and 300 K for same set of parameters (Supporting Information Table 4.1). From Figure 4.16, it is clear that calculations mimic fairly well the differences observed between the experimental Co XAS spectra for the two temperatures.

On the basis of the LFM calculations, it can therefore be concluded that the electronic structure of Co II HS ions is the same in the 300 K paramagnetic phase and in the 4 K photo-induced phase. This is in agreement with the K edge XAS and XRD results reported by Sekine et al. in the square molecules of FeCo PBA where they confirmed that the electronic structure of the low temperature light-induced state is similar to the one of the high temperature state. [START_REF] Sekine | X-ray-Induced Phase Transitions by Selective excitation of Heterometal ions in a Cyanide-bridged Fe-Co Molecular Square[END_REF][START_REF] Sekine | Investigation of the Light-Induced Electron-Transfer-Coupled Spin Transition in a Cyanide-bridged [Co 2 Fe 2 ] omplex by X-ray Diffraction and Absorption Measurements[END_REF] gested. [START_REF] Goujon | Photo-Excitation from Dia-to Ferri-Magnetism in a Rb-Co-Hexacyanoferrate Prussian Blue Analogue[END_REF][START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF][START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF] Since measurements have been performed at 2 K, our results indicate that the exchange coupling constant J between Fe and Co ions is such that J/k B < 2 K.

In order to gain more information, the XAS and XMCD signals from the two precursors (samples 2 and 3, see experimental section) of sample 1 were recorded at 4 K and in an external magnetic induction of 6.5 T. The Fe L 2,3 edges for samples 1 and 2 are very similar (Figure 4.14). One observes the same series of spectral features, with mainly peak a that is characteristic of Fe III LS and shoulder e that is a signature of Fe surrounded by 3 cyanido ligands. The intensity of features b, c and d are rather different as can be expected from the presence of the (NC-Co) bond in sample 1. The XMCD features are also very similar and almost homothetic for both samples. If one focuses on features a in the XAS and α in the XMCD, the ratio α/a is 66 % for sample 1 while it is 70 % for its precursor sample 2. [START_REF] Sadaf | Large Orbital Magnetic Moment Measured in [T P Fe III (CN) 6 ]the Precursor of Photomagnetic Molecular Prussian Blue Analogues[END_REF] For samples 1 and 3, the situation is somewhat different at the Co L 3 edge. Indeed the local organization of Co ions is very different in these compounds, so that both Co XAS spectra are quite different (Figure 4.15). On the opposite, both Co XMCD signals present some similarity but for some intensity ratio at the L 3 edge and rather large differences at the L 2 edge. The general shape is in agreement with what is the expected for a Co II HS ion in 6-fold coordination. One then concludes that at 6.5 T, the magnetization of Fe and Co ions in sample 1 are quite similar to the magnetizations for isolated paramagnetic ions, as it is the case in samples 2 and 3. This again confirms that if an antiferromagnetic coupling does exist between Fe and Co in the pair 1, then the coupling constant has to be well below 2 K.

Conclusion

The electronic and magnetic structures of Fe and Co ions in a dinuclear photomagnetic PBA have been measured for the first time in an element selective way. Using a combination of XAS and XMCD spectroscopies supported by LFM calculations, it is proved unambiguously that (i) the 300 K phase and the light-induced excited state at 4 K are built from Fe III LS -Co II HS paramagnetic pairs and (ii) the 100 K phase is built from Fe II LS -Co III LS diamagnetic pairs. Both paramagnetic phases at 300 K and at 4 K after light irradiation are identical, with no apparent reorganization of the local structure around either Fe or Co.

In the paramagnetic pairs at 2 K and under an external magnetic induction of 6.5 T, both Fe and Co ions exhibit a rather large orbital magnetic moments: it is equal to 0.31 µ B for Fe and 0.32 µ B for Co. In the case of Fe, the orbital magnetic moment is likely to be larger than the spin magnetic moment as for FeTp precursor, i.e. sample 2. [START_REF] Sadaf | Large Orbital Magnetic Moment Measured in [T P Fe III (CN) 6 ]the Precursor of Photomagnetic Molecular Prussian Blue Analogues[END_REF] The total magnetic moment of Co is larger than the one of Fe and we do not observe any antiferromagnetic coupling between Fe and Co, indicating that the coupling constant is likely well below 2 K. The light induced excited state is relaxed at 50 K, so that at temperatures below 50 K sample 1 present a bistability that could be driven by an appropriate application of light and temperature. XMCD measurements at very low temperature (below 500 mK) [START_REF] Letard | Remnant Magnetization of Fe8 High-Spin Molecules: X-ray Magnetic Circular Dichroism at 300 mK[END_REF] might help further characterizing the sign and magnitude of the magnetic coupling between Fe and Co ions.

Fe and Co XAS spectra at K edges

For completeness we have also recorded the Fe and Co K edges in sample 1 at 300 K and at 4 K, as shown in Figure 4.10. When the temperature is lowered, the main rising edge of both Fe and Co K edges are slightly shifted, to lower energy (≈ 0.8 eV) for Fe, to higher energy (≈ 2.2 eV) for Co. These changes are compatible with a reduction of Fe and an oxidation of Co when the temperature is lowered.

In addition, the features at high energy for the Fe K edge are hardly modified whereas the shape resonances for Co K edge at 7742 eV and 7770 eV are shifted by several electron-Volts to higher energy. This indicates that the local environment around Fe is not much modified while the coordination sphere of Co is strongly shortened, as it is expected for a high spin to low spin conversion. These various features are fully compatible with the expected temperature-induced electron transfer between a high temperature Fe III LS and Co II HS paramagnetic pair and a low temperature Fe II LS and Co III LS diamagnetic pair. A closer look to the pre-edge region confirms the Co II HS to Co III LS conversion. This is best seen by comparison with previously published spectra by Poneti et al. [START_REF] Poneti | X-ray Absorption Spectroscopy as a Probe of Photo-and Thermally Induced Valence Tautomeric Transition in a 1:1 Cobalt-Dioxolene Complex[END_REF] As, well resolved distinct features of pre-edge cannot be compared by spectra reported by Sekine et al. [START_REF] Sekine | X-ray-Induced Phase Transitions by Selective excitation of Heterometal ions in a Cyanide-bridged Fe-Co Molecular Square[END_REF][START_REF] Sekine | Investigation of the Light-Induced Electron-Transfer-Coupled Spin Transition in a Cyanide-bridged [Co 2 Fe 2 ] omplex by X-ray Diffraction and Absorption Measurements[END_REF] Only a few reference spectra for Fe K edge have been published with good enough resolution in order to help for the identification of Fe III LS and Fe II LS . [START_REF] Westre | A Multiplet Analysis of Fe K-edge 1s → 3d Pre-edge Features of Iron Complexes[END_REF] The difference signal between the 300 K and the 2 K spectra is plotted (green solid line) in Figure 4.12 for both Fe and Co K edges. In order to check for light induced photoconversion at 4 K, sample 1 was irradiated for three hours with an intense white light delivered by a tungsten halogen lamp. The difference between the spectra before and after the white light irradiation is reported in Figure 4.12. The thermal-induced difference signal (green line) comes from the subtraction of XAS spectrum at 300 K and XAS spectrum at 2 K before laser irradiation. The light-induced difference signal (red line) comes from the subtraction of XAS spectrum in light-induced state at 2 K and XAS spectrum at 2 K before light irradiation. The Chapter 4 percentage of the light-induced and thermal-induced electron paramagnetic species have been calculated by taking the peak-to-peak ratio at the difference spectra. One observes that the light-induced transformation has roughly the same shape as the thermal-induced transformation for both Fe and Co K edges. One also notices that the light-induced conversion amounts to around 7 % to 8 % of the thermal-induced conversion, so that we can consider that the present photoconversion induced by the tungsten halogen lamp is not very efficient. This is most likely due to some simple geometrical factor since the lamp was rather far away (≈1 m) from the sample and the exposition time was 4 times shorter than in Koumousi et al. [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] The reversibility of the electron transfer process after temperature and light-irradiation treatment is complete as can be seen from Figure 4.13.

Comparison of XAS and XMCD for sample 1 with those of the Fe and Co precursors

The comparison of the Fe in sample 1 and 2 ( Chapter 4

barely larger than 0.1% of the absorption edge. In 3d transition metal ions and in the electric dipole approximation, XMCD signal at K edges cannot come from the presence of spin-orbit interaction on the core-hole since it is a 1s core-hole. XMCD signal then comes from the spin-orbit coupling acting on the 4p levels in the continuum. This spin-orbit coupling is very weak and thus XMCD signals at K edges are small compared to XMCD signals at L 2,3 edges. [START_REF] Westre | A Multiplet Analysis of Fe K-edge 1s → 3d Pre-edge Features of Iron Complexes[END_REF][START_REF] Olivier Mathon | Xmcd Under Pressure at the Fe K edge on the Energy-Dispersive Beamline of the ESRF[END_REF] Therefore, ID12 beamline has been carefully optimized for polarization dependent XAS measurements with incident X-rays in the energy range of 2-15 keV. The production of circularly polarized X-rays is achieved by using APPLE-II or HELIOS-II undulators. [START_REF] Goulon | Optical Activity Probed with X-rays[END_REF][START_REF] Goulon | Instrumentation Developments for X-ray Linear and Circular Dichroism at the ESRF Beamline ID12a[END_REF][START_REF] Rogalev | Instrumentation Developments for Polarization Dependent X-ray Spectroscopies[END_REF] The beamline is equipped with a UHV compatible Si( 111) double crystal monochromator. The XMCD measurements can be performed with magnetic induction as large as 17 T. The details of the beamline optics and the working end station can be found in the work by Rogalev et al. [START_REF] Rogalev | Instrumentation Developments for Polarization Dependent X-ray Spectroscopies[END_REF] All spectra are collected in the temperature range of 300 K to 2 K. At 2 K, the sample is irradiated by a laser (λ = 940 nm, P = 5 mW) during 8 hours. In the photo-induced state, XAS and XMCD at Fe and Co K edges were recorded. which arises from the 4p-3d low symmetry mixing. [START_REF] Juhin | X-ray Linear Dichroism in Cubic Compounds: The Case of Cr 3+ in MgAl 2 O 4[END_REF][START_REF] Westre | A Multiplet Analysis of Fe K-edge 1s → 3d Pre-edge Features of Iron Complexes[END_REF][START_REF] Anne Arrio | Calculation of Multipole Transitions at the Fe K Pre-Edge through pd Hybridization in the Ligand Field Multiplet model[END_REF]

Thermal and Photo-induced electron transfer

In a first step, XANES spectra at 300 K and at 2 K were recorded before irradiation to follow the thermal-induced electron transfer. LS . [START_REF] Bleuzen | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 1. Conditions to Observe the Phenomenon[END_REF][START_REF] Yokoyama | Local Structure of a Trapped Photoexcited State of a Fe-Co cyanide studied by X-ray-Absorption Fine-Structure Spectroscopy[END_REF][START_REF] Yokoyama | Characterization of magnetic CoFe cyanides by x-ray-absorption fine-structure spectroscopy[END_REF][START_REF] Bleuzen | CoFe Prussian Blue Analogues under Variable Pressure. Evidence of Departure from Cubic Symmetry: X-ray Diffraction and Absorption Study[END_REF] Hence, it confirms the transition from the paramagnetic state to the diamagnetic one due to thermal-induced electron transfer in 2•2DMF. The XANES part of the Co K edge spectra is also modified during the transitions, for instance, a significant decrease in intensity at the shoulder in the main rising edge at 7724 eV is observed. In the high energy region, the first EXAFS oscillations between 7146.5 eV and 7170 eV are not modified at Fe K edge, whereas, noticeable changes are observed in the shape resonance region in Co K edge XANES spectra between 7740.2 eV and 7770 eV. This is attributed to the change in environment around Co since a change in Co spin state from high spin to low spin significantly shortens the Co coordination sphere. [START_REF] Escax | Nature of the Long-Range Structural Changes Induced by the Molecular Photoexcitation and by the Relaxation in the Prussian Blue Analogue Rb 1[END_REF][START_REF] Hanawa | Coherent Domain Growth Under Photo-excitation in a prussian Blue Analogue[END_REF][START_REF] Maurin | Evidence for Complex Multistability in Photomagnetic Cobalt Hexacyanoferrates from Combined Magnetic and Synchrotron 135 X-ray Diffraction Measurements[END_REF] The change from Fe III LS to Fe II LS does not modify much the distances between Fe and its neighbors so that the first shape resonance is only slightly modified. These structural modifications have been confirmed by X-ray diffraction measurements in PBA systems. [START_REF] Escax | Nature of the Long-Range Structural Changes Induced by the Molecular Photoexcitation and by the Relaxation in the Prussian Blue Analogue Rb 1[END_REF] At 2 K, we irradiated the sample with λ = 940 nm laser (P = 5 mW) for 8 hours and the XAS spectra were recorded at Fe and Co K edges (Fig 4 .21). Both pre-edge regions and XANES regions from the K edges recorded at 300 K and at 2 K after laser irradiation superpose nicely. This confirms that the Fe ions have the same oxidation states at 300 K and in the paramagnetic metastable state at 2 K with quite similar environments. [START_REF] Yokoyama | Local Structure of a Trapped Photoexcited State of a Fe-Co cyanide studied by X-ray-Absorption Fine-Structure Spectroscopy[END_REF] The same is also true for Co ions. For comparison of thermal and light-induced electron transfer, we have plotted Fe and Co K edge XANES at 300 K, at 2 K before irradiation and at 2 K after irradiation in Figure 4.22. In a next step, we have warmed the sample back to 300 K to check for the reversibility of the electron transfer process. compares the Fe and Co K edge XANES spectra at 300 K before and after light irradiation.

The spectra superimpose completely, thus it confirms that the electron transfer process is indeed completely reversible. direction with respect to the magnetic induction. [START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF] The positive K edge XMCD peak for Fe can be attributed to the magnetization of the Fe 4p levels but not much can be said about the Fe 3d levels. [START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF]

XMCD detected magnetization curves at Fe and Co K edges

In a next step, XMCD detected magnetization curves are recorded at 2 K after laser irradiation as a function of magnetic induction by setting the monochromator at E = 7727 eV and E = 7131 eV for Co and Fe respectively. Fe and Co at 2 K. Whether there is a ferromagnetic coupling between Fe and Co ions or whether the two paramagnetic ions are similarly polarized by the magnetic induction remains still a matter of debate that cannot be solved by the present set of measurements.

Chapter 5

The XMCD technique is capable of tracking the exact orientation of the magnetization of the absorbing atom with respect to the X-ray propagation vector. gives information on the 4p orbital magnetic moment and whether the 4p orbital magnetic moment is proportional or at least oriented in the same direction as the 3d magnetic moment is likely although never demonstrated. In addition to XMCD, Neutron scattering technique has been employed to extract information about the magnetic structure and the magnetic moments associated to the different crystallographic positions. Pajerowski et al. [START_REF] Daniel M Pajerowski | Magnetic Neutron Scattering of Thermally Quenched K-Co-Fe Prussian Blue Analog Photomagnet[END_REF] reported the parallel alignment of Co and Fe magnetic moments in a thermally quenched magnetic state of a Fe/Co PBA coordination polymer

K α Co[Fe(CN) 6 ] β •nD 2 O.
They observed that at 4 T and 1 T the Co sites contribute to most of the magnetization. Interestingly, this result is contrary to the K edge XMCD results

by Champion et al. where an antiparallel alignment of the magnetic moments has been observed for an external induction of 1 T. [START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF] To our knowledge, the antiferromagnetic interaction in the photo-induced state of PBA

Introduction

Fe/Co Prussian blue Analogues (PBAs) are well-known for their bi-stable physical properties tuned by external stimuli. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Sato | Control of magnetic properties through external stimuli[END_REF] The discovery of photo-induced magnetization in tridimensional K 0.2 Co 1.4 [Fe(CN) 6 ]•6.9H 2 O PBA by Sato et al. [START_REF] Sato | Photoinduced Magnetization of a Cobalt-Iron Cyanide[END_REF] directed the research towards the rational design of PBA magnets exhibiting externally controlled reversible magnetization. Several Fe/Co PBA such as A x Co y [Fe(CN) 6 ] z •nH 2 O with z=(x+8)/3 if y=4 (A: K + , Rb + , Na + , Cs + ) have been synthesized and investigated to understand thermal-and photo-induced magnetic transitions. [START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF][START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Bleuzen | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 1. Conditions to Observe the Phenomenon[END_REF][START_REF] Escax | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 3. Control of the Photo-and Thermally Induced Electron Transfer by the [Fe(CN) 6 ] Vacancies in Cesium Derivatives[END_REF][START_REF] Shimamoto | Control of Charge-Transfer-Induced Spin Transition Temperature on Cobalt-Iron Prussian Blue Analogues[END_REF][START_REF] Goujon | Photo-Excitation from Dia-to Ferri-Magnetism in a Rb-Co-Hexacyanoferrate Prussian Blue Analogue[END_REF][START_REF] Escax | Photoinduced electron transfer in ferrimagnetic Prussian-blue analogues X I x Co 4 [Fe(CN) 6 ] y (X I = alkali cation)[END_REF] Bleuzen and co-workers performed a systematic study on series of Fe/Co Prussian blue analogues including RbCoFe

PBAs to characterize and control the electron transfer mechanism and associated magnetic properties. [START_REF] Bleuzen | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 1. Conditions to Observe the Phenomenon[END_REF][START_REF] Escax | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 3. Control of the Photo-and Thermally Induced Electron Transfer by the [Fe(CN) 6 ] Vacancies in Cesium Derivatives[END_REF][START_REF] Bleuzen | Photomagnetism in C x Co 4 [Fe(CN) 6 ] (8+x)/3 •nH 2 O Prussian Blue Analogues: Looking for the Maximum Photo-Efficiency[END_REF][START_REF] Bleuzen | Thermally Induced Electron Transfer in a CsCoFe Prussian Blue Derivative: The Specific Role of the Alkali-Metal Ion[END_REF][START_REF] Escax | Photoinduced electron transfer in ferrimagnetic Prussian-blue analogues X I x Co 4 [Fe(CN) 6 ] y (X I = alkali cation)[END_REF][START_REF] Bleuzen | CoFe Prussian Blue Analogues under Variable Pressure. Evidence of Departure from Cubic Symmetry: X-ray Diffraction and Absorption Study[END_REF] These fascinating photomagnetic properties of the Fe/Co Prussian Blue family were found to depend upon the nature and amount of alkali cations inserted in the structure. [START_REF] Escax | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 3. Control of the Photo-and Thermally Induced Electron Transfer by the [Fe(CN) 6 ] Vacancies in Cesium Derivatives[END_REF][START_REF] Bleuzen | Photomagnetism in C x Co 4 [Fe(CN) 6 ] (8+x)/3 •nH 2 O Prussian Blue Analogues: Looking for the Maximum Photo-Efficiency[END_REF] RbCoFe PBAs with different stoichiometries have been Chapter 5

studied extensively to explore the photo-induced metastable state. [START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF][START_REF] Goujon | Photo-Excitation from Dia-to Ferri-Magnetism in a Rb-Co-Hexacyanoferrate Prussian Blue Analogue[END_REF] This compound displays a large photomagnetic effect. [START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF] The change in local magnetization is crucial to understand the response of the molecular paramagnetic species to external stimulus.

Neverthless, one pertinent question about the nature of the magnetic coupling between Fe and Co in the photo-induced state of Rb 2 CoFe PBA has remained puzzling. It was shown that in the Rb 2 CoFe PBA, the diamagnetic to ferrimagnetic transition is observed after irradiation with a Curie temperature T c ≈ 21 K. [START_REF] Goujon | Photo-Excitation from Dia-to Ferri-Magnetism in a Rb-Co-Hexacyanoferrate Prussian Blue Analogue[END_REF] In Fe/Co PBAs, SQUID measurements [START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF][START_REF] Shimamoto | Control of Charge-Transfer-Induced Spin Transition Temperature on Cobalt-Iron Prussian Blue Analogues[END_REF][START_REF] Goujon | Photo-Excitation from Dia-to Ferri-Magnetism in a Rb-Co-Hexacyanoferrate Prussian Blue Analogue[END_REF] indicated an antiferromagnetic order below T c . In mixed valence manganese PBA neutron diffraction study shows antiferromagnetic arrangements of the magnetic moments. [START_REF] Franz | Crystalline, Mixed-Valence Manganese Analogue of Prussian Blue: Magnetic, Spectroscopic, X-ray and Neutron Diffraction Studies[END_REF] However, for Fe/Co cyanide coordination polymer, the parallel alignment of Co and Fe has also been reported. [START_REF] Daniel M Pajerowski | Magnetic Neutron Scattering of Thermally Quenched K-Co-Fe Prussian Blue Analog Photomagnet[END_REF] Following these magnetic observations in PBAs, the ferrimagnetic nature of photo-induced state is attributed to the "antiferromagnetic" coupling between Fe and Co ions. XMCD is an excellent tool to solve this question, since it can directly probe the nature of the magnetic interaction thanks to its atomic selectivity.

The "direct" evidence of an antiferromagnetic coupling in photo-induced state of RbCoFe PBA is reported by Champion et al. [START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF] which is in line with SQUID measurements on several PBA systems. [START_REF] Goujon | Photo-Excitation from Dia-to Ferri-Magnetism in a Rb-Co-Hexacyanoferrate Prussian Blue Analogue[END_REF] In K 0.1 of the exchange interaction between the magnetic moments of Co II HS and Fe III LS ions which results in a ferrimagnetic photo-induced metastable state. [START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF] However, this antiparallel alignment of Fe and Co magnetic moments has never been observed so far at L 2,3 edges in tridimensional Fe/Co PBA and their associated nanostructures. [START_REF] Michael | X-ray Magnetic Circular Dichroism Investigation of the Electron Transfer Phenomena Responsible for Magnetic Switching in a cyanidebridged [CoFe] Chain[END_REF][START_REF] Sadaf | Atomic Scale Evidence of the Switching Mechanism in a Photomagnetic CoFe Dinuclear Prussian Blue Analogue[END_REF]

Experimental Section

The synthesis of Rb 2 Co 4 [Fe(CN) 6 ] 3.3 •11H 2 O, referred to as sample 1 in the following, has been performed following the procedure reported by Cafun et al. [START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF] Sample 1 was dropcasted in milli-Q water on a silicon wafer which was mounted on a standard copper sample holder used for low temperature measurements. XAS and XMCD signals at Fe and Co L 2,3 edges were measured on DEIMOS beamline at SOLEIL synchrotron (France). [START_REF] Ohresser | DEIMOS: A Beamline Dedicated to Dichroism Measurements in the 350-2500 eV Energy Range[END_REF] There are two undulators, working as the photon source, namely an Apple-II helical undulator and an EMPHU undulator with different functions. The Apple-II helical undulator delivers a flux of circularly and linearly polarized X-rays for X-ray absorption, X-ray circular and linear dichroism measurements in the energy range 350-2500 eV. The EMPHU undulator is built with electromagnets and permanent magnets tailored to deliver The main end station at DEIMOS beamline consists of the cryogenic magnet CroMag which can provide a ± 7 T magnetic induction along the incoming X-ray beam and a ± 2 T magnetic induction perpendicular to the beam. The sample is attached to a variable temperature insert that controls the sample temperature between 1.5 K and 370 K.

For the present study, all spectra are recorded in the total electron yield mode under UHV conditions. Sample [START_REF] Brouder | Prolegomena to Magnetic Circular Dichroism in X-ray Absorption Spectroscopy[END_REF] σ L (σ R ) is the cross-section with left (right) polarized X-rays, and B + (B -) the magnetic induction parallel (antiparallel) to the X-ray propagation vector. With these definitions, a negative XMCD signal at the L 3 edge of 3d metals corresponds to a magnetic moment pointing in the same direction as the external magnetic induction. The background is subtracted using two arctangent functions that model the 2p 3/2 → continuum and 2p 1/2 → continuum transitions following the method described by Chen et al. [START_REF] Chen | Experimental Confirmation of the X-ray Magnetic Circular Dichroism Sum rules for Iron and Cobalt[END_REF] XMCD signals for Fe and Co in the photo-induced state at 2 K were also recorded at various magnetic induction values to get a deeper understanding of the contributions to the total XMCD signal. To take advantage of the sensitivity of the dichroic measurements by EMPHU, the XMCD detected magnetization curves have been measured as a function of the applied magnetic induction to check for the possible antiferromagnetic coupling between Fe and Co. For this, one needs to set the monochromator at a given energy where the XMCD signal is maximum in absolute value. For Fe the monochromator is set at 705.6 eV and for Co it is set at 777.3 eV. The applied induction is then varied while the circular polarization delivered by the EMPHU is switched at 1 Hz to record the variation of the maximum of the L 3 edge XMCD signal for each absorbing ion. Such XMCD detected magnetization curves have been recorded for temperatures ranging between 2 K and 30 K.

XMCD = σ --σ + where σ -= [σ L (B -) + σ R (B + )]/2 and σ + = [σ L (B + ) + σ R (B -)]/2.
In addition, soft X-ray induced electron transfer has been studied by measuring the XAS signals at 200 K and at 2 K before laser irradiation (see supporting information). During the measurements, we carefully checked that the sample 1 remains (i) free from radiation damage from the X-ray beam (ii) with no degradation related to vacuum environment (iii) stable in temperature (as it goes several heating and cooling cycles). The reversibility of photo-induced electron transfer process has been checked by warming the sample back to precursor which is referred as sample 2 and a comparison is made between sample 1 and 2 at Fe L 2,3 edges to obtain complementary information.

Results and Discussion

Light-induced metal-to-metal electron transfer

The electronic states of the diamagnetic Fe II LS or Co III LS ions and the paramagnetic Fe III LS or Co II HS ions can be easily detected by recording the XAS spectra at L 2,3 edges. [START_REF] Escax | The Co Ligand Field: A Key Parameter in Photomagnetic CoFe Prussian Blue Derivatives[END_REF][START_REF] Cartier Dit Moulin | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 2. X-ray Absorption Spectroscopy of the Metastable State[END_REF][START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF][START_REF] Sadaf | Large Orbital Magnetic Moment Measured in [T P Fe III (CN) 6 ]the Precursor of Photomagnetic Molecular Prussian Blue Analogues[END_REF] We then recorded Fe and Co L 2,3 edges at 200 K where the two ions are in a diamagnetic state and at 2 K after laser irradiation (Figure 5.1) where part of the diamagnetic ions transform into paramagnetic ones. At 200 K, the ground state for Fe is a mixture of Fe II LS and Fe III LS and similarly the ground state for Co is a mixture of Co III LS and Co II HS . Such mixed states for Fe and Co have already been reported elsewhere. [START_REF] Cartier Dit Moulin | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 2. X-ray Absorption Spectroscopy of the Metastable State[END_REF][START_REF] Cartier Dit Moulin | Structural Rearrangements Induced by Photoexcitation in a RbCoFe Prussian Blue Derivative[END_REF][START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF]37] We have reference spectra for pure Fe LS and ≈66 % of Co II HS (see S.I. for linear combinations). The information obtained for Fe is fully compatible with the one obtained for Co if one considers errors close to ±5 % during the fitting process. After laser irradiation (λ = 635 nm) at 2 K, between half and two thirds of the diamagnetic ions transform into paramagnetic ones. At 2 K, the linear combination fit yields ≈70 % Fe III LS and ≈88 % Co II HS . Although the observed conversion is not complete, one can notice that peak a of the Fe L 3 edge is larger than the one reported by Cartier dit Moulin et al. [START_REF] Cartier Dit Moulin | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 2. X-ray Absorption Spectroscopy of the Metastable State[END_REF] We attribute this difference to a larger conversion rate in the present measurements. Co II ions, one finds that the magnetic moment of the Co ions are likely all oriented parallel to the external magnetic induction. The same comparison for Fe shows that the Fe ions are only partially magnetized (see S.I. and Jafri et al. [START_REF] Sadaf | Atomic Scale Evidence of the Switching Mechanism in a Photomagnetic CoFe Dinuclear Prussian Blue Analogue[END_REF] ). In addition, the shape of the XMCD signal at the Fe L 2,3 edges is quite different from the one observed for potassium hexacyanidoferrate(III) precursor (see Fig. 5.14 in Supporting Information). In the case of Rb 2 CoFe, one observes two peaks (β,γ) around 710 eV, whereas there is only one for potassium hexacyanidoferrate(III). Peak is as large as peak α whereas it is three times smaller for potassium hexacyanidoferrate(III). One simple way to interpret the reduced intensity and the additional features is to consider that there are two sites for Fe ions with one site, labelled site a where Fe ions are polarized parallel to the external magnetic induction and another one, labelled site b where the Fe ions are magnetized antiparallel to the external magnetic induction. In the two sites, Fe is clearly in the Fe III LS configuration but with slightly different environments and crystal fields so that β and γ features do not superimpose. At 6.5 T and 2 K, the magnetization from site a is larger than the one from site b as can be guessed from the mainly negative signal at the L 3 edge. To get more information on these possible two sites, we have recorded the XMCD detected magnetization curves for Fe and Co.

Induction dependent XMCD investigation

In order to record the element specific magnetization curve for Co, the energy of the X-rays have been set to 777.3 eV and the external magnetic induction is switched between +6.5 T and -6.5 T. The Co magnetization curve at 2 K is reported in Fig. 5.3. One observes a sharp rise of the magnetization in the first 500 mT to which a linear increase shows that the difference spectrum is very much alike the XMCD signal for pure potassium hexacyanidoferrate(III), i.e. sample 2.

From what precedes, we know that the Co sites in the antiferromagnetic phase and in the paramagnetic one are both very similar. For Fe III ions, the Fe III site in the antiferromagnetic phase is much alike the Fe III site in potassium hexacyanidoferrate(III) and the Fe III site in the paramagnetic phase would be similar to the one for a strongly distorted site such as FeTp. The easiest way to accommodate for the two phases is to consider that the bulk of the tridimensional PBA is indeed the antiferromagnetic phase whereas the paramagnetic phases comes from the Fe III and Co II ions at the surface of the PBA grains for which the crystallographic and the magnetic disorder would destroy the antiferromagnetic interactions. The previous depth analysis is fully consistent with our interpretation of contribution from the different sites. One contribution is coming from the bulk and the other is coming from the very surface.

Conclusion

The main conclusion from the present piece of work is that it has been possible to prove at the atomic level the existence of an antiferromagnetic interaction between Fe ions and

Co ions in Rb 2 Co 4 [Fe(CN) 6 ] 3.3 •11H 2 O.
From SQUID measurements and by comparison with non photomagnetic systems, the existence of such an interaction was considered as almost certain but this is the first time to our knowledge that such an antiferromagnetic coupling is confirmed by both experimental and theoretical XMCD signatures from both Fe and Co edges. The conclusion is very robust as can be seen from the large difference in XMCD intensity between Fe and Co ions, the negative slope of the magnetization at Fe L 2,3 edges and the exact shape of the XMCD signal at the Fe L 2,3 edges that perfectly mimics the one for potassium hexacyanidoferrate(III) but for a reversed magnetization with respect to the external magnetic induction. In addition, it is found that the Fe-Co pairs at the surface of the PBA grains do not experience the same antiferromagnetic interaction Chapter 5 because of geometric disorder and a lack of magnetic neighbors. This raises the question of the nature of the magnetic interaction in photomagnetic molecular Fe/Co PBA such as the cube, [START_REF] Li | Magnetic and Optical Bistability Driven by Thermally and Photoinduced Intramolecular Electron Transfer in a Molecular Cobalt-Iron Prussian Blue Analogue[END_REF] the square, [START_REF] Mondal | On/Off Photoswitching in a Cyanide-Bridged {Fe 2 Co 2 } Magnetic Molecular Square[END_REF][START_REF] Zhang | Reversible Thermally Photoinduced Electron Transfer in a Cyano-Bridged {Fe 2 Co 2 } Square Complex[END_REF][START_REF] Zhang | Thermochromic and Photoresponsive Cyanometalate Fe/Co Squares: Toward Control of the Electron Transfer Temperature[END_REF][START_REF] Mercurol | Fe II LS Co III LS[END_REF][START_REF] Nihei | Thermally Two-stepped Spin Transitions Induced by Intramolecular Electron Transfers in a Cyanide-bridged Molecular Square[END_REF][START_REF] Nihei | Controlled intramolecular electron transfers in cyanide-bridged molecular squares by chemical modifications and external stimuli[END_REF] or the dinuclear [START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF][START_REF] Jeon | Spin Crossover or Intra-Molecular Electron Transfer in a Cyanido-Bridged Fe/Co Dinuclear Dumbbell: A Matter of State[END_REF] complexes that have been recently synthesized.

Acknowledgement

This work was supported by the Centre National de la Recherche Scientifique (CNRS, France), the Ministère de l'Enseignement Supérieur et de la Recherche (MESR, France), and the GdR MCM2. We are thankful to SOLEIL staff for running the machines.

Chapter 5. Probing the Magnetic interaction in tridimensional Fe/Co Prussian Blue Analogues 109

Supporting Information of Paper III

Reversibility of electron transfer process

The reversibility of light-induced electron transfer is confirmed by recording XAS spectra at T = 200 K before and after laser irradiation (Figure 5.8).

X-ray induced metal-to-metal electron transfer

To follow the X-ray induced electron transfer, XAS spectra at Fe and Co L 2,3 edges are recorded at 200 K and 2 K before irradiation. At 200 K, the ground state is a mixture of Fe II LS , Co III LS and Fe III LS , Co II HS species [START_REF] Cartier Dit Moulin | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 2. X-ray Absorption Spectroscopy of the Metastable State[END_REF] . From figure 5.9, one observes that characteristic features for Fe II LS (b and c) and for Co III LS peak (e') are the dominant features. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Escax | The Co Ligand Field: A Key Parameter in Photomagnetic CoFe Prussian Blue Derivatives[END_REF][START_REF] Cartier Dit Moulin | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 2. X-ray Absorption Spectroscopy of the Metastable State[END_REF][START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF]37] Upon cooling down to 2 K, no thermal-induced electron transfer is expected in this Fe/Co PBA. [START_REF] Bleuzen | Photomagnetism in C x Co 4 [Fe(CN) 6 ] (8+x)/3 •nH 2 O Prussian Blue Analogues: Looking for the Maximum Photo-Efficiency[END_REF][START_REF] Cafun | Photomagnetic CoFe Prussian Blue Analogues : Role of the Cyanide Ions as Active Electron Transfer Bridges Modulated by Cyanide-Alkali Metal Ion Interactions[END_REF] Chapter 5 HS has been reported in Fig. 5.12. We attribute the difference between the concentrations of and Fe II LS and Co II HS to the existence of the surface paramagnetic phase for which the stoichiometric ratio might be different from the bulk value for sample 1.

X-ray induced vs light-induced electron transfer

XMCD detected magnetization curves for Fe and Co in sample 1

The XMCD detected magnetization curves of Fe in sample 1 as function of external induction recorded for T = 2 K, 10 K, 20 K, 30 K are given in Figure 5.16. As the temperature reaches the Curie temperature (T c = 21 K), the system tends to loose the ferrimagnetic order and at 30 K the magnetization of Fe and Co ions are both aligned parallel to the external magnetic induction as expected for non coupled paramagnetic ions.

Linear combinations

The reference spectra of pure Co II HS , Co III LS and Fe II LS , Fe III LS used for linear combination are presented in Figure 5.

Summary of Chapter 5

In this chapter, we have proved the existence of an antiferromagnetic coupling between (i) the intensity of the Fe XMCD signals is 9 times smaller than the Co one, (ii) the XMCD detected magnetization curve for Fe proves that the magnetization of a majority of Fe ions is aligned antiparallel to the external magnetic induction when the magnetic induction is such that -1.5 T ≤ B ≤ +1.5 T , (iii) the shape of the XMCD signal for the antiferromagnetically coupled Fe III ions is identical to the one for potassium hexacyanidoferrate(III) except for the direction of magnetization.

Our findings confirm the previously reported data by Champion et al. at the Fe and Co K edges for similar tridimensional systems for which the analysis was far from obvious. [START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF] Whether this result found for a tridimensional PBA still holds for the Fe/Co molecular complexes such as the dimers, the squares or the cubes cannot be inferred from the present results. At least, it can be said that there is no antiferromagnetic coupling at 2 K in the From the XMCD detected magnetization curves, the Fe and Co magnetic moments were found to be aligned parallel to the external magnetic induction and no opening of the curve was observed. The second dinuclear complex namely 2•2DMF preserved the electron transfer properties in presence of solvent molecules. In this complex, XMCD measured at the Fe and Co K edges confirmed the thermal-and light-induced electron transfer. Both complexes were found to display bistability below 50 K.

At L 2,3 edges, measurements of XAS and XMCD spectra for the photomagnetic electron transfer systems need special conditions. To obtain the good data, damaging of sample under X-ray irradiation can be avoided only working with low flux of incoming X-rays. Based on these precautions, a systematic experimental investigation in tridimensional RbCoFe PBA confirmed the antiferromagnetic interaction between Fe and Co at L 2,3 edges that had been previously alleged. The XMCD technique is proved to be an excellent technique that can separate the antiferromagnetic coupled Fe-Co from other surface contributions.

Concerning the questions that were not fully answered and that would require further investigations, I would suggest the possible strategy.

1) What is the nature of coupling in dinuclear PBA molecules?

For this, the antiferromagnetic coupling should be checked in sub-kelvin temperature range. Further developments in the experimental set-up at L 2,3 edges requires a cell specifically designed for the study of solutions under UHV conditions. The liquid cell is in development by Niéli DAFFE a Ph.D. student in our group. The 2•2DMF dinuclear complex which exhibits electron transfer in presence of solvent molecules could be studied by XMCD at L 2,3 edges under UHV conditions. In addition, comparison of the XMCD signals of the two dinuclear complexes at 400 mK using French TBT set-up at SLS might help understanding the nature of magnetic interaction in smallest units of Fe/Co PBA.

2) What can be said about the nature of coupling from the measurements at K edges?

To answer this question, further investigations are required to explain the differences observed in XMCD signals in Fe-precursor and in the dinuclear PBA complexes at K edge.

Moreover, these K edge data can be compared with the K edge data of the tridimensional PBA. In addition, photon-in photon-out Resonant Inelastic X-ray Scattering combined with magnetic circular dichroism (RIXS-MCD) can be performed. At K pre-edge of the 3d elements, the high resolution of RIXS is an advantage combined with the bulk sensitivity and the low self-absorption effects. It was shown that hard X-ray RIXS-MCD can be a valuable alternative to soft X-ray XMCD, when using demanding sample environments, such as liquids and gas cells, or when investigating materials whose surface may be non representative of bulk properties.

The Density Functional Theory (DFT) at K edges can be applied to extract the information about the electronic structure. A project is dedicated to the application of DFT theory at transition metal K edges in our group at IMPMC. Although, DFT lacks the multiplet effects at present, the development of the theory is in progress by a Ph.D.

student Nadejda BOULDI (IMPMC).

3) How can we estimate the number of antiferromagnetically coupled Fe sites in tridimensional PBA?

A detailed LFM investigation is required to estimate the number of Fe and Co sites where the magnetic moments are aligned antiparallel. This could be achieved by simulating the XMCD signal for various magnetic induction values. The orbit and spin magnetic moments can be extracted once a good agreement between the experimental XAS/XMCD and the LFM calculated spectra is achieved. Moreover, it is worth trying to record the K edge XMCD spectra in tridimensional PBA with special attention to the K pre-edge region. This could be compared with the K edge XMCD signals of dinuclear complex 1 and 2•2DMF.

Ligand Field Multiplet calculations need to be improved to simulate XAS and XMCD spectra of Co ions in dinuclear complex. The preliminary LFM calculations suggest that the electronic structures of Co ions in photo-induced paramagnetic state and high temperature paramagnetic state are similar. This would need a project dedicated to the LFM investigations reproducing the spectral changes with good symmetry in high temperature paramagnetic state, low temperature diamagnetic state and low temperature photo-induced state.

5) What is the next step in exploring the magnetic properties of the photomagnetic molecular systems?

The magnetic bistability occur at low temperature, so can this phenomenon of magnetic bistability be observed at higher temperatures in the sub-picosecond time domain which is the fundamental time scale of molecular motion? Thus, probing the length-and timescales on which the photo-induced processes take place can gain a significant insight into the processes during and after the photo-induced conversion. In this regard, femtosecond optical spectroscopy and time resolved X-ray diffraction is a powerful technique for studying photoswitching dynamics. Recently, femtosecond XAS at X-FEL and optical spectroscopy are combined and the structural stabilization of photo-induced state is observed in ultrafast time scale. Thus, there is a great scope to study the ultrafast structural dynamics of the photo-induced state of PBA systems to answer the questions, for instance, why is there a slower response to the laser irradiation? Furthermore, the cooperative effects should be investigated especially for Prussian Blue Analogues where metal-to-metal electron transfer accompanies the structural relaxation around metal ions. The cooperative response in PBA can be observed on ultra-fast time scale which will enable to check whether the similar cooperative effects are present in dinuclear complexes?

The

I

  also would like to thank all the beamline staff from DEIMOS beamline (SOLEIL, France), ID12 beamline(ESRF, France) and SIM beamline(SLS, Switzerland) for their technical support. Beamtimes are tiring and stressful and the beamline staff does whatever it takes to help experiments run smoothly. Special thanks to Edwige OTERO from DEIMOS beamline (SOLEIL, France) and Fabrice Wilhelm from ID12 beamline (ESRF, France) for their help during the experiments. I would like to thank my colleagues, friends and Post docs at IMPMC with whom I have shared some great moments. Florent, Nadejda, Nieli, Aisha, Ruidy, Mathieu, Lousiane Sara, Manoj, Myrtille, Vincent, Adrient, Nicholas,Areej, Sandy, Pauline, Natan, Guilherme, Henri and Maud. Friends outside the lab have been invaluable. I would like to thank Soria, Florian, Maria, Julie, Eva and David. They were fully confident that I would nail my PhD defense. My hearfelt appreciation is for my mentor Dr. Sadia MANZOOR who always supported me and encouraged me. She recognized and appreciated my talent. I would like to thank my undergraduate advisor Dr. Iqbal Ahmed KHAN, a dedicated teacher who used to tell me, "Sadaf always do things in the best possible way." I would like to thank Erasmus Mundus Europe Asia (EMEA) program which provided me the opportunity to study the NANOMAT masters at University of Pierre and Marie Curie (UPMC) as Erasmus Mundus Scholar and to discover the French culture. Many thanks to my mentors during my NANOMAT masters at INSP (UPMC): Prof. William SACKS, Prof. Nadine WITKOWSKI and Prof. Masimiliano MARANGOLO. I also would like to thank ecole doctorale 397 "Physics and Chemistry of Materials" to give me PhD scholarship to pursue my research at UPMC.

1 . 5 [

 15 Fe(CN) 6 ]•6H 2 O is an alkali free compound which served as a model system to look for the effects induced by alkali metal ions. Upon comparison, Rb 0.66 Co 1.25 [Fe(CN) 6 ]•4.3H 2 O was mainly composed of Fe II LS -CN-Co III LS diamagnetic species whereas Co 1.5 [Fe(CN) 6 ]•6H 2 O contained paramagnetic Fe III LS -CN-Co II HS species at 5 K. This is attributed to the difference in average coordination sphere of Co in both compounds. The Co/Fe ratio is different in both compounds and this is responsible for the existence of [Fe(CN) 6 ] vacancies in Rb 0.66 Co 1.25 [Fe(CN) 6 ]•4.3H 2 O.

Chapter 1 . 21 Figure 1 . 1 -

 12111 Figure 1.1 -Schematic representation of a Fe/Co Prussian blue network with formula A x Co y [Fe(CN) 6 ]•nH 2 O (A: alkaline ions, which have been omitted for clarity; C: grey; N: light blue; Co: blue; Fe: yellow; O: red.This figure is taken from the review by Aguilà et al.[START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF]

Chapter 1 Figure 1 . 2 -

 112 Figure 1.2 -Interconversion between the paramagnetic (Fe III LS -CN-Co II HS ) and diamagnetic (Fe II LS -CN-Co IIILS ) electronic configurations due to thermally and photo-induced metal-to-metal electron transfer processes. This figure is taken from the review by Aguilà et al.[START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF]

Figure 1 . 3 -

 13 Figure 1.3 -(left) Schematic representation of the molecular structure of the cube analogue [(pzTp)Fe III (CN) 3 ] 4 [Co II (pz) 3 CCH 2 OH] 4 •13DMF•4H 2 O at 260 K (the core [Co 4 Fe 4 ] is emphasized). Lattice solvent molecules, anions, and hydrogen atoms are omitted for clarity. Fe, Co, N, C, O and B atoms are indicated in orange, dark blue, light blue, light grey, red and pink, respectively. (right) Temperature dependence of the χT product at 0.4 K/min for [Co 4Fe 4 ] before (black dots), after irradiation (red dots); and after thermal quenching (blue dots). This figure is taken from the review by Aguilà et al.[START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Li | Magnetic and Optical Bistability Driven by Thermally and Photoinduced Intramolecular Electron Transfer in a Molecular Cobalt-Iron Prussian Blue Analogue[END_REF]

Figure 1 . 4 -

 14 Figure 1.4 -(left) Schematic representation of molecular structure of the square analogue [(Tp * )Fe(CN) 3 ] 2 [Co II (bipy) 2 ] 2 .[(OTf)] 2 •4DMF•2H 2 O at T = 230 K (the core [Co 2 Fe 2 ] is emphasized). Lattice solvent molecules, anions, and hydrogen atoms are omitted for clarity. Fe, Co, N, C, O and B atoms are indicated in orange, dark blue, light blue, light grey, red and pink, respectively. (right) Temperature dependence of the χT product at 0.4 K/min for [Co 2Fe 2 ] before (black dots), after irradiation (green dots); and after thermal quenching (purple dots). This figure is taken from the review by Aguilà et al.[START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Zhang | Reversible Thermally Photoinduced Electron Transfer in a Cyano-Bridged {Fe 2 Co 2 } Square Complex[END_REF]

Figure 1 . 5 -

 15 Figure 1.5 -Representation of the molecular structure of the dinuclear complex [(Tp)Fe(CN) 3 Co(PY5Me 2 )](OTf)•2DMF at T = 180 K (left). Hydrogen atoms, triflate and lattice-solvent molecules are omitted for clarity. Fe,Co, N and C atoms are indicated in orange, dark blue, light blue and light grey, respectively. χT versus time (blue circles) of the desolvated compound, at 1 T and 10 K under white light irradiation (3 mW cm -2) and temperature before (black dots) and after (red dots) white light irradiation with a sweep rate of 0.4 K/min (right). This figure is taken from the review by Aguilà et al.[START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF][START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF]

Figure 2 . 1 -

 21 Figure 2.1 -Principle of X-ray absorption spectroscopy (XAS) When the X-ray energy is close to the binding energy of a core-level, a sharp variation of the absorption coefficient is observed as a function of the X-ray energy, that is called an absorption edge. The characteristic edge jumps are the result of the consecutive excitation of core levels. Core level binding energies are specific for each atom and the absorption edges are labelled as K, L 1 , L 2,3 , M 1 , M 2,3 , or M 4,5 edges when the core level is present in the |1s , |2s , |2p , |3s , |3p , or |3d respectively. The transition matrix elements

Figure 2 . 2 - 2 -

 222 Figure 2.2 -Principle of X-ray Magnetic Circular Dichroism (XMCD)The XMCD signal can be obtained either by taking the difference of two XAS spectra measured for two different circular polarization state (right and left) at a given magnetic induction direction or by keeping the circular polarization state of incoming X-rays fixed and then take the difference of two XAS spectra with two magnetic induction directions parallel and antiparallel to the propagation vector. The XMCD signals thus obtained in both cases remain equivalent. In this case it is useful to express XMCD signal in another notation such as σ ab . In this notation, the superscript a represents the polarization state of the incoming X-ray beam and b represents the direction of the applied magnetic induction B with respect to the propagation vector k of the incoming X-ray beam. Then, a = ↓ ( ↑) for right (left) circular polarization and b = ↑ ( ↓) for magnetic induction B parallel (antiparallel) to k. The equivalence between the inversion of polarization state or magnetic induction B direction is only fully valid in the electric dipole approximation and allows to write:

Figure 2 . 3 -

 23 Figure 2.3 -Experimental XAS (black line) and XMCD (green line) at Fe L 2,3 edges is presented for illustration.

Figure 2 . 4 -

 24 Figure 2.4 -Experimental XAS (black line), integrated intensity of XAS (black dashed line) (left) and XMCD (red line), integrated intensity of XMCD (red dashed line) (right) at Fe L 2,3 edges is presented for illustration.

  Most of the findings are obtained from XMCD measured at the Fe L 2,3 edges. Following are the chemical formulae of the four precursors : (NEt 4 )[(Tp*)Fe III (CN) 3 ] (Tp*=tris(3,5-dimethyl)pyrazolyl borate) FeTp * (NEt 4 )[(pzTp)Fe III (CN) 3 ], (pzTp = tetra-pyrazolyl borate) FepzTp (NBu 4 )[(Tp)Fe III (CN) 3 ] (Tp = hydridotris-pyrazolyl borate) FeTp K 3 [(Fe III (CN) 6 ] Potassium hexacyanidoferrate(III)

Figure 3 . 1 -

 31 Figure 3.1 -Structure of the complex anions of (a) FeTp [(Tp)Fe III (CN) 3 ] -, (b) FeTp * [(Tp*)Fe III (CN) 3 ] -, (c) FepzTp [(pzTp)Fe III (CN) 3 ] -and (d) Potassium hexacyanidoferrate(III) [Fe III (CN) 6 ] 3-. Color Scheme: Iron ions are drawn in red, Carbon atoms in black, Nitrogen atoms in blue and Boron atoms in grey. Hydrogen atoms and counterions (NBu + 4 , NEt + 4 , NEt + 4 and K + 3 respectively) are omitted for clarity.

Figure 3 . 2 -

 32 Figure 3.2 -ORTEP-type view of the anionic complex (N(C 4 H 9 ) 4 )[TpFe III (CN) 3 ]•3H 2 O (FeTp) at 120 K. Thermal ellipsoids are depicted at the 50 % probability level. All anions, solvent molecules and hydrogen atoms are omitted for clarity. Fe, N, C and B atoms are indicated in orange, light blue, grey and pink, respectively.

  where µ B is positive and L z and S z are defined by L z = Lz / , S z = Ŝz / , where Lz and Ŝz are the z components of the orbital and spin kinetic momentum operators; g 0 ≈ 2 is the electron Landé factor and O = i|O|i is the expectation value of operator O (calculated over the ground state at 0 K, or its average calculated over all populated states at a finite temperature). With p =

|2p 6 3d 5 43 Figure 3 . 3 -

 54333 Figure 3.3 -Experimental isotropic XAS (thick purple line) and XMCD (cyan line) spectra for sample FeTp at ± 6.5 T and 2 K. XAS spectra with left (thin purple line) and right (dotted purple line) circular polarization are shown. XAS and XMCD signals are normalized to peak c of the isotropic XAS.

3 Figure 3 . 4 -

 334 Figure 3.4 -Comparison of the normalized XAS (purple line) and XMCD (cyan line) experimental spectra, at ±6.5 T and 2 K, and calculated XAS and XMCD (thin black line) at the Fe L 2,3 edge for FeTp. Upper panel: calculations in C 3v with π back donation. Middle panel: calculation in O h symmetry with π back donation. Lower panel: calculation in O h symmetry without π back donation. All calculations include 70 % of nephelauxetic reduction. Isotropic XAS and XMCD are normalized to peak c of the isotropic XAS.

Figure 3 .

 3 4 reports XAS and XMCD spectra calculated for a pure ionic model (single |2p 6 3d 5 configuration) in regular octahedral (O h ) symmetry, where the large crystal field (10Dq = 2.8 eV) and the nephelauxetic reduction (κ = 70 %) imposed by the cyanido ligands were taken into account, but not the associated π back bonding effect. In addition, the XAS and XMCD spectra calculated in O h symmetry and including MLCT due to π back bonding are shown in the middle panel of Figure 3.4.

  2), ground state expectation at T = 0 K are: L LF M z = -1.236, S LF M z = -0.488 and T LF M z = -0.115. Since T z is significantly different from zero, it has to be taken into account in the spin sum rule. Then, from the values of S z and T z , one obtains the effective spin kinetic momentum S eff z = S z + 7 2 T z = -0.889. At 0 K, the spin magnetic moment for the Fe ion is m spin = -2 S z µ B = 0.98µ B as can be expected for an S = 1/2 low spin Fe III ion and in agreement with the magnetic measurements (Supporting information Figure 3.7).

z=

  -0.615, which is very different from the value obtained from the LFM calculation (i.e. S LFM,eff z = -0.889), with a corresponding deviation larger than 30%. From S eff z = -0.615 and T z = -0.115, the sum rule yields S z = -0.214 (m spin = 0.43µ B ) whereas the LFM calculation gives S LF M z = -0.488 (m spin = 0.98µ B ).

z 3 Figure 3 . 5 -

 335 Figure 3.5 -Variation of error in the spin sum rule as a function of 2p spin-orbit coupling.

  .7) have been recorded on a fully isotropic powder for which the sample grains are physically aleatory blocked in the measured sample at low temperature, while XMCD measurements were made on drop cast. The LFM calculations shown in Figure 3.4 were performed for an external magnetic field parallel to the C 3 axis of the molecule. We performed complementary calculations by varying the respective orientation of the magnetic field B and the C 3 axis. We found that the XMCD intensity as well as S z and L z are highly dependent on the α angle between B and the C 3 axis. In the local orthonormal frame where [001] is along the C 3 axis and [010] lies in one of the three σ V planes, we tested the following orientations for B parallel to [001] (α = 0 • ), [100] (α = 90 • ), [010] (α = 90 • ), [110] (α = 90 • ), [011] (α = 45 • ), [101] (α = 45 •

  The baseline function (bl(E) with E the photon energy in eV) is a linear combination of two arctangent function to fit the absorption step edge at L 3 (711.4 eV) and L 2 (723.7 eV) edges: bl(E) = { 1 π arctan(Energy -711.4) + After subtraction of the baseline, the XAS spectrum is normalized to 1 at peak c of the L 3 edge i.e is divided by the absorption value at the energy of peak c. The XMCD

Figure 3 . 6 -

 36 Figure 3.6 -Projection view of the crystal structure of FeTp at 120 K showing the packing of the anionic complexes, the [N(C 4 H 9 ) 4 ] + cations and the lattice water molecules in the (ac) plane. All the hydrogen atoms are omited for clarity. Fe, N, C, O and B atoms are indicated in orange, light blue, grey, red and pink, respectively. The light blue dotted lines are indicating the H-bonding between the cyanide groups and the lattice water molecules.

Figure 3 . 7 -

 37 Figure 3.7 -(top) χT versus T curves at 0.1 T, (bottom right) reduced magnetization curve (M versus B/T ), and (bottom left) magnetization versus field B for FeTp at different temperatures. χ is defined as the molar magnetic susceptibility and equal to M/B, M being the magnetization and B the dc applied magnetic field.

Figure 3 . 8 - 56 Chapter 3 3. 3 . 5

 3856335 Figure 3.8 -Experimental XAS spectrum (blue line), XAS spectrum before the edge set to zero (black line), XAS spectrum after subtraction (green line) of the arctangent functions (dashed red line) for sample FeTp at 2 K.

Figure 3 . 9 -

 39 Figure 3.9 -Unconvoluted transition intensities (sticks : | f |ε • r|i | 2 ) for the XMCD spectrum calculated at T = 0 K using the parameters listed in Table 3.2 (main text). Insert : zoom of the region between L 3 and L 2 edges

Chapter 3 . 59 3. 4

 3594 Fe-bearing Precursors of Photomagnetic FeCo Prussian Blue Complexes Probing the electronic and magnetic structures of FeTp*, FepzTp and Potassium hexacyanidoferrate(III) 3.4.1 XMCD at L 2,3 edges X-ray absorption and X-ray magnetic circular dichroism experiments have been performed at the L 2,3 edges in three low spin Fe III paramagnetic precursors other than FeTp. XAS and XMCD spectra were recorded at 2 K under a magnetic field of 6.5 T on DEIMOS beamline of SOLEIL synchrotron. In this section, a comparison between FeTp * , FepzTp, and Potassium hexacyanidoferrate(III) precursors and FeTp is presented. Figure 3.10 shows the XAS and XMCD experimental spectra. Each XAS spectra is normalized to 1 at peak c, and the XMCD signals are normalized to the maximum of peak c. Hence, the comparison of different spectral features and their respective intensities can be made directly.

L 3

 3 edge contains four main peaks. Except for Potassium hexacyanidoferrate(III), the peaks at L 3 edge are at the same energy (a: 705.8 eV, b: 708.5 eV, c: 709.3 eV, e: 712.3 eV), the small shoulder d at 709.8 eV and the L 2 edge has three peaks (f : 718.5 eV, g: 721.8 eV, h: 725.8 eV). For Potassium hexacyanidoferrate(III), at the L 3 edge peak positions are a: 705.8 eV, b: 709.1 eV, c: 709.8 eV, and at the L 2 edge the peak positions are f : 718.5 eV, g: 722.5 eV, h: 725.4 eV. The intensity of Fe III LS signature peak (705.8 eV) varies in all precursors. This characteristic peak of low spin Fe III ion corresponds to the transition from 2p 6 t 5 2g to 2p 5 t 6 2g in a simple monoelectronic picture. From the comparison of isotropic spectra, one can see that the intensity of Fe III LS signature peak (705.8 eV) (a/c) is ≈ 1 in Potassium hexacyanidoferrate(III) (1.08) and FeTp (1.01) whereas it is ≈ 0.76 for FepzTp and FeTp*. On the high energy side of the L 3 edge of Potassium hexacyanidoferrate(III), a sharp peak e is present at 712 eV. The presence of this feature is attributed to the 6 cyanido ligands in K 3 [(Fe III (CN) 6 ] as shown in Figure 3.1 (d). Due to the presence of 6 cyanido ligands in K 3 [(Fe III (CN) 6 ] one expects a charge transfer between the Fe ion and

Figure 3 .

 3 Figure 3.12 compares the XMCD spectra of the different precursors. The shape of the XMCD signal is rather similar in all precursors. L 3 edge XMCD spectra has two main negative features α (705.8 eV) and γ (709.3) eV. For Potassium hexacyanidoferrate(III) feature γ is at 709.9 eV. The intensity of α changes considerably. The ratio α/c is 86.9 % for Potassium hexacyanidoferrate(III), 110.7 % for FeTp, 75.6 % for FeTp* and 62.6 % for FepzTp. The intensity of the α XMCD peak for samples Potassium hexacyanidoferrate(III), FeTp* and FepzTp are respectively ≈ 20 % , 30 % and 40 % smaller than for sample FeTp. These variations probably find their origin in the angular

Figure 3 . 11 -

 311 Figure 3.11 -Experimental XAS spectra measured at 2 K with 6.5 T for samples Potassium hexacyanidoferrate(III) K 3 [(Fe III (CN) 6 ] (purple line), FeTp (NBu 4 )[(Tp)Fe III (CN) 3 ] (green line), FeTp* (NEt 4 )[(Tp*)Fe III (CN) 3 ] (red line) and FepzTp (NEt 4 )[(pzTp)Fe III (CN) 3 ](blue line).

Figure 3 . 12 -

 312 Figure 3.12 -Experimental XMCD spectra measured at 2 K and with 6.5 T for samples Potassium hexacyanidoferrate(III) K 3 [(Fe III (CN) 6 ] (purple line), FeTp (NBu 4 )[(Tp)Fe III (CN) 3 ] (green line),FeTp* (NEt 4 )[(Tp*)Fe III (CN) 3 ] (red line) and FepzTp (NEt 4 )[(pzTp)Fe III (CN) 3 ] (blue line).

Figure 3 . 13 -

 313 Figure 3.13 -Experimental XAS spectra measured at 2 K for samples Potassium hexacyanidoferrate(III) K 3 [(Fe III (CN) 6 ] (thin purple line), FeTp (NBu 4 )[(Tp)Fe III (CN) 3 ](thick green line), FeTp* (NEt 4 )[(Tp*)Fe III (CN) 3 ](thick red line) and FepzTp (NEt 4 )[(pzTp)Fe III (CN) 3 ](thick blue line).

Figure 3 . 14 -

 314 Figure 3.14 -Comparison of XMCD detected magnetization curves (light green line) at T = 2 K with 6.5 T and SQUID measurements (top left) for FepzTp (NEt 4 )[(pzTp)Fe III (CN) 3 ](blue), (top right) for FeTp* (NEt 4 )[(Tp*)Fe III (CN) 3 ] (red line), and (bottom) for Potassium hexacyanidoferrate(III) K 3 [Fe III (CN) 6 ] (purple line).

Figure 3 . 15 -

 315 Figure 3.15 -Theoretical XNLD spectra of FeTp calculated in absence of magnetic field with the parameters given in table 3.2. The absorption cross sections are calculated for the polarization vector, ε, parallel (black line) and perpendicular (red line) to the C 3 axis of FeTp.

Figure 3 . 2 20 1. 3 22 1. 4

 32203224 Figure 3.15) and this opens the door to experimental measurements of XNLD or even X-ray Magnetic Linear Dichroism.

  .1). At room temperature, the Fe/Co PBA is in the Fe III LS (S=1/2)-CN-Co II HS (S=3/2) paramagnetic state and it undergoes a temperature induced Chapter 4

Figure 4 . 1 -

 41 Figure 4.1 -Molecular structure of the cationic complex of dinuclear Fe/Co PBA. All anions, lattice solvents, and hydrogen atoms are omitted for clarity. Fe, Co, N, C, and B atoms are indicated in orange, dark blue, light blue, gray, and pink, respectively.

Chapter 4 .

 4 Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 73 LS transition of the Co ions. On cyanido-bridged tetranuclear systems of Fe/Co PBA, investigation of thermal-and photo-induce electron transfer by XAS is reported by Sekine

Fe

  and Co are (NBu 4 )[(Tp)Fe III (CN) 3 ] and [(Tp)Co II (PY5Me 2 )•H 2 O](BF 4 ) 2 respectively.

Chapter 4 .

 4 Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 75 mainly built from paramagnetic Fe III LS and Co II HS species. The respective contributions of low spin and high spin characteristic features in the Fe and Co L 3 XAS spectra therefore clearly confirm the existence of thermal-and photo-induced electron transfer.

Figure 4 . 2 -

 42 Figure 4.2 -Experimental XAS spectra at the Fe (left) and Co (right) L 3 edge before laser irradiation at 300 K (red line), 100 K (blue line) and 4 K (green line) after irradiation (λ = 660 nm, 2 hours) at B = 2 T.

then from 10 K

 10 to 50 K by steps of 5 K. At each temperature point, Fe and Co L 3 edges spectra are recorded (Figure 4.3). When the temperature increases, one observes a gradual decrease from the main signature of Fe III LS (peak a) and Co II HS (peak a') ions. As mentioned before, at 100 K the signals for Fe and Co before and after irradiation are built from 78 % of Fe II LS -Co III LS diamagnetic pairs and 22 % of residual Fe III LS -Co II HS paramagnetic pairs. At a given temperature, each spectrum is analyzed as a linear combination of the spectra measured at T = 4 K and T = 100 K (see supporting Information Figure 4.17), which allows plotting the fraction of each paramagnetic ion as a function of temperature (Figure 4.4). One observes that the relaxation curves for Fe and Co are almost identical indicating that the reduction of Fe ions is accompanied by the oxidation of Co ions, as expected for the electron transfer mechanism. The relaxation is almost finished at 50 K.

Figure 4 . 3 - 4 Figure 4 . 4 -

 43444 Figure 4.3 -L 3 edge XAS spectra measured for Fe (left) and Co (right), following the relaxation of the light-induced excited state Fe III LS -Co II HS as a function of temperature under B = 2 T.

Figure 4 . 8 )

 48 Figure 4.8). They bear the signature of Fe II LS and Co III LS ions with small contributions from Fe III LS and Co II HS ions. At 300 K, the two spectra recorded at the beginning of the temperature cycle and at the very end bear the clear signature of Fe III LS and Co II HS ions (Supporting Information: Figure 4.9). This confirms the complete reversibility of the electron transfer

Chapter 4 .

 4 Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 77

Figure 4 . 5 -

 45 Figure 4.5 -Experimental XAS (black line) and XMCD (red line) at the Fe (left) and Co (right) L 2,3 edges at T = 4 K and B = 6.5 T.

  The magnetization curves detected by XMCD independently for Fe and Co ions are shown in Figure4.6. They have been recorded by setting the monochromator at maximum of L 3 edge XMCD signal for Fe (E = 709.33 eV) and Co (E = 779.18 eV) between +5 T and -5 T. one sees that complete magnetic saturation is not achieved for both Fe and Co.

Figure 4 . 6 -

 46 Figure 4.6 -Field dependence of the maximum of XMCD signal at the L 3 edge for Fe (red line) and Co (black line), measured respectively at 709.33 eV and 779.18 eV at T = 2 K. Since the largest feature in the XMCD signal is negative for a positive values of B, XMCD detected magnetization curves were multiplied by -1 in order to present them with the same convention as for SQUID detected magnetization curves. The XMCD intensity are normalized with respect to XAS as in figure 4.5.

Figure 4 . 7 -

 47 Figure 4.7 -XAS spectra measured at the Fe (left) and Co (right) L 3 edge at 300 K before irradiation (red line) and at 4 K after irradiation (green line). In Figure 4.6, the XMCD-detected magnetization curves for Fe and Co ions are superimposed. Within the uncertainty on the experimental measurement there is no hint for an antiferromagnetic coupling between Fe III LS -Co II HS , contrary to what is usually sug-

Chapter 4 . 4 4. 3 Supporting Information of Paper II 4 . 3 . 1

 443431 Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 81 Chapter Reversibility of the electron transfer process The reversibility of the photo-induced electron transfer process has been checked by measuring XAS spectra at the Fe and Co L 3 edges at 100 K and 300 K, before and after the laser irradiation as shown in Figures 4.8and 4.9.

Figure 4 . 8 -

 48 Figure 4.8 -Reversibility of the electron transfer process: XAS at the Fe and Co L 3 edge before (red line) and after irradiation (black line) at 100 K and B = 2 T.

Figure 4 . 9 -

 49 Figure 4.9 -Reversibility of the electon transfer process: XAS at the Fe and Co L 3 edge before (red line) and after irradiation (black line) at 300 K and B = 2 T.

Chapter 4 .

 4 Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 83

Figure 4 . 10 -

 410 Figure 4.10 -Experimental K edge XAS spectra of Fe (left) and Co (right) at 300 K (red line) and 2 K (green line). The insets display the zoom view in the pre-edge region.

Figure 4 . 11 -

 411 Figure 4.11 -Experimental K edge XAS spectra of Fe (left) and Co (right) at 300 K (red line), 2 K before laser irradiation (green line) and 2 K after laser irradiation (blue line).

Figure 4 . 12 -

 412 Figure 4.12 -Difference in Normalized Absorption at the Fe (left) and Co (right) K edges after thermal-induced (green line) and light-induced (red line) conversion.

Figure 4 . 13 -

 413 Figure 4.13 -Experimental Fe and Co K edge normalized XAS at 300 K before (red line) and after irradiation (black line).

Figure 4 .

 4 14) and the comparison of Co in sample 1 and 3 (Figure 4.15) is presented in the discussion section.

Chapter 4 .

 4 Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 85

Figure 4 . 14 -

 414 Figure 4.14 -Experimental XAS (black line) and XMCD (red line) spectra at the Fe L 2,3 edges in sample 1 (left) and sample 2 (right) at T = 4 K and B = 6.5 T.

Figure 4 . 15 -

 415 Figure 4.15 -Experimental XAS (black line) and XMCD (red line) spectra at the Co L 2,3 edges in sample 1 (dinuclear complex, left) and sample 3 (Co precursor of 1, right) at T = 4 K and B = 6.5 T.

Figure 4 . 16 -

 416 Figure 4.16 -Left: Experimental Co L 3 edge at 300 K before irradiation (red line) and at 4 K after irradiation (green line) (left). Right: Spectra calculated in the Ligand Field Multiplet (LFM) approach.

Figure 4 . 19 - 4 . 4 . 1 . 3

 4194413 Figure 4.19 -The front (left) and side (right) views of the sample holder where the crystals of 2•2DMF are placed under the kapton foil.

Figure 4 . 20 -

 420 Figure 4.20 -Experimental Fe and Co K edges normalized XAS spectra at 300 K before laser (red line) and 2 K before laser (blue line). The insets display the zoom view of the pre-edge region.When comparing the Fe and Co K edges at 300 K and 2 K, one observes that the absorption maximum for Fe at 2 K is shifted by ≈1.2 eV to lower energy (7130.5 eV) while the Co K edge at 2 K is shifted by ≈2.4 eV to high energy (7730.2 eV). This shift in the energy of absorption maxima at both edges is characteristic of the change in oxidation state for Fe ions from Fe III LS to Fe II LS and for Co ions from Co II HS to Co III LS .[START_REF] Bleuzen | Photoinduced Ferrimagnetic Systems in Prussian Blue Analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 1. Conditions to Observe the Phenomenon[END_REF][START_REF] Yokoyama | Local Structure of a Trapped Photoexcited State of a Fe-Co cyanide studied by X-ray-Absorption Fine-Structure Spectroscopy[END_REF][START_REF] Yokoyama | Characterization of magnetic CoFe cyanides by x-ray-absorption fine-structure spectroscopy[END_REF][START_REF] Bleuzen | CoFe Prussian Blue Analogues under Variable Pressure. Evidence of Departure from Cubic Symmetry: X-ray Diffraction and Absorption Study[END_REF] Hence, it confirms the transition from the paramagnetic state to the diamagnetic one due to

Figure 4 . 23 Chapter 4 Figure 4 . 21 -

 4234421 Figure 4.21 -Experimental Fe and Co K edge normalized XAS spectra at 300 K before laser (red line) and at 2 K after laser (green line).

Figure 4 . 22 -

 422 Figure 4.22 -Experimental Fe and Co K edge normalized XAS spectra at 300 K before laser (red line), at 2 K before laser (blue line) and at 2 K after laser (green line).

Figure 4 . 23 -

 423 Figure 4.23 -Experimental Fe and Co K edge normalized XAS spectra at 300 K before laser (red line) and after laser (black line).

Chapter 4 .

 4 Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 91 4.4.3 XMCD at Fe and Co K edges

Figure 4 . 24 -

 424 Figure 4.24 -Experimental Fe and Co K edge normalized XAS spectra (black line) and XMCD signals (red line) at 2 K after white light irradiation under B = 17 T.

Figure 4 .

 4 Figure 4.25 shows the corresponding magnetization curves. Both Fe and Co XMCD magnetization signals have similar shape and can be superimposed. The magnetization does not seem to be fully saturated at 17 T. Interestingly if the Fe and Co XMCD features at 7131 eV and 7727 eV can be said to be proportional to the 3d magnetizations of Fe and Co, Figure 4.25 would tend to prove that there is no antiferromagnetic coupling between

  has never been observed by XMCD at L 2,3 edges. This motivated us to perform XMCD in the tridimensional PBA Rb 2 Co 4 [Fe(CN) 6 ] 3.3 •11H 2 O to check for antiferromagnetic or ferromagnetic interactions between Fe and Co ions. The details of the XMCD investigations are presented as a paper in next section. The present work has been performed in collaboration with Prof. Anne Bleuzen and her team from ICMMO who synthesized the samples and recorded SQUID magnetometric data.

  This has galvanized our efforts to look for the reversal of the local magnetization in tridimensional Fe/Co PBA by recording XMCD at L 2,3 edges. We report here the XMCD results at the Fe and Co L 2,3 edges of tridimensional Rb 2 Co 4 [Fe(CN) 6 ] 3.3 •11H 2 O PBA in the photo-induced state. These results have unearthed significant information on the nature of the magnetic interaction between both metallic ions. Ligand Field multiplet (LFM) calculations have been further employed to calculate the electronic structure of the Fe and Co ions and to quantify the amount of paramagnetic and diamagnetic Fe-Co pairs in the photo-induced metastable phase.

Chapter 5 .

 5 Probing the Magnetic interaction in tridimensional Fe/Co Prussian Blue Analogues 101 circularly polarized X-rays with a fast switching of the polarization state of the incoming X-rays. The fast switching of polarization between 1 Hz and 5 Hz makes it possible to record XMCD signals by switching the polarization at each energy point of a spectrum.

Chapter 5 200

 5 K and XAS spectra are compared with those at the beginning of the experiment. In a last step, we have recorded the XAS and XMCD signals at Fe L 2,3 edges of K 3 [Fe(CN) 6 ]

Figure 5 . 1 - 103 5. 2 . 3 . 2

 51103232 Figure 5.1 -Experimental XAS spectra at Fe (left) and Co (right) L 2,3 edges before laser irradiation at 200 K (red line) and after 5 hours laser irradiation at 2 K (black line). Reversibility of the electron transfer process has been checked by recording Fe and Co L 2,3 edges at 200 K before and after laser irradiation (Figure 5.8 Supporting Information). The diamagnetic Fe II LS and Co III LS species are recovered although a minor percentage (≤ 5 %) of additional Co II HS species is present which did not undergo the transition from Co II HS → Co III LS when the temperature was raised to 200 K.

Figure 5 . 2 -

 52 Figure 5.2 -Experimental XAS (black line) and XMCD (red line) spectra at Fe (left) and Co (right) L 2,3 edges at 2 K after a 5 hours laser irradiation.

Chapter 5 . 105 Figure 5 . 4 - 7 5 Figure 5 . 5 -

 5105547555 Figure 5.4 -Slope at B = 0 T for the Fe and Co magnetization curves as a function of temperature.

Figure 5 . 6 - 107 Figure 5 . 7 -

 5610757 Figure 5.6 -Difference of two XMCD signals at Fe L 2,3 edges (blue line) recorded at B = 6.5 T and 0.45 T. The XMCD signal at B = 0.45 T is normalized so that peak β superimpose with the one from the XMCD signal at B = 6.5 T.

Figure 5 . 8 -

 58 Figure 5.8 -Experimental XAS spectra at Fe (left) and Co (right) L 2,3 edges at 200 K before irradiation (red line) and after irradiation at 2 K and warming up back at 200 K (black line).

  Under X-ray beam at 2 K, a partial electron transfer between Fe and Co transforms Fe II LS into Fe III LS and Co III LS into Co II HS . This conversion is manifested by an intensity of increase in Fe III LS signature (peak a) and the corresponding decrease in Co III LS signature (peak e').

Figure 5 . 9 -

 59 Figure 5.9 -Experimental XAS spectra at Fe (left) and Co (right) L 2,3 edges at 200 K (red line) and at 2 K before laser irradiation (black line).

Figure 5 .

 5 Figure 5.10 shows the Fe and Co L 2,3 XAS spectra in the X-ray induced and the lightinduced paramagnetic state. The X-ray induced metal-to-metal electron transfer results from the measurement at 2 K of the Fe and Co L 2,3 edges before laser irradiation. The light-induced metal-to-metal electron transfer results from laser irradiation during 5 hours. For comparison, the XAS spectra at 200 K, at 2 K in the X-ray induced magnetic phase, and at 2 K in the laser induced magnetic phase are plotted together. After X-ray irradiation and after laser irradiation, the intensity of the characteristic features for Fe III LS (peak a) increases as a signature of the metal-to-metal electron transfer. The ratios of peaks a/b are 0.37, 0.58, 0.88 at 200 K and at 2 K before and after laser respectively. For the Co L 2,3 edges, the ratio e'/c' are 1.62, 1.35, 0.53 at 200 K, at 2 K before and after laser irradiation respectively, indicating a decrease of the number of Co III LS ions.

Figure 5 . 10 -

 510 Figure 5.10 -Experimental XAS and XMCD spectra at Fe (left) and Co (right) L 2,3 edges at 200 K before irradiation (red line), 2 K before laser irradiation (black line) and after 5 hours laser irradiation (green line). We have compared the electron transfer process induced by X-ray and light irradiation and extracted the fraction of Fe II LS , Fe III LS , Co III LS and Co II HS at 200 K, at 2 K under X-ray irradiation and at 2 K after 5 hours laser. At 200 K, 40 % of the Fe ions are Fe III LS paramagnetic ions. At the end of X-ray irradiation, one measures 52 % of Fe III LS so that only ≈20 % of the existing Fe II LS have been converted. For laser irradiation, we have shined sample 1 for different time durations from 15 minutes up to 5 hours and we have found that the converted sample contained ≈70 % of Fe III LS ions (Fig 5.11). For Co ions the same type of analysis can be made. The percentage of Co IIHS has been reported in Fig.5.12. We attribute the difference between the concentrations of and Fe II LS and Co II HS to the existence of the surface paramagnetic phase for which the stoichiometric ratio might be different

Figure 5 .Figure 5 . 111 Figure 5 . 11 -

 55111511 Figure 5.13 shows the effect of laser irradiation when sample 1 is irradiated for different time intervals.5.3.4 Fe XMCD signals and magnetization curves in sample 1 vs sample 2 (Potassium hexacyanidoferrate(III))Figure5.14 shows the experimental XAS and XMCD spectra at Fe L 2,3 edges of sample 1 and for potassium hexacyanidoferrate(III) (sample 2). One can see that the shape and

Figure 5 . 12 -

 512 Figure 5.12 -The Co III LS fraction as a function of number of scans under X-ray (left) and laser irradiation (right) respectively. The sample was irradiated with laser for time = 15 min, 1.5 hours and 5 hours.

Figure 5 . 13 -

 513 Figure 5.13 -Experimental XAS spectra at Fe (left) and Co (right) L 3 edge (zoom) at 2 K after laser irradiation for time t = 15 min (green line), t = 1.5 hours (blue line) t = 5 hours (red line).

Chapter 5 ions

 5 antiferromagnetically coupled to Co II HS ions.

Figure 5 . 14 -

 514 Figure 5.14 -Experimental XAS spectra (black line) and XMCD signals (red line) at Fe L 2,3 edges of sample 1 (left) and its potassium hexacyanidoferrate(III) precursor K 3 [Fe III (CN) 6 ] (right) at 2 K, B = 6.5 T.

Figure 5 .

 5 Figure 5.15 reports the XMCD detected magnetization curves of Fe as a function of the external magnetic induction at T = 2 K in sample 1 and 2. The magnetization curve of the potassium hexacyanidoferrate(III) follows the direction of external magnetic induction as it is expected for isolated paramagnetic ions. On the contrary, the XMCD signal in sample 1 clearly indicates that the Fe magnetization is antiparallel to the external magnetic induction between -1.5 T and 1.5 T.

Figure 5 . 15 -

 515 Figure 5.15 -Induction dependence of the maximum of the XMCD signal at the Fe L 3 edge (Energy = 705.7 eV) induction at 2 K in RbCoFe sample 1 (left panel) and in potassium hexacyanidoferrate(III) sample 2 (right panel).

Chapter 5 . 113 Figure 5 . 16 -

 5113516 Figure 5.16 -XMCD detected magnetization curves at Fe L 3 edge, E = 705.7 eV (left panel) and Co L 3 edge, E = 777.3 eV (right panel) at 2 K (black line), 4 K (pink line), 10 K (green line), 20 K (red line) and 30 K (blue line).

5. 3 . 6

 36 LFM calculations of Co L 2,3 edges The Co II XAS spectra and XMCD signals are simulated by Ligand Field Multiplet Calculations in D 4h symmetry with Dt = 0.02 eV, Ds = 0.043 eV, 10Dq = 1.23 eV and κ = 0.7.

Figure 5 . 17 -

 517 Figure 5.17 -Theoretical XAS and XMCD spectra at L 2,3 edges for Co obtained for Dt = 0.02 eV, Ds = 0.043 eV and 10Dq = 1.23 eV in D 4h symmetry at T = 2 K with B = 6.5 T.

  18 and Figure 5.19 respectively. The Co II HS , Co III LS references are simulated using LFM calculations whereas Fe II LS , Fe III LS XAS spectra are the experimental cross-sections for K 4 [Fe(CN) 6 ] and K 3 [Fe(CN) 6 ] at T = 2 K and B = 6.5 T. The Co II XAS spectra and XMCD signals are simulated by Ligand Field Multiplet Calculations in D 4h symmetry with Dt = 0.02 eV, Ds = 0.043 eV, 10Dq = 1.23 eV and κ = 0.7. For the Co III , the LFM parameters for O h symmetry are Dt = 0 eV, Ds =0 eV, 10Dq = 2.5 eV and κ = 0.7.

Chapter 5 Figure 5 . 18 -

 5518 Figure 5.18 -Theoretical XAS spectra at L 2,3 edges for Co (left) and the linear combination (right).

Figure 5 . 19 -

 519 Figure 5.19 -Experimental XAS spectra at Fe L 2,3 edges of K 3 [Fe(CN) 6 ] and K 2 [Fe(CN) 6 ] used for the linear combination (left) and the linear combinations (right).

  Fe and Co ions in Rb 2 Co 4 [Fe(CN) 6 ] 3.3 •11H 2 O (sample 1) when the sample is in its lightinduced metastable state below 15 K. This finding has mainly been obtained from the XMCD signal recorded at the Fe L 2,3 edges and also by comparison with the Co XMCD signal. The antiferromagnetic coupling is strongly supported by the following:

Chapter 5 .

 5 Probing the Magnetic interaction in tridimensional Fe/Co Prussian Blue Analogues 115 Fe/Co dinuclear complex [(Tp)Fe III (CN) 3 Co II PY5Me 2 ](PF 6 )•2DMF as it has been found from our XMCD data at the Fe and Co K edges in paragraph 4.4. In a next step, two Fe/Co photomagnetic dinuclear complexes were studied. The two dinuclear complexes have FeTp precursor as one of the building blocks. The first dinuclear complex referred as 1 exhibited thermal-and light-induced electron transfer properties in solid state, confirmed by XMCD at K and L 2,3 edges. At 2 K no signature of antiferromagnetic coupling is observed between Fe and Co ions in photo-induced state.

  three years of the Ph.D. training provided me the opportunities to work in collaboration with different groups of chemists and physicists. Using the cutting-edge experimental facilities at SOLEIL, ESRF and SLS synchrotron sources helped in developing my experimental approach towards problem solving, critical thinking skills and team work. During my 120 doctoral thesis, I presented my research work in several conferences including ICMM-2014 (Saint Petersburg, Russia), JMC, CMD-2014 (Paris, France), SUM-SOLEIL (2014, 2015 and 2016), XAFS16 (Karlsruhe, Germany), GDR-MCM2 (Dourdan), Hi-SPEAR meeting (SOLEIL, 2016) and synchrotron summer school (Compinas, Brazil). Meeting people from diverse cultural and scientific backgrounds and exchange of scientific ideas have been a wonderful experience that instilled in me the vision to keep up the scientific standards in my present and future research projects.

  Chapter 5 presents the L 2,3 edges XMCD results in Rb 2 Co 4 [Fe(CN) 6 ] 3.3 •11H 2 O tridimensional PBA. The antiferromagnetic coupling between Fe and Co ions is observed in the photo-induced state. This finding is presented in a paper to be submitted.

	Chapter 1. Photomagnetism in Molecule-Based Magnets: The Fe/Co Prussian Blue
	Family	19
	Chapter 1
	Photomagnetism in
	Molecule-Based Magnets: The
	Fe/Co Prussian Blue Family
	1.1 Introduction

  Chapter 1. Photomagnetism in Molecule-Based Magnets: The Fe/Co Prussian Blue Family 25 Chapter 3 and Chapter 4. In a second part, a tridimensional PBA system has been studied in collaboration with Prof. Anne Bleuzen's group at ICMMO. The XMCD at L 2,3 edges is performed in Rb 2 Co 4 [Fe(CN) 6 ] 3.3 •11H 2 O PBA system. The K edge XMCD results

Potassium hexacyanidoferrate(III) K

  3 [(Fe III (CN) 6 ], π-back bonding is larger than for the three other Fe precursors because of the six NC-Fe III bonds. The σ bonding and π-back

	bonding are described as ligand-to-metal charge transfer (LMCT) and metal-to-ligand
	charge transfer (MLCT) respectively.
	Compound	FeTp*	FepzTp	FeTp	Potassium hexacyanidoferrate(III)
	Crystal system	trigonal	monoclinic	triclinic	monoclinic
	Space group	P3 1	P2 1 /n	P 1	P2 1 /c
	Temperature / K	90	90	120	295
	a / Å	9.77400(10) 10.2580(2) 11.1956(4)	7.047
	b / Å	9.77400(10) 15.2386(3) 11.2191(4)	10.4
	c / Å	26.1990(4) 16.9912(4) 15.9740(6)	8.384
	α / •	90.00	90.00	87.2840(10)	90
	β / •	90.00	96.1396(7) 76.7360(10)	107.29
	γ / •	120.00	90.00	60.8650(10)	90

  network of PBA, K 0.2 Co 1.4 [Fe(CN) 6 ]•6.9H 2 O, that crystallizes in a face-centered cubic Chapter 3. Fe-bearing Precursors of Photomagnetic FeCo Prussian Blue Complexes 39 lattice. Upon irradiation with visible light (λ = 660 nm), an electron transfer converts diamagnetic Fe II (d 6 , low spin, S = 0)-CN-Co III (d 6 , low spin, S = 0) units into paramagnetic Fe III (d 5 , low spin, S = 1/2)-CN-Co II (d 7

Table 3 . 2

 32

-Parameters used in the Ligand Field Multiplet simulations for B = 6.5 T and T = 2 K. All energies are given in eV (1 eV corresponds to 11605 K), κ is dimensionless. The 3d and 2p spin-orbit coupling constants are the atomic values: ζ 3d = 0.059 eV and ζ 2p = 8.199 eV. 10Dq Dσ Dτ κ

Table 3 . 3 -

 33 L z , S z , S eff z and T z obtained from LFM calculations (expectation values obtained from the ground state calculation), from sum rules applied to LFM calculated spectra and from sum rules applied to the experimental spectra. Expectation values obtained from the ground state calculation at 0 K; b Using T z obtained from the LFM calculation.

		LFM calculation	Experiment
		i|O z |i (a)	sum rules	sum rules
	L z	-1.236	-1.236	-0.88
	S z	-0.488	-0.214 b	-0.17 b
	S eff z	-0.889	-0.615	-0.57
	T z	-0.115	-	-
	a

Table 3 .

 3 6. Compound (N(C 4 H 9 ) 4 )[(Tp)Fe III (CN) 3 ]•3H 2 O

	Chapter 3

3 1700.91

(11)

Table 3 . 4 -

 34 Crystallographic data of FeTp.

		10Dq Dσ Dτ	κ	∆ i ∆ f V eg V t2g B
	C 3v with MLCT 2.8	0.07 0.12 0.7 3.0 3.4 -0.8 1.8 6.5
	C 3v no MLCT	2.8	0.07 0.12 0.7	-	-	-	-	6.5
	O h with MLCT 2.8	0	0	0.7 3.0 3.4 -0.8 1.8 6.5
	O h no MLCT	2.8	0	0	0.7	-	-	-	-	6.5

Table 3 . 5 -

 35 Parameters used in the Ligand Field Multiplet simulations. All the calculations were made with ζ 3d = 0.059 eV, ζ 2p = 8.199 eV (atomic values). κ is dimensionless, B is expressed in Tesla. The other parameters are given in eV.

		L z	S z	T z
	C 3v with MLCT -1.2361 -0.4882 -0.1146
	C 3v no MLCT	-1.3941 -0.5012 -0.0924
	O h with MLCT -0.7754 -0.1704 -0.0594
	O h no MLCT	-0.8521 -0.1786 -0.0523

Table 3 .

 3

6 -Expectation values for the orbit magnetic moments, the spin magnetic moments and the magnetic dipole terms.

Table 3 . 7 -

 37 Ground state average values of L z , S z and S eff z extracted from multiplet calculations and spin sum rules (on calculated spectra and sticks of calculated spectra) at 0 K, 2 K and 4 K for the atomic value of 2p spin-orbit coupling ζ 2p = 8.199 eV.

		2361 -1.2359 -1.2216 -1.2358 -1.2357	-1.2225 -1.2363 -1.2362	-1.2230
	S z	-0.4882 -0.4881 -0.4825 -0.2135 -0.2136	-0.2117 -0.2319 -0.2318	-0.2295
	S eff z	-0.8894 -0.8893 -0.8791 -0.6149 -0.6149	-0.6083 -0.6331 -0.6330	-0.6261

3.

3.6 Angular dependence of the orbit and spin magnetic moments and average values 3.3.6.1 Angular dependence

	[ijk] α( • )	S z	S z (0) × cos (α)	L z	L z (0) × cos (α)	T z
	[001]	0	-0.4882	-0.4882	-1.2361	-1.2361	-0.1146
	[100]	90	-0.0060	0.0	-0.0636	0.0	-0.0989
	[010]	90	-0.0060	0.0	-0.0636	0.0	-0.0989
	[110]	90	-0.0060	0.0	-0.0636	0.0	-0.0989
	[011]	45	-0.3476	-0.3452	-0.8758	-0.8740	-0.0827
	[101]	45	-0.3476	-0.3452	-0.8758	-0.8740	-0.0827
	[111] 54.7 -0.2850	-0.2821	-0.7163	-0.7143	-0.0689

Table 3 . 8 -

 38 S z , L z and T z values calculated in the LFM model for different orientations of the external magnetic field relative to the C 3 axis of the molecule. The C 3 axis is along the [001]

  Potassium

			than in other three precursors
	(FeTp (1.3), FeTp* (1.1) and FepzTp(1.1)). Also, β and , two positive peaks at the L 3
	edge XMCD spectra are more pronounced in Potassium hexacyanidoferrate(III) than
	in the other precursors.
	Precursor	α a	α c	γ a	γ c
	FeTp	109.4 110.7 82.8 83.9
	FeTp*	99.2	75.6 91.8 69.9
	FepzTp	82.0	62.6 73.7 56.3

hexacyanidoferrate(III) 80.5 86.9 57.6 62.2

Table 3 . 9

 39

-% XMCD for the four precursors.

, FeTp* and Potassium hexacyanidoferrate(III) that

  6 µ B for FepzTpis the averaged expected value at 0 K for fully magnetized

	Fe III LS ion in a completely disordered system (powder). This tends to indicate that the four
	Fe III LS ions behave in a very similar way.
	Precursor	L z
	FeTp	-0.88
	FeTp*	-0.52
	FepzTp	-0.45
	Potassium hexacyanidoferrate(III) -0.45

Table 3 . 10 -

 310 Value of L z from sum rules applied to the experimental spectra of precursors at T = 2 K and B = 6.5 T.

  group of Prof. Corine Mathonière and Dr. Rodolphe Clérac at University of Bordeaux). The results on 1 are presented in Sections 4.2 and 4.3 and the results for 2•2DMF are presented in Section 4.4 of this chapter.

(former Ph.D. student in the Chapter 4

  At 300 K, Fe K edge XAS has intense absorption maximum at 7131.7 eV (E1 allowed 1s → 4p transitions) and a weak pre-edge feature (E2 allowed 1s → 3d transitions) at 7114.5 eV. For Co, the maximum in K edge absorption is observed at 7727.8 eV and a pre-edge at 7712.1 eV (fig 4.20). The absorption Chapter 4. Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 89 edge of Fe displays a broad peak whereas for Co this peak is sharper in comparison. The large intensity of Fe pre-edge feature compared to Co, is due to the easy p-d mixing inligand field around Fe III LS -sites and to large π back bonding.[START_REF] Westre | A Multiplet Analysis of Fe K-edge 1s → 3d Pre-edge Features of Iron Complexes[END_REF][START_REF] Anne Arrio | Calculation of Multipole Transitions at the Fe K Pre-Edge through pd Hybridization in the Ligand Field Multiplet model[END_REF]

  The local orientation of magnetization of Fe and Co ions in two tridimensional Fe/Co PBA (Rb 1.8 Co 4 [Fe(CN) 6 ] 3.3 •13H 2 O and K 0.1 Co 4 [Fe(CN) 6 ] 2.7 •18H 2 O) has experimentally been confirmed by Champion et al. thanks to XMCD at Co and Fe K edges.[START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF] They reached the conclusion that Fe and Co ions were coupled antiferromagnetically. Unfortunately, the conclusion is based on several assumptions that have never been fully ascertained: (i) the XMCD signals recorded by Champion et al. completely miss the pre-edge features that are smeared into the noise although they are the only ones to be safely considered as being proportional to the Fe or Co magnetizations, (ii) the main XMCD feature observed by Champion et al.

  Co 4 [Fe(CN) 6 ] 2.7 •18H 2 O and Rb 1.8 Co 4 [Fe(CN) 6 ] 3.3 •13H 2 O, K edge, XMCD measurements have successfully confirmed the antiferromagnetic nature

  1 was first measured at Fe and Co L 2,3 edges at 200 K where it is believed to be in the diamagnetic state. It is then cooled down to 2 K with no intermediate temperature measurements since no thermally induced electron transfer is expected. At 2 K, sample 1 has been irradiated with laser (λ = 635 nm) for 5 hours. During the XAS and XMCD measurements, laser is switched off. XMCD signals at Fe and Co L 2,3 edges were then recorded after light induced excited spin state trapping (LIESST). To compensate for possible errors induced by spurious signals, XMCD signal was measured by taking the difference of two XAS spectra recorded for left and right polarized X-rays with the propagation vector parallel or antiparallel to the direction of the external

magnetic induction B. By definition, the XMCD signal is given by σ

  III LS , Fe II LS , Co III LS and Co II HS from which we can by linear combination estimate the decomposition into paramagnetic and diamagnetic species (see S.I. Section 5.3.7). At 200 K, we find that Fe ions are ≈40 % Fe III LS and ≈60 % Fe II LS whereas Co ions are ≈34 % Co III

Acknowledgements

Acknowledgements

Résumé

Acknowledgement

This work was supported by the Centre National de la Recherche Scientifique (CNRS, France), the Ministère de l'Enseignement Supérieur et de la Recherche (MESR, France), the Aquitaine region, the Institut Universitaire de France (IUF) and partially funded by ANR (ANR-10-BLAN-0712; ANR-09-BLAN-0175; ANR-12-PDOC-0038), and GDR MCM2. We thank SOLEIL staff for running the machines, Abhishake Mondal (CRPP) for helping with the FeTp crystallization, Lorenzo Paulatto and Alain Soyer (IMPMC) for computing support and Rodrigue Lescouëzec (IPCM) for fruitful discussion on magnetic anisotropies.

Acknowledgements

This work was supported by the Centre National de la Recherche Scientifique (CNRS, France), the Ministère de l'Enseignement Supérieur et de la Recherche (MESR, France), the Aquitaine region, the Institut Universitaire de France (IUF) and partially funded by ANR (ANR-10-BLAN-0712; ANR-09-BLAN-0175; ANR-12-PDOC-0038), and GDR MCM2. The staff from SOLEIL, SLS and ESRF is acknowledged for operating the synchrotron sources and beamlines. We are glad to acknowledge Dr. Armin Kleibert for his technical support on the SIM beamline. We also thank Bernard Muller (IPCMS, Strasbourg) for instrumental developments on the French TBT dilution cryomagnet.

Linear combination of the XAS spectra

In Figure 4.17 an example is presented to explain how the linear combination is used to get the amount of paramagnetic species at a given temperature. To extract the Co II HS amount at T = 10 K, the selected references for Co III LS and Co II HS are the experimental Co XAS spectra at 4 K after laser irradiation and at 100 K respectively. These reference spectra are considered as the limiting compositional cases corresponding to 100% and 0%

Co II HS .

Figure 4.17 -The linear combination (blue line) of the reference XAS spectra for Co III LS at 100 K (red line) and Co II HS at 4 K after laser (black line) for selected Co XAS at T = 10 K to fit (green line).

Chapter 4. Photomagnetism in Dinuclear Fe/Co Prussian Blue Analogues probed by K and L 2,3 edges XMCD 87

XAS and XMCD investigations of complex 2•2DMF at

Fe and Co K edges

The present XAS and XMCD study at the Fe and Co K edges is aimed to follow the thermal-and light-induced electron transfer in 2•2DMF. Since 2•2DMF needs to be preserved from desolvation to maintain its properties, it cannot be studied easily under UHV. The sample needs to be inserted in a sealed cell and this can be done for the measurements at the K edges but not yet at L 2,3 edges. XMCD at K edges can give information on the Co and Fe magnetic interaction in the photo-induced excited spin state but since the analysis of the K edges requires involved theoretical developments, it is usually difficult to extract quantitative magnetic information. The molecular structure of 2•2DMF is presented in Figure 4.18. [START_REF] Koumousi | Synthesis and Characterization of Dinuclear Fe/Co Complexes Exhibiting Metal-to-Metal Electron Transfer Properties[END_REF] In

Experimental section

Sample preparation

The FeCo PBA dinuclear complex 2•2DMF (DMF = N,N-dimethylformamide) was synthesized by following the procedure developed by Koumousi et al. [START_REF] Koumousi | Synthesis and Characterization of Dinuclear Fe/Co Complexes Exhibiting Metal-to-Metal Electron Transfer Properties[END_REF] The compound has been characterized by the standard magnetometric techniques and elemental analyses. [START_REF] Koumousi | Synthesis and Characterization of Dinuclear Fe/Co Complexes Exhibiting Metal-to-Metal Electron Transfer Properties[END_REF] The Fe and The XAS and XMCD spectra recorded for Fe and Co precursors at 2 K are displayed in

Fe and Co Precursors of 2•2DMF dinuclear complex

Thermal-and light-induced transitions in 2•2DMF complex followed by XAS, XMCD and SQUID magnetometry

The thermal-induced electron transfer and the relaxation of the photo-induced metastable state have been recorded from XAS as a function of temperature and are presented for Co in The relaxation temperature is defined as the temperature for which more than 95% of paramagnetic pairs have been converted to diamagnetic ones.

Summary of Chapter 4

In this chapter we have presented XMCD results on two photomagnetic Fe/Co dinuclear complexes, 1 and 2•2DMF, which exhibit thermal-and light-induced electron transfer properties. This is the first XAS and XMCD study which reports on the metal-to-metal electron transfer between Fe and Co in photo-induced state in solid state as well as in solution. The reversibility of electron transfer as detected by XAS has been confirmed

for both complexes. The study of complex 1 has been performed at the Fe and Co L 2,3

and provided information on the orbit and spin magnetic moments carried by the 3d electrons. The study of complex 2•2DMF has been performed at Fe and Co K edges for which only qualitative results can be obtained. For both complexes, one could not observe any antiferromagnetic coupling between Fe and Co at 2 K in the photomagnetic state. From XMCD detected magnetization curves at L 2,3 edges for 1 and K edges for 2•2DMF both magnetization for Fe and Co ions superimpose rather nicely. Whether the Fe and Co ions are ferromagnetically coupled or not could not be determined from our measurements. These results have to be compared with those obtained by Koumousi et al. [START_REF] Koumousi | Synthesis and Characterization of Dinuclear Fe/Co Complexes Exhibiting Metal-to-Metal Electron Transfer Properties[END_REF][START_REF] Koumousi | Metal-to-Metal Electron Transfer in Co/Fe Prussian Blue Molecular Analogues: The Ultimate Miniaturization[END_REF] From Champion et al., a fingerprint analysis of the XMCD signals at Fe and Co K edges had been performed. [START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF] The comparison of the XMCD signal at the Fe K edge . The SQUID data are taken from the thesis by E.S. Koumousi. [START_REF] Koumousi | Synthesis and Characterization of Dinuclear Fe/Co Complexes Exhibiting Metal-to-Metal Electron Transfer Properties[END_REF] framework for the interpretation of the XMCD signals at L 2,3 edges is well mastered within the Ligand Field Multiplet approach developed by Theo Thole, [START_REF] Poneti | X-ray Absorption Spectroscopy as a Probe of Photo-and Thermally Induced Valence Tautomeric Transition in a 1:1 Cobalt-Dioxolene Complex[END_REF][START_REF] Anne Arrio | Calculation of Multipole Transitions at the Fe K Pre-Edge through pd Hybridization in the Ligand Field Multiplet model[END_REF] the theoretical framework for the XMCD at K edges is still in its infancy and heavy developments are still required.

Chapter

Introduction

After the first example of photo-induced magnetization reported by Sato et al. [START_REF] Sato | Photoinduced Magnetization of a Cobalt-Iron Cyanide[END_REF] in Fe/Co PBA, there has been a great deal of efforts to understand photomagnetism as can be seen from the recent review by Aguilà and coauthors. [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF] However, some aspects remain elusive in the understanding of the photomagnetism in these systems. One of the most important questions concerning the nature of the magnetic interaction between the metal centers in Prussian Blue analogues is not fully answered, i.e. whether the Fe-Co interaction is ferromagnetic or antiferromagnetic and how does this interaction depend on the structure of the Fe/Co PBA. To bring information on this question, Fe/Co based PBA have been explored by various techniques [START_REF] Aguilà | Switchable Fe/Co Prussian Blue Networks and Molecular Analogues[END_REF] such as for instance SQUID magnetometry, [START_REF] Sato | Photoinduced Long-Range Magnetic Ordering of a Cobalt Iron Cyanide[END_REF][START_REF] Shimamoto | Control of Charge-Transfer-Induced Spin Transition Temperature on Cobalt-Iron Prussian Blue Analogues[END_REF][START_REF] Goujon | Photo-Excitation from Dia-to Ferri-Magnetism in a Rb-Co-Hexacyanoferrate Prussian Blue Analogue[END_REF] X-ray diffraction, [START_REF] Bleuzen | CoFe Prussian Blue Analogues under Variable Pressure. Evidence of Departure from Cubic Symmetry: X-ray Diffraction and Absorption Study[END_REF][START_REF] Maurin | Evidence for Complex Multistability in Photomagnetic Cobalt Hexacyanoferrates from Combined Magnetic and Synchrotron 135 X-ray Diffraction Measurements[END_REF] Neutron diffraction, [START_REF] Daniel M Pajerowski | Magnetic Neutron Scattering of Thermally Quenched K-Co-Fe Prussian Blue Analog Photomagnet[END_REF] and XMCD. [START_REF] Champion | Photoinduced ferrimagnetic systems in prussian blue analogues C i x Co 4 [Fe(CN) 6 ] y (C i = Alkali Cation). 4. Characterization of the Ferrimagnetism of the Photoinduced Metastable State by K edge X-ray Magnetic Circular Dichroism[END_REF][START_REF] Michael | X-ray Magnetic Circular Dichroism Investigation of the Electron Transfer Phenomena Responsible for Magnetic Switching in a cyanidebridged [CoFe] Chain[END_REF][START_REF] Sekine | Investigation of the Light-Induced Electron-Transfer-Coupled Spin Transition in a Cyanide-bridged [Co 2 Fe 2 ] omplex by X-ray Diffraction and Absorption Measurements[END_REF][START_REF] Cafun | XMCD at the Transition Metal K-Edges as a Probe of Small Pressure-Induced Structural Distortions in Prussian Blue Analogues[END_REF][START_REF] Bonhommeau | Metal-to-Ligand and Ligand-to-Metal Charge Transfer in Thin Films of Prussian Blue Analogues Investigated by X-ray Absorption Spectroscopy[END_REF] The ground state is composed of diamagnetic Fe II LS -CN-Co III LS species which are converted into paramagnetic Fe III LS -CN-Co II HS ones upon irradiation because of a metal-to-metal electron transfer. The conventional characterization of the photo-induced state is not possible by χ M T because (i) the irradiation of the sample is not necessarily complete and the mass of the converted phase is unknown and (ii) the thermal relaxation of the photo-induced state at low temperatures imposes a too limited range of temperature for the analysis of the χ M T curves. of magnetization is superimposed. The variation of the Co magnetization is monotonous indicating that the Co ions are always magnetized parallel to the external magnetic induction but Co magnetization seems difficult to saturate in inductions as large as 6.5 T.

On the contrary, the magnetization curve for Fe measured at 705.7 eV is much different. Between 1.5 T and 6.5 T, one observes a linear variation of the magnetization parallel to the external magnetic induction and between -1.5 T and +1.5 T, there is a clear inversion of the magnetization, i.e. the Fe magnetization is antiparallel to the external magnetic induction. Hence, the direct observation of the element specific magnetization curves show without ambiguity that between -1.5 T and +1.5 T, Fe and Co ions are coupled antiferromagnetically with the Co magnetic moment being larger than the Fe one. From From the literature, the Curie temperature of 1 is 21 K so that we expect that the signature of the antiferromagnetic phase will change if the temperature is raised from 2 K up to 30 K. Obviously, the signature from the paramagnetic phase will also change with increasing temperature. We have recorded Fe and Co XMCD detected magnetization curves at T = 2 K, 4 K, 10 K, 20 K and 30 K (Figure 5.4). As we approach the Curie temperature, the signature of the antiferromagnetic phase (i.e. the non-monotonous behavior of the Fe magnetization curve) tends to disappear. At 30 K the magnetization curve is almost a straight line with no accident in the region between ±1.5 T. In Fig. 5.4, we have reported the slope of the magnetization curves at B = 0 T as a function of the temperature. For Co, the slope of the magnetization curves remain positive for all temperature values and decreases when temperature is increased. The slope of Fe magnetization is negative and it decreases in absolute values when the temperature increases from 2 K to 30 K. Around

Conclusion and Perspective

This thesis was dedicated to the investigation of photo-switchable Fe/Co Prussian Blue Analogues and their corresponding precursors. The presence of magneto-optical bistabilities make these molecular complexes potential candidate for energy efficient, photo-switchable molecule-based information storage. For the technological interests, the manipulation of physical properties requires the investigation of these materials by state-of-the-art techniques. The present study on Fe/Co PBA has brought new insights towards the understanding of photomagnetic properties of these systems through experimental XMCD measurements enlightened when possible by a theoretical description within the LFM theory.

After the review of literature I had many questions and problems at hand that were not fully answered.

1)

To what extent reducing the dimensionality of magnetic materials can affect their physical properties?

2) Can the building block precursors preserve their individual magnetic properties in an associated molecular system? If yes then to what extent the properties of PBAs are altered?

3) What is the role of magnetic anisotropy in low dimensional magnetic molecular systems? How the external perturbations, for instance laser irradiation vs X-ray irradiation, can change the magnetic interaction between the metallic ions? 4) What is the magnetic interaction between Fe and Co ions in the photo-induced state of Fe/Co PBA?

To answer these questions, a detailed experimental and theoretical study was performed on molecular complexes which include Fe-bearing precursors of photomagnetic Prussian Blue Analogues, two photomagnetic dinuclear complexes, and a tridimensional RbCoFe PBA.

LFM calculations in FeTp precursor revealed a large value of orbit magnetic moment. This value was in contradiction with that measured from SQUID magnetometry. To account for this difference, angular dependence of orbit and spin magnetic was checked and a strong anisotropy in the low spin Fe III FeTp precursor was confirmed. In addition, a methodological approach was developed to investigate the origin of spin sum rules failure which can be extended to other systems where the application of spin sum rules is under question.