François Liger

Florence Cadarossanesaib

Thibaut Iecker

Dr Christian Tourvieille

Prof. Dr Didier Le Bars

Prof. Dr Thierry Billard
email: thierry.billard@univ-lyon1.frwww.fmi-lyon.fr

C labeling: Intracyclic incorporation of carbon-11 into heterocycles

Keywords: Carbon-11, Heterocycles, Radiochemistry, Radiolabeling, Positron emission tomography

HAL is

Introduction

Positron emission tomography (PET) is a non-invasive medical imaging technique used as diagnostic tool in several pathologies. [1] PET is also more and more applied in drug design, allowing in vivo quantitative biodistribution and pharmacokinetic studies. [2] This method requires radiolabeling of molecules with a positron emitting radioisotope. [3] Among the most useful isotopes, fluorine-18 and carbon-11 are preferentially employed. Even if fluorine-18 is preferred due to its superior radioactive half-life (109 min for fluorine-18 vs 20 min for carbone-11), 11 C-molecules are still predominantly used for research purposes. Indeed, it is easier to obtain radiolabeled equivalent of existing drugs by "isotopic replacement" of carbon atom. The main strategy for compounds labeling is generally peripheral introduction of 11 C-subtituents. [3a, 4] Radiolabeling inside the molecules core, in particular of heterocyclic structures, has been scarcely described. Few intracyclic labelings with carbon-11 have been previously performed with various 11 C-reagents: [5] [ 11 C]phosgene, [6] [ 11 C]formic acid or derivatives, [7] [ 11 C]formaldehyde, [8] [ 11 C]cyanide, [9] [ 11 C]thiocyanate, [10] [ 11 C]CS2 [11] or [ 11 C]CO. [12] However, all these reagents require their preliminary preparation, often in tedious conditions, which is time consuming. The starting material is generally [ 11 C]CO2 produced with a cyclotron by 14 N(p, a) 11 C nuclear reaction. Consequently, direct use of cyclotronproduced [ 11 C]CO2 could be of interest to obtain intracyclic radiolabeled heterocycles. Nevertheless, because of low reactivity of CO2, this approach has so far been little investigated.

A first approach has been described by an in situ formation of isocyanates. [13] [ 11 C]CO2 has been trapped by a diamine or an amino-alcohol in a first step, followed by a dehydration in a second step, mediated by POCl3. The resulting isocyanates were then cyclized to provide corresponding imidazolones or oxazolidinones. This method still requires two steps and appears limited in term of substrates scope. More recently, cyclic ureas were synthesized by cyclization of azidoamines with [ 11 C]CO2, mediated by phosphine. [14] However, this method is limited to urea compounds. Furthermore, heteroaromatic compounds cannot be directly obtained following these strategies.

Results and Discussion

We have previously described direct 11 C-methylation of amines through an in situ metal/carbene-mediated reduction of carbon dioxide. [15] During this process, the intermediate formation of formamides has been demonstrated. Consequently, we supposed that a similar strategy applied to diamines could lead to cyclic compounds. This hypothesis has been evaluated with 1,2-phenylenediamine (1a) as starting material to obtain the corresponding benzimidazole (2a) (Table 1). Starting from the described conditions for methylation of amines (entry 1), we were delighted to observe the formation of the expected benzimidazole 2a, with good radiochemical yields (entry 1). However, in this assay, 10 mg of diamine 1a have been used. Generally, smaller amounts (ca. 20 µmol) of starting material are engaged in radiolabeling reactions. Unfortunately, by decreasing the diamine 1a quantity (1.1 mg), to match with a more traditional amount, radiochemical yield also dramatically diminished (entry 2). By using a slight excess of ZnCl2 and IPr (1,3-Bis(2,6diisopropylphenyl)imidazol-2-ylidene), a satisfactory result was reobtained (entry 3). However, an excess of silane appeared to be necessary to observe the expected cyclization (entries 3-4). Some similar cyclizations have also been described with nonradioactive CO2. [16] Described conditions did not use any metal catalysts with a reaction time of 24h. Nevertheless, in our case the use of ZnCl2 appeared to be crucial to observe cyclization in a reaction time of only 20 min, more consistent with carbon-11 half-life (entry 5). The metal certainly contributes to accelerate reaction so fitting with the short time imposed by radioactive decay. With PhSiH3 as reducing agent, the cyclization reaction is in competition with methylation of amino groups which can proceed in similar conditions. [15] Indeed, some side-products arising from this methylation competitive reaction were also observed. To circumvent this drawback, less reducing silanes have been envisaged. If only low yields were obtained with PMHS (Poly(methylhydrosiloxane)), a higher and very good radiochemical yield was observed with Ph2SiH2 (entries 6-7). In this case, no methylation of amines was detected. Finally, FeCl3 has also been envisaged as catalyst but without any success (entry 8).

Even if a reaction time of 20 min is compatible with carbon-11 radiolabeling, shorter durations are generally expected. Consequently, with optimal conditions (entry 7), reaction time was reduced to 10 min. An important decrease of radiochemical yield has been observed (Table 2, entries 1-2). Microwave activation was deleterious for the reaction, as already observed in the previously described radiomethylation reactions (entry 3). [15] Doubling catalysts amounts did not bring significant improvement (entry 4). In contrast, an increase of concentration of precursor 1a, associated with a decrease of reaction volume, brought positive effects and excellent radiochemical yields were observed (entries 5-7). By switching from 200 µL to 100 µL, no significant improvement was observed. An attempt to reduce reaction time to 5 min led only to a medium result (entry 8). In view of these results, a volume of 200 µL will be generally preferred for further investigations, to avoid potential solubility problems.

Table 2. Effect of reaction time and solvent volume [a] Entry Reaction time (min) Diglyme volume (µL) 2a(%) [b] 1 20 400 83 2 10 400 25 3 10 [c] 400 1 4 10 [d] 400 38 In these optimal conditions, molar activity of produced benzimidazole 2a was around 18 GBq/µmol. To study the scope of this radiolabeling, various aromatic diamines were then studied (Scheme 1).

5
Various benzimidazoles were obtained with, in general, satisfactory to good radiochemical yields. Substitution onto nitrogen atom does not significantly influence the obtained results (2a-c). Whatever the electronic character (electron withdrawing or donor) of aromatic substituents, similar yields were observed (2af). However, slightly lower yields were observed with 2g and 2h, maybe due to a competitive coordination of ZnCl2 catalyst by the carbonyl function (2g) or the nitrogen atom of the pyridine core (2h). Interestingly, reaction is compatible with functional groups such as ketone (2g), ester (2e) or bromine (2d). In particular, no reduction side-products were detected.

To extend this radiolabeling methodology, 6-membered rings have been also studied. Thus, perimidine 2i was obtained with similar good yields compared to benzimidazoles. More interestingly, quinazolinone 2j was also synthesized starting from corresponding 2-aminobenzamide. Because of the weakest nucleophilicity of amide group, the expected cyclic product was formed with only a medium radiochemical yield. However, a good result was achieved by doubling reaction time to 20 min. By decreasing solvent volume to 100 µL, a better yield was also observed in 10 min. If benzimidazoles represent privileged structure in medicinal chemistry and drugs, [17] benzothiazoles are also important heterocyclic compounds in drug design and pharmaceutical agents. [18] This heterocycle is also used in radiotracers development, as illustrated by β-amyloid radioligand [ 11 C]PIB. [19] Consequently, our method was extended to aminobenzenethiols (3) to obtain, for the first time, intracyclically However, in view of the low reactivity of the starting diamine, the result remains quite satisfactory and demonstrates the usefulness of this method to label elaborated molecules.

During these previous investigations, some reproducibility issues were observed with a batch of IPr. Despite various analyses of the different batches of IPr, we have not succeeded to determine the reasons of such issues. Consequently, to try to circumvent such potential drawback, a preliminary preparation of IPr solutions in diglyme, just before use, was envisaged (Scheme 4).

In comparison to commercial IPr, similar results were observed with benzimidazole or benzothiazole. This use of home-made solution of IPr constitutes a valuable alternative to potential reproducibility issue and we warmly recommend this simple to implement solution to avoid some disappointments during radiolabelings. Finally, in order to demonstrate the effective productivity of this new radiolabeling approach, a full radiosynthesis, with HPLC ZnCl 2 (1.2 equiv.) [a] 66% (n = 3) [b] O [a] 4b 35% (n = 4) [a] 4c 36% (n = 2) [a] (11 equiv.) purification, was performed with perimidine 2i (Scheme 5). Noteworthy, a home-made solution of IPr was preferred. A good radioactive quantity (140 mCi, 5.2 GBq) of [ 11 C]perimidine (2i) was produced with a high radiochemical yield (RCY = 75%) and with a good radiochemical and chemical purity. This result is very encouraging and demonstrates the usefulness of this original radiolabeling method to produce radiotracers.

[ 11 C]CO 2 + 1 2 Br MeO 2 C N MeO MeO 2a 86% (n = 13) 2b 90% (n = 2) 2c 70% (n = 2) 2d 74% (n = 2) 2e 89% (n = 2) 2f 80% (n = 2) 2h 54% (n = 3) 2i 83% (n = 3) 37% (n = 2) 81% (n = 2)
O Ph 2g 52% (n = 2) N R N = 11 C N H N N N N N N H N N H N N H N N H N N H N Ph NH N N NH 2j Cl F 3 C 4a 36% (n = 2) 55% (n = 3)

Conclusions

To conclude, cyclization reactions by direct use of cyclotronproduced [ 11 C]CO2 were described to obtain in a late stage and one-pot process, heterocyclic and heteroaromatic compounds intracyclically labeled with carbon-11. This strategy constitutes a proof of concept about direct use of [ 11 C]CO2 in "radiocyclization" reactions and should open the way to new developments concerning radiolabeling of heterocyclic molecules.

Experimental Section

Synthesis of [ 11 C]perimidine (2i): 200 µL of freshly prepared IPr solution in diglyme (24 µmol, 1.2 eq) was added to a 1 mL vial containing 3.15 mg of 1,8-diaminonaphtalene (20 µmol, 1eq). The resulting solution was sonicated for 2 min and transferred to a 1.1 mL conical vial pre-charged with 3.35 mg of zinc chloride (24.2 µmol, 1.21 eq). After addition of 40 µL of diphenylsilane (0.215 mmol, 11 eq), the vial was sealed and placed into the automated synthesis module 10 min before end of bombardment. When the desired level of radioactivity was reached in (nearly 3000 mCi -111 GBq), reaction with [ 11 C]CO2 proceeded according previous general procedure (see SI). After 10 min of heating at 150°C, the reaction vial was cooled at 20°C for 2.5 minutes. Then, 2 x 100 µL of MeOH were sequentially added to the reaction mixture (30 seconds apart) and after further 20 seconds, the whole content of the reaction vial was loaded into a 3 mL HPLC loop. 700 µL of additional MeOH were used for rinsing the reaction vial and loaded into the HPLC loop before injection on semipreparative HPLC column (Macherey-Nagel Nucleodur C18 HTec column (10µm, 10 x 250mm). HPLC purification was conducted at 3 mL/min with acetate buffer pH 5.2/MeCN (55/45) as mobile phase. Radioactive and UV monitoring at 254 nm allowed the collection of 346-386 mCi (12.8-14.3 GBq, decay-corrected) of purified 1H-[ 11 C]Perimidine 2i. Retention time was 8 minutes. Radiochemical yields were ranging from 70 to 80% decaycorrected.

  Scheme 1. Cyclizations of aromatic diamines with [ 11 C]CO2. Radiochemical yields are mean values and were estimated from trapped [ 11 C]CO2 within the reactor and are decay-corrected from end of [ 11 C]CO2 trapping inside reactor. [a] reaction time = 20 min. [b] diglyme volume = 100 µL.

Scheme 4 .

 4 Scheme 4. Cyclization reactions with home-made solution of IPr. Radiochemical yields are mean values and were estimated from trapped [ 11 C]CO2 within the reactor and are decay-corrected from end of [ 11 C]CO2 trapping inside reactor.

Scheme 5 .

 5 Scheme 5. Production of perimidine 2i. The RCY value is mean value and was estimated from trapped [ 11 C]CO2 within the reactor and are decay-corrected from end of [ 11 C]CO2 trapping inside reactor.

Table 1 .

 1 Cyclization reaction with 1a and [ 11 C]CO2.

	Entry	1a	ZnCl2	IPr	Silane	2a(%) [a]
		(mg)	(equiv.)	(equiv.)	(equiv.)
	1	10	0.15	0.15	PhSiH3	68
					(1.00)
	2	ca. 1.1	0.15	0.15	PhSiH3	27
					(8.50)
	3	ca. 1.1	1.2	1.2	PhSiH3	52
					(8.50)
	4	ca. 1.1	1.2	1.2	PhSiH3	-
					(1.60)
	5	ca. 1.1	-	1.2	PhSiH3	-
					(8.50)
	6	ca. 1.1	1.2	1.2	PHMS	32
					(28.90)
	7	ca. 1.1	1.2	1.2	Ph2SiH2	83
					(11.00)
	8	ca. 1.1	1.2 [b]	1.2	Ph2SiH2
					(11.00)

-

[a] Radiochemical yields (RCY) were estimated from trapped [ 11 C]CO2 within the reactor and are decay-corrected from end of [ 11 C]CO2 trapping inside reactor.

[b]

with FeCl3 instead of ZnCl2.

  Cyclizations of aminobenzenethiols with [ 11 C]CO2. Radiochemical yields are mean values and were estimated from trapped [ 11 C]CO2 within the reactor and are decay-corrected from end of [ 11 C]CO2 trapping inside reactor.

	11 C-labeled
	benzothiazoles 4 (Scheme 2).
	With optimal conditions used for benzimidazoles, only modest
	radiochemical yield was observed (4a). As demonstrated
	previously (Scheme 1; 2j), by decreasing solvent volume (100 µL
	instead of 200 µL), a better result is obtained. Nevertheless, in
	general, radiochemical yields remain modest, but suitable for
	workable radiolabelings.

Scheme 2.

[a] diglyme volume = 100 µL.

  This one-step, late stage, intracyclic labeling has been applied to the first 11 C-labeling of theophylline drug (2k), with intracyclic incorporation of radioisotope (Scheme 3).

	Scheme 3. Intracyclic labelling of theophylline. Radiochemical yields are mean
	values and were estimated from trapped [ 11 C]CO2 within the reactor and are
	decay-corrected from end of [ 11 C]CO2 trapping inside reactor. [a] diglyme
	volume = 100 µL

[ 11 C]Theophylline was obtained in a modest radiochemical yield.

Acknowledgements ((optional))

This work was supported by European Union (EU) through the project Radiochemistry for Molecular Imaging (project number EU FP7-PEOPLE-2012-ITN-RADIOMI).

Frédéric Bonnefoi (CERMEP -in vivo imaging) is acknowledged for his technical assistance. The authors wish to thank the Centre National de la Recherche Scientifique (CNRS), Institut national de la santé et de la recherche médicale (INSERM) and University of Lyon 1 for financial support.


Umberto Raucci

Marika Savarese

Carlo Adamo

Ilaria Ciofini

Nadia Rega
email: nadia.rega@unina.it

Toward the Theoretical Design of Artificial Photosynthetic Machines

The development of efficient artificial leaves relies on the subtle combination of molecular assemblies able to absorb sunlight, converting light energy into electrochemical potential energy and finally transducing it into chemical accessible energy. The electronical design of these charge transfer molecular machines is crucial to build a complex supramolecular architecture for the light energy conversion. Here, we present an ab initio simulation of the whole decay pathways of a recently proposed artificial molecular reaction center. A complete structural and energetic characterization has been carried out with methods based on density functional theory, its time dependent version and broken symmetry approach. On the basis of our findings we provide a relevant revision of the pathway only indirectly postulated from an experimental point of view, along with unprecedented and significant insights on the electronic and nuclear structure of intramolecular charge separated states, which are fundamental for the application of this molecular assembly in photoelectrochemical cells. Importantly, we unravel the molecular driving forces of the various charge transfer steps, in particular those leading to the proton coupled electron transfer final product, highlighting key elements for the future design strategies of such molecular assays.

Main Text:

Conversion of light into electric or chemical energy is undoubtedly a very attractive solution for the global energy problem. [START_REF] Grätzel | Recent Advances in Sensitized Mesoscopic Solar Cells[END_REF][START_REF] Berardi | Molecular artificial photosynthesis[END_REF][START_REF] Gust | Realizing artificial photosynthesis[END_REF][START_REF] Llansola-Portoles | Artificial Photosynthesis: From Molecular to Hybrid Nanoconstructs[END_REF][START_REF] House | Artificial photosynthesis: Where are we now? Where can we go?[END_REF][START_REF] Fukuzumi | Bioinspired artificial photosynthesis systems[END_REF][START_REF] Gaut | Toward artificial photosynthesis[END_REF][START_REF] Ye | Water Oxidation Catalysts for Artificial Photosynthesis[END_REF][START_REF] Zhang | Artificial photosynthesis: opportunities and challenges of molecular catalysts[END_REF][START_REF] Dogutan | Artificial Photosynthesis at Efficiencies Greatly Exceeding That of Natural Photosynthesis[END_REF] Analogously, storage of solar energy into chemical fuels through the development of efficient photoelectrochemical cells (PECs) [START_REF] Fujishima | Electrochemical Photolysis of Water at a Semiconductor Electrode[END_REF][START_REF] Grätzel | Photoelectrochemical cells[END_REF][START_REF] Ohashi | Stable photoelectrochemical cells for the splitting of water[END_REF] opens the route for new and environmentally friendly energy sources. Nevertheless, the development of these devices is not straightforward since several entangled processes have to be finely combined and controlled (i.e light harvesting, charge separation, electron transfer). The best inspiration for the design of such devices is definitely provided by Nature that developed an extremely efficient molecular machine -the photosystem II (PSII)-able to convert sunlight into chemically accessible energy. 8- 10, 14 PSII uses solar photons to drive the oxidation of water to dioxygen in an amazing way, combining different specialized molecular units (e.g. chlorophyll complex P680, oxygen evolving center, redox active tyrosine-histidine pair). [START_REF] Barber | Photosystem II: the engine of life[END_REF][START_REF] Barber | Photosystem II: an enzyme of global significance[END_REF][START_REF] Vinyard | Photosystem II: The Reaction Center of Oxygenic Photosynthesis[END_REF] Therefore, this system is an optimum starting point for the construction of artificial photosynthetic machines. In this perspective, Moore and co-workers proposed a molecular triad (hereafter named BiPhOH-PF 10 -TCNP and depicted in Figure 1) functionally mimicking the highly efficient initial photo-induced charge separated state in PSII. [START_REF] Megiatto | Mimicking the electron transfer chain in photosystem II with a molecular triad thermodynamically capable of water oxidation[END_REF] This system is composed by : i) a functionalized porphyrin moiety (PF 10 ) acting as primary electron donor and mimicking the chlorophyll P680 exciton trap of PSII; ii) a tetracyanoporphyrin (TCNP) ring that acts as electron acceptor simulating the pheophytin moiety; and iii) a benzimidazole-phenol group (BiPhOH) that models the tyrosine hystidine pair of PSII. This pair is involved in a Proton Coupled Electron Transfer (PCET) reaction during the photosynthetic cycle. Moore and co-workers provided a detailed Raucci, U. et al.

3

spectroscopic and electrochemical characterization of this molecular triad leading to the complex decay pathways reported in the inset of Figure 2. [START_REF] Megiatto | Mimicking the electron transfer chain in photosystem II with a molecular triad thermodynamically capable of water oxidation[END_REF] Based on experimental data, their hypothesis is that the initial excitation of the PF 10 group is followed by singlet energy transfer to the TCNP moiety, whose excited state can relax by a photoinduced electron transfer (PET) toward a charge separated state giving rise to a Bi-PhOH-PF 10 + • -TCNP -• species. They proposed that this species rapidly undergoes a PCET reaction in which an electron is transferred from the phenol to the PF 10 + • group, while the phenolic proton is transferred towards the benzimidazole group providing the final species, postulated to be the BiH + -PhO • -PF Nevertheless, for the time being, the nature and the relative energies of all the electronic states involved in this complex mechanism have been only experimentally and indirectly estimated by combining redox measurements with absorption and emission data of isolated form of the three molecular fragments composing the triad. At the present, no clear direct evidence for the formation of the final PCET product have been obtained from experiments. Indeed, in a recent publication [START_REF] Llansola-Portoles | Artificial Photosynthesis: From Molecular to Hybrid Nanoconstructs[END_REF] Moore and co-worker stated that "indirect evidence for PCET comes from reduction potentials of model compounds [START_REF] Moore | Effects of Protonation State on a Tyrosine-Histidine Bioinspired Redox Mediator[END_REF] which indicate that PF 10 would not generate sufficient driving force for the formation of the Bi-PhOH • + -PF 10 -TCNP -• and thus implies the formation of the BiH + -PhO • -PF 10 -TCNP -• state." [START_REF] Llansola-Portoles | Artificial Photosynthesis: From Molecular to Hybrid Nanoconstructs[END_REF] In order to tune and control the properties of such a triad as well as to help in the design on new systems a more detailed knowledge of the electronic structure of all the intermediate states involved in the excited state evolution is mandatory. Here, for the first time, we provide a complete theoretical structural and energetic characterization of all the crucial species involved in the decay pathway (Bi-PhOH-PF 10 + • -TCNP -• , Bi-PhOH • + -PF 10 -TCNP -• and BiH + -PhO • -PF 10 -TCNP -• ). By studying the complete triad we show how the final PCET product, BiH + -PhO • -PF 10 -TCNP -• , is energetically more stable than the Bi-PhOH • + -PF 10 -TCNP -• side adduct, highlighting the principal structural differences between them. Furthermore, we investigate the proton coupled electron transfer reaction reconstructing the reaction path and individuating the structural motifs driving it. Describing the driving force of the various charge transfer steps is one of our principal aims, especially to support the future design strategies of such molecular devices.

The theoretical simulation of the experimentally proposed decay pathways it's far from being straightforward due to the necessity of accurately simulating the excited state evolution of a large system in presence of a medium -the solvent-with can play an important role in the stabilization of the different states.

Density Functional Theory (DFT) [START_REF] Parr | Density Functional Theory of Atoms and Molecules, Horizons of Quantum Chemistry[END_REF] and its time dependent counterpart (TD-DFT) level [START_REF] Stratmann | An efficient implementation of timedependent density-functional theory for the calculation of excitation energies of large molecules[END_REF][START_REF] Runge | Density-Functional Theory for Time-Dependent Systems[END_REF] offer valuable tools for the description of excited states processes in condensed phase, [START_REF] Adamo | The calculations of excited-state properties with Time-Dependent Density Functional Theory[END_REF][START_REF] Jacquemin | Excited-state calculations with TD-DFT: from benchmarks to simulations in complex environments[END_REF][START_REF] Jacquemin | The geometries, absorption and fluorescence wavelengths of solvated fluorescent coumarins: A CIS and TD-DFT comparative study[END_REF][START_REF] Chiariello | Exploring Nuclear Photorelaxation of Pyranine in Aqueous Solution: an Integrated Ab-Initio Molecular Dynamics and Time Resolved Vibrational Analysis Approach[END_REF] although this choice makes the accurate simulation of excited states with a net intramolecular charge transfer character far to be trivial. [START_REF] Dreuw | Failure of Time-Dependent Density Functional Theory for Long-Range Charge-Transfer Excited States: The Zincbacteriochlorin-Bacteriochlorin and Bacteriochlorophyll-Spheroidene Complexes[END_REF][START_REF] Tozer | Does density functional theory contribute to the understanding of excited states of unsaturated organic compounds?[END_REF] For this reason, we complemented the TD-DFT description of such states resorting on the broken symmetry approach (BS) originally developed by Noodleman and co-workers [START_REF] Noodleman | The Xα valence bond theory of weak electronic coupling. Application to the low-lying states of Mo2Cl84[END_REF][START_REF] Noodleman | Valence bond description of antiferromagnetic coupling in transition metal dimers[END_REF][START_REF] Norman | Electronic structure of 2-Fe ferredoxin models by X.alpha. valence bond theory[END_REF][START_REF] Ovchinnikov | Simple spin correction of unrestricted densityfunctional calculation[END_REF] to describe magnetic coupling [START_REF] Ciofini | DFT calculations of molecular magnetic properties of coordination compounds[END_REF] and thus open shell singlet states using a single determinant approach. This kind of approach enables the setup of computationally stable protocols for the description of excited state dealing with charge transfer processes, which might be of interest in the design of new synthetic models for photoelectrochemical devices.

To simplify the following discussion each excited state of the triad will be labelled as S X n . The X superscript identifies the diabatic composition of the excited state based on the molecular moiety mostly involved in the excitation (e.g. X can be TCNP or PF 10 ) while the subscript n specifies the adiabatic electronic state number according to its energy. S indicates that each excited state computed is a singlet. The computational details are provided in the Supplemental Information (SI). Initially the triad is excited from its ground electronic state (S 0 ). The two subunits PF 10 and TCNP of BiPhOH-PF 10 -TCNP are almost perpendicular in S 0 , while the BiPhOH and PF 10 rings are twisted by roughly 67° ( 1 =-67°, see Figure 1 for the labelling and Table 1 for the values of the other principal dihedral angles) suggesting a certain electronic coupling among them. The PF 10 moiety is highly symmetric with the pentafluorephenyl groups similarly oriented with respect to the plane of the porphyrin ring. The TCNP unit assumes a non-planar structure due to steric interactions between the cyano and phenyl groups, respectively in the beta and meso positions of the tetrapyrrolic ring. Steric interactions also lead to an orientation for the phenyl groups far from the perpendicular one (see  2 ,  3 , and  4 dihedral angles in Table 1 and Figure 1). ) localized respectively on the TCNP and on the PF 10 groups. Starting from the absorption event, the simulated pathway can be followed by inspecting Figure 2.

Table 1. Characteristic dihedral angles (in degree, refer to Figure 1 for labels) computed for the triad in the relevant electronic states. All parameters are computed on the relative minimum energy structure.

After the excitation to the state S 7 PF10 a fast internal conversion to a state still localized on PF 10 but at lower energy (state S 2 PF10 ) can take place (see Figure 2). This is in line with the photochemistry of porphyrin molecules that, following the absorption to higher excited electronic states, give rapid internal conversion to S 1 , from where emission is observed. [START_REF] Mataga | Internal Conversion and Vibronic Relaxation from Higher Excited Electronic State of Porphyrins: Femtosecond Fluorescence Dynamics Studies[END_REF] The S 2 PF10 state has been vertically computed at 2.11 eV (f=0.017) on the S 0 minimum energy structure and it is characterized by the transition between frontier molecular orbitals reported in Electronic state ). This step corresponds to the experimentally hypothesized energy transfer from PF 10 to TCNP in the triad (first step in the Figure 2 inset).

 1  2  3  1  2  1  2  3   4  S 0 -
The TCNP ring distortion is one the main degree of freedom involved in the S 2 PF10 toward S 2 TCNP path. Indeed, starting from the Franck Condon region, the  1 dihedral angle changes of about 4 degrees when passing to the S 2 TCNP excited state energy minimum.

The fluorescence from the TCNP is experimentally observed at 1.72 eV and it is computed at 2.02 eV (f=0.409) in the S 2 TCNP excited state energy minimum. From an experimental point of view, it has been hypothesized that this state corresponds to the reactant for the first ET process (see inset in Figure 2). Nevertheless, from our calculations it was no possible to individuate a CT character from the PF 10 to the TCNP unit in structures close to the S 2 TCNP energy minimum, which would have been a reasonable indication of the possible ET process. Indeed, in this structure another electronic excited state (S 1

TCNP

) with energy of 1.63 eV (f=0.473) has been calculated, characterized by an electronic excitation still completely localized on the TCNP group (Figure S1 for the MOs involved in the transition). The main difference between the S 2 TCNP and S 1 TCNP states is a significant change of both the electronic and nuclear arrangements during the S 1 TCNP relaxation. As matter of fact, the charge transfer character of the S 1 TCNP excitation drastically increases when going from the S 2 TCNP to the S 1 TCNP minimum energy structure: while at the S 2 TCNP minimum the MOs involved in the S 1 TCNP transition are completely localized on the TCNP moiety, the character of charge transfer from the PF 10 to the TCNP unit increases at the S 1 TCNP minimum energy structure (see Figure S3 for the MOs involved in the electronic excitation). Considering that the energy difference (0.39 eV) between S 1 TCNP and S 2 TCNP corresponds to about 3100 cm -1 , we propose an internal conversion occurring between the S 2 TCNP and S 1 TCNP states, and assume the S 1 TCNP state as the electron transfer reactant (Figure 2).

The distortion of the TCNP tetrapyrrolic ring is the main degree of freedom involved during the structural relaxation of S 1 TCNP and it promotes the charge transfer from the PF 10 to the TCNP unit (see Table 1). Indeed, the  1 dihedral angle, describing the distortion of the porphyrin ring, changes from -18° to -25° during this relaxation, driving the variation in the nature of the MOs involved in the S 1 TCNP electronic transition. This deformation increases the steric repulsions between the cyano and phenyl groups that, in turn, assume a more planar orientation with respect to the porphyrin ring. The TCNP deformation is, thus, a key structural motif for the charge transfer event. Interestingly, this change in the nature of the excited S 1 TCNP state was observed only for calculations performed in benzonitrile solution, while it was not reproduced in analogue S 1 TCNP optimization in cyclohexane. In this case, the excitation remains localized on the TCNP moiety. This clearly indicates that only polar solvents with high dielectric constant are able to stabilize the electron transfer product and it is in fair agreement with the experimental evidences indicating that a high quantum yield for the PET reaction is observed only in polar medium (benzonitrile). The energy of the relaxed S 1 TCNP state is computed at 1.40 eV (f=0.565). Within the TD-DFT framework this is the best picture of the electron transfer product. In order to describe the evolution of this charge separated state in the ET product, the BS approach was

applied. An open shell BS singlet state characterized by a spin density localized on both the PF 10 and the TCNP groups was computed. The spin density plot and the Mulliken spin density (MSD) integrated for fragments are reported for this structure in In order to characterize the PCET reaction, we chose the phenol oxygen-hydrogen (O Ph H) distance as degree of freedom representative of the proton transfer coordinate. We obtained an energy profile by a relaxed scan along this coordinate at TD-DFT level. The S 1 TCNP electronic structure showed only a negligible variation along this coordinate, that means no ET accompanied the PT event. On the other hand, a BS solution was obtained on the PT product, corresponding to the BiH + -PhO • -PF 10 -TCNP -• PCET adduct. In Figure 3b we showed the spin density plot and the MSD integrated for fragments of this species. This latter analysis shows the electronic holes localized on both the TCNP (-1.0e -) and phenol (0.78e -) units. The O Ph H distance is 1.863 Å in this structure, while the imidazole nitrogenhydrogen (N Im -H) distance is 1.023 Å .

We also observed a small spin polarization on the PF 10 moiety. This is principally due to the strong electronic coupling between the BiPhOH and PF 10 . The transition state (TS) for the PCET step has been also computed (the spin density plot is reported in Figure S5), with an imaginary frequency at -1169cm -1 (the displacement vectors for the imaginary frequency at the transition state are reported in Figure S6). The O Ph H and N Im -H distance are respectively of 1.272 and 1.205 Å at the transition state. The integration of the intrinsic reaction coordinate has been also carried out in order to follow the variation of the spin density along the reaction path (Figure 4a). Figure 4a shows that starting from the Bi-PhOH-PF 10 + • -TCNP -• species, an electron is transferred from the phenol toward the PF 10 group saturating its electronic hole when the proton is bounded to the imidazole nitrogen. The spin density on the TCNP fragment is constant, revealing the formation of the BiH + -PhO • -PF 10 -TCNP -• species. In spite of a barrier of 4.44 kcal/mol, the PCET product is slightly favoured of about 0.16 kcal/mol. From a mechanistic point of view, the  1 dihedral angle is the degree of freedom principally involved in the PCET reaction (see Table 1). This angle defines the relative orientation between the BiPhOH and the PF 10 units varying of about 5 degrees during the reaction.  1 is an important parameter controlling the electronic coupling between the two units, thus modulating the electron transfer among them. To further analyse this point, the variation of the MSD on the PF 10 and Ph fragments with respect to the  1 dihedral angle is reported in Figure 4b. This plot has been obtained scanning the  1 dihedral angle from -45° to -90° on the broken symmetry BiH + -PhO • -PF 10 -TCNP -• state. When the two rings are almost perpendicular ( 1 = -90°) the spin density on the PF 10 fragment is zero and that on Ph is about one. Varying the  1 angle the spin density on the PF 10 moiety gradually increases, reaching its maximum value (about 0.2) when the two rings become more planar. At the same time the spin density on the Ph fragment decreases reaching at least the value of about 0.8. This internal mode is crucial to drive the PCET event, and it has to be considered as a critical motif for the future design of these charge transfer molecular machines.

We also computed the alternative BS solution corresponding to the transfer of an electron from the Ph group towards the PF 10 one, with no PT between phenol and benzimidazole groups, namely the Bi-PhOH • + -PF 10 -TCNP -• species, (Figure 3c).

This state is found to lie 0.60 eV (13.89 kcal/mol) higher in energy with respect to the Bi-PhOH-PF 10 + • -TCNP -• one (Figure 2). Its formation is, thus, energetically unfavourable. Once again Bi-PhOH • + -PF 10 -TCNP -• and Bi-PhOH-PF 10 + • -TCNP -• differ principally for the mutual orientation of the BiPh and PF 10 moiety, namely for the  1 dihedral angle (Table 1). Indeed, this degree of freedom changes of about 40° between the two structures, with the Bi-PhOH • + -PF 10 -TCNP -• species favoured by the perpendicular arrangement between the Ph and PF 10 rings.

In conclusion, the complete excited state cascade of the triad BiPhOH-PF 10 -TCNP has been simulated within the TD-DFT and BS frameworks. This combined approach allowed to describe the complexity of the structural and electronic evolution of the charge transfer steps following the electronic excitation of the triad. Furthermore, the internal degrees of freedom involved during the various steps have been successfully analysed. We individuate the dihedral angles involved in the modulation of the electronic coupling between the BiPhOH and PF 10 moieties as crucial parameters for the formation of the various charge transfer species.

The combination of TD-DFT and broken symmetry approaches paves the way to disentangle the complex electronic structure of PSII mimics and for the successful design of charge transfer molecular machines suitable for artificial photosynthesis.

Figure 1 .

 1 Figure 1.Molecular structure of triad BiPhOH-PF 10 -TCNP composed of three covalently linked subunits: BiPhOH, PF 10 and TCNP. Labelling of critical dihedral angles is also provided. The dihedral angle 1 is that defined by the , , ,  atoms.

Figure 2 .

 2 Figure 2. Simulated decay pathway for BiPhOH-PF 10 -TCNP. Excitation, Internal conversion (IC), Energy Transfer (EnT), Electron Transfer (ET) and Proton Coupled Electron Transfer (PCET) steps are represented. Energy levels have been computed at TD-DFT and Broken Symmetry level of theory. The vertically computed excited states are reported in the Franck Condon region, and S 2 energy minimum. For comparison, in the inset it is reported the experimentally proposed energy level diagram of decay pathways for triad according to ref.17.

Figure S1 .

 S1 Figure S1. Another excited state (S 3 TCNP ) can be found close in energy to S 2 PF10 , and it is calculated at 2.13 eV (f=0.103) in the S 2 PF10 Franck Condon region. This state is characterized by

Figure 3a ,

 3a with the fragment definition provided in Figure S4. Raucci, U. et al. 10 Looking at the fragments MSD it's clear that the BS calculated singlet state represents the PET product, namely the Bi-PhOH-PF 10 + • -TCNP -• adduct. Indeed, two unpaired electrons with opposite spin are localized on the PF 10 and TCNP moieties, respectively, with negligible contribution on the BiPhOH group. The Mulliken charge analysis for fragments reveals a net positive charge of +1.10 on the PF 10 unit and a net negative charge of -0.93 on the TCNP fragment. This configuration is that expected following an electron transfer from the PF 10 to the TCNP group. The Bi-PhOH-PF 10 + • -TCNP -• species, on turn, represents the reactant for the next PCET step.

Figure 3 .

 3 Figure 3. (a) Spin density plot for the electron transfer product (Bi-PhOH-PF 10 + • -TCNP -• ) in the broken symmetry approximation. (b) Spin density for the proton coupled electron transfer product (BiH + -PhO • -PF 10 -TCNP -• ). (c) Spin density plot for the electron transfer product (Bi-PhOH • + -PF 10 -TCNP -• ). Integration for fragments of the Mulliken spin density is also reported.

Figure 4 .

 4 Figure 4. (a) Mulliken spin density (MSD) integrated for fragment along the IRC for the PCET reaction. (b) Mulliken spin density integrated for fragment along the variation of the  1 dihedral angle on the BiH + -PhO • -PF 10 -TCNP -• state.

  10

Table of Content.

 of


A S Sukhanov

B E Zuniga Cespedes

P Vir

A S Cameron

A Heinemann

N Martin

G Chaboussant

V Kumar

P Milde

L M Eng

C Felser

D S Inosov

Editors' Suggestion Anisotropic fractal magnetic domain pattern in bulk Mn 1.4 PtSn

The tetragonal compound Mn 1.4 PtSn with D 2d symmetry recently attracted attention as the first known material that hosts magnetic antiskyrmions, which differ from the skyrmions known so far by their internal structure. The latter have been found in a number of magnets with the chiral crystal structure. In previous works, the existence of antiskyrmions in Mn 1.4 PtSn was unambiguously demonstrated in real space by means of Lorentz transmission electron microscopy on thin-plate samples (∼100 nm thick). In the present study, we used small-angle neutron scattering and magnetic force microscopy to perform reciprocal-and real-space imaging of the magnetic texture of bulk Mn 1.4 PtSn single crystals at different temperatures and in applied magnetic field. We found that the magnetic texture in the bulk differs significantly from that of thin-plate samples. Instead of spin helices or an antiskyrmion lattice, we observe an anisotropic fractal magnetic pattern of closure domains in zero field above the spin-reorientation transition temperature, which transforms into a set of bubble domains in high field. Below the spin-reorientation transition temperature the strong in-plane anisotropy as well as the fractal self-affinity in zero field is gradually lost, while the formation of bubble domains in high field remains robust. The results of our study highlight the importance of dipole-dipole interactions in thin-plate samples for the stabilization of antiskyrmions and identify criteria which should guide the search for potential (anti)skyrmion host materials. Moreover, they provide consistent interpretations of the previously reported magnetotransport anomalies of the bulk crystals.

I. INTRODUCTION

Solids exhibiting topological properties are promising for future applications, in particular for spintronics. In the case of magnetic materials with the ferromagnetic spin-spin exchange coupling, the presence of the antisymmetric Dzyaloshinskii-Moriya interaction (DMI) may twist the otherwise homogeneous collinear spin texture into a two-dimensional lattice of densely packed nanometer-sized whirls. Each of these whirls is formed by a spatial distribution of the regularly canted magnetic moments that wrap a whole unit sphere, if mapped out onto it. The mutual noncoplanar orientation of the neighboring spins can be described by the topological charge (or the skyrmion winding number) N sk that takes values ±1 and differentiates two types of the topologically protected magnetic structures: skyrmions and antiskyrmions [1][2][3][4][5][6].

While there are an increasing number of the discovered skyrmion-hosting compounds, such as B20-type chiral magnets (e.g., MnSi, FeGe, Fe x Co 1-x Si) [7][8][9][10][11][12], β-Mn-type Co-Zn-Mn alloys [13][14][15][16][17], Cu 2 OSeO 3 [18][19][20][21][22][23], which support Bloch-type skyrmions, and lacunar spinels (e.g., GaV 4 S 8 , GaV 4 Se 8 ) [24][25][26], which support Néel-type skyrmions, antiskyrmions have been observed only in thin plates of Mn 1.4 Pt(Pd)Sn [27][28][29][30] and Mn 2 Rh 0.95 Ir 0.05 Sn [31] to date. In contrast to the skyrmion materials with cubic (P2 1 3 and P4 1 32 space groups) or rhombohedral C 3v crystal structures (space group R3m), tetragonal Mn 1. 4 PtSn belongs to the D 2d symmetry class (space group I42d), which is a prerequisite of antiskyrmions [4,27,32,33]. In agreement with the symmetry-based theoretical predictions, the first Lorentz transmission microscopy (LTEM) measurements of Mn 1. 4 PtSn demonstrated nucleation of the triangular lattice of magnetic antiskyrmions in a magnetic field of ∼0.2 T, applied perpendicular to the surface of a thin lamella sample and parallel to the [001] crystallographic direction (the tetragonal c axis). The antiskyrmions are ∼200 nm in diameter and were observed in a wide temperature range below T C of ∼400 K down to T ≈ 150 K [27,28].

Subsequent LTEM experiments revealed that the antiskyrmions in Mn 1. 4 PtSn can also arrange in a square lattice in some particular temperature and field regions of the phase diagram, which may be affected by the sample thickness [29,30]. Moreover, elliptically distorted skyrmions of both handednesses and the nontopological bubble lattice were shown to appear when a symmetry-breaking in-plane magnetic field is applied in combination with the out-of-plane field [29,30]. This makes Mn 1. 4 PtSn a unique compound hosting a rich variety of controllable topological magnetic objects.

Because the previous studies on thin lamellae of Mn 1. 4 PtSn pointed out that the sample geometry and the sample preparation process can alter some aspects of the material properties [29,30], it is essential to characterize the magnetic structure of the compound in the bulk. Due to a very high penetration depth of the neutron radiation, neutron scattering techniques allow investigations of the magnetic structure of bulk samples. Taking into account the long-periodic modulations of the magnetic texture in Mn 1.4 PtSn, small-angle neutron scattering (SANS) is a suitable probe, which enables reciprocal-lattice imaging of magnetic structures with periods ranging from ∼2 to ∼400 nm [34]. For real-space investigations of the magnetic texture of bulk samples, mostly, surface-sensitive techniques are available. Magnetic force microscopy (MFM) proved to be a valuable tool when studying complex spin textures such as helices and skyrmions as well as complex domain patterns on length scales between ∼20 nm and ∼100 μm and can be applied at various temperatures as well as in external magnetic fields [11,21,24,[START_REF] Hubert | Magnetic Domains: The Analysis of Magnetic Microstructures[END_REF].

In the present study, we employ both SANS and MFM to resolve the nanometer-scale magnetic texture of Mn 1.4 PtSn in the bulk single-crystalline form and observe how it changes when the sample temperature and the applied magnetic field are varied. We discuss the characteristic features of the obtained reciprocal-space and real-space patterns and demonstrate that the magnetic structure of the bulk Mn 1.4 PtSn differs dramatically from the previously reported LTEM observations obtained using samples in thin-plate geometry. Instead of helices or an antiskyrmion lattice, we observe an anisotropic fractal magnetic pattern of closure domains in zero field above the spin-reorientation transition temperature T SR , with characteristic hints for the DMI inherent in the D 2d symmetry of the crystal, which transforms into a set of bubble domains in high field. Below T SR the strong in-plane anisotropy and the fractal self-affinity in zero field are gradually lost, while the formation of bubble domains in high field remains robust. The results of our study highlight the importance of dipoledipole interactions in thin-plate samples for the stabilization of antiskyrmions and identify search criteria for potential (anti)skyrmion host materials.

This paper is organized as follows. After a description of the experimental details, we first discuss the experimental results obtained in zero field and above T SR . Then, we describe the field dependency above T SR . Finally, we discuss the temperature dependence.

II. EXPERIMENTAL DETAILS

Our SANS measurements were performed at the instruments SANS-1 (FRM-II, Garching, Germany) and PA20 (LLB-Orphée, CEA Saclay, France) [START_REF] Chaboussant | [END_REF]. In both experiments, we used the same sample, which consisted of 17 crystals coaligned together with a relative misalignment not worse than 3 • , mounted on an aluminum plate holder. The crystals were coaligned to increase the total volume of the sample and the resulting experimental signal-to-noise ratio (see the Supplemental Material [37] for a photograph of the sample). All the crystals were grown by the self-flux method, as described in [38,39]. The high quality of the crystals was confirmed by means of magnetic susceptibility, resistivity, and x-ray diffraction measurements. Their stoichiometry was examined by energy-dispersive x-ray spectroscopy, which did not reveal any variation of the chemical composition between the crystals of the same batch or within a surface of each crystal within the precision of this method.

MFM measurements were performed with two instruments. For room-temperature measurements without external fields we used the Park Systems NX10 [40] with PPP-MFMR probes from Nanosensors [41] at lift heights between 100 and 150 nm. Low-temperature measurements with external field were performed in an Omicron cryogenic ultrahigh-vacuum scanning tunneling microscopy/atomic force microscopy instrument [42] using the RHK R9s electronics [43] for scanning and data acquisition. We employed PPP-QMFMR probes from Nanosensors driven at mechanical oscillation amplitudes A ≈ 20 nm at lift heights between 400 and 800 nm. All data analysis was performed with the GWYDDION [44] software. Two samples have been investigated. Sample A is a single crystal of Mn 1.4 PtSn, whose native surface was gently polished with a focused ion beam using Xe ions at currents below 10 nA. After the polishing, we checked with MFM that the resulting amorphous surface layer did not alter the domain pattern. Sample B is a polycrystalline sample of Mn 1.4 Pt 0.9 Pd 0.1 Sn that was carefully polished. Measurements of sample A are presented in the main text, while measurements of sample B can be found in the Supplemental Material.

III. RESULTS

A. Magnetic texture at T > T SR

Figure 1(a) shows a SANS pattern collected at the sample temperature T = 250 K and zero magnetic field (no prior field history). The sample was oriented with its tetragonal c axis parallel to the incident neutron beam. In this scattering geometry, the reciprocal (HK0) plane is imaged at the position-sensitive detector. The in-plane orientation of the sample corresponds to the momentum component q x aligned with the [110] direction. Thus, the scattering pattern in Fig. 1(a) represents spin-texture modulations in the ab plane of Mn 1.4 PtSn. As can be seen, there is a clear scattering intensity distribution that covers almost the whole imaged reciprocal space in the momentum range 0.002 < Q < 0.017 Å -1 . The scattering is diffuse and does not have sharp features, such as Bragg peaks one would expect in SANS of helimagnets [7,8,12,13,19,23] for a helical state with a period λ of 37-315 nm. This is in strong contrast to the LTEM observations of the helical spin structure with a period of ∼100 nm in the thin lamellae samples, including at T = 250 K and B = 0 T [27][28][29][30], and implies that the magnetic structure of the bulk Mn 1.4 PtSn is not a spin helix, as was previously anticipated.

The observed SANS pattern is diffuse yet strongly anisotropic and can be viewed as eight streaks (stripes) of intensity, which can be considered a sum of two four-pointed stars (crosses), one of which is higher in intensity and points to the 100 directions, whereas the other is weaker and oriented with respect to 110 .

It should be noted that a presence of the spiral state with λ > 315 nm in bulk Mn 1.4 PtSn would result in the Bragg peaks in SANS that are not resolved within the direct beam in our experimental setup. However, a possibly unresolved helical state cannot cause the observed diffuse scattering. Moreover, as shown below, the MFM imaging did not reveal the presence of a helical state with λ > 315 nm, which further supports the conclusions drawn from the SANS measurements.

The origin of this scattering can be understood when a saturating magnetic field is applied parallel to the c axis (i.e., along the neutron beam). Figure 1(b) depicts the SANS pattern at B = 0.57 T, which is well above the saturation field of ∼0.5 T [38]. As one can see, the stripes of intensity along 100 disappeared, but the weaker stripes along 110 remained unchanged, which implies that only the former are of magnetic origin. Hence, the pattern in Fig. 1(b) can be used as a background, and we subtracted the intensity I (Q, 0.57 T) from the pattern I (Q, 0 T). Both the foreground data and the background data were normalized by the monitor counts for the correct subtraction. The resulting pattern is shown in Fig. 1(c), which represents the pure magnetic intensity. To highlight the difference between the zero-field and the field-saturated states, intensity profiles are plotted for the momentum directions (H00) and (HH0) in Fig. 1(d). Figure 1(e) demonstrates the anisotropy of the intensity distribution cut at Q = 0.01 Å -1 as a function of the in-plane (azimuthal) angle φ. As can be seen from the azimuthal profile, each stripe has a base width of ∼45 • .

The observation of diffuse anisotropic scattering suggests that Mn 1.4 PtSn develops a magnetic texture of rectangularshaped domains with domain walls oriented strictly perpendicular to the crystallographic [100] and [010] axes. The well-defined orientation of the magnetic domains follows from the cross-shaped scattering within the reciprocal (HK0) plane. The domains, however, do not feature any regularity either in their sizes or in the domain-wall spacing, which can be concluded from the smooth radial profile of the diffuse scattering. Furthermore, the SANS patterns collected when the sample is oriented by its [110] axis along the incident neutron beam showed the absence of scattering intensity along the reciprocal L direction, which confirms that the spin correlations are homogeneous (ferromagnetic) along the tetragonal c axis (see Fig. S3 in the Supplemental Material [37]).

For further analysis, the radial profile along the stripe of the background-subtracted SANS pattern taken at T = 250 K and B = 0 T is plotted in Fig. 1(f) on a log-log scale. I (q) obeys a power-function trend I ∝ q -D with two different exponents below and above the crossover momentum q 0 = 0.013 Å -1 , where the slope changes. The fitting yields D = 2.65 for momenta below q 0 down to the lowest accessible momentum of ∼0.002 Å -1 , which is a signature of the scattering from fractal objects [START_REF] Schmidt | The Modern Aspects of Small-Angle Scattering[END_REF][START_REF] Mildner | [END_REF][47][48]. This implies a complex intertwined arrangement of the domain walls of the rectangular domain pattern. The momentum q 0 then determines the lowest real-space scale down to which the fractal self-affinity holds, which is here ∼48 nm. The upper limit of the fractal structure cannot be reached within the accessible q range and lies above 315 nm. Above q 0 the exponent D changes to D = 5.8, which can be attributed to scattering from density profiles without sharp (D = 4) contrast (either due to roughness along the profile or a smoothness of the profile) [START_REF] Schmidt | The Modern Aspects of Small-Angle Scattering[END_REF][START_REF] Mildner | [END_REF]. A similar analysis was applied in a SANS study of Nd 2 Fe 14 B [49], where anisotropic For comparison, we show a MFM measurement on the ab plane of the Mn 1.4 PtSn single crystal (sample A) at room temperature in Fig. 2(a). The domain pattern is highly reminiscent of the fractal magnetic closure domains observed in the low-temperature easy-cone anisotropy phase of Nd 2 Fe 14 B [49][50][51]. It consist of lamellar domains with smaller nested closure domains arranged in a fractal pattern resembling the Sierpinski carpet [START_REF] Mandelbrot | The Fractal Geometry of Nature[END_REF]. The width of the lamellar domains sets the upper boundary of ∼3 μm, which is one order of magnitude higher than the upper fractal scale accessed in SANS. The in-plane orientation of the domain walls is highly anisotropic with pinning to two perpendicular directions within the ab plane. In the Fourier transform [see Fig. 2(b)], the same cruciform pattern as in SANS is visible. Hence, we can safely assume that our SANS and MFM results describe the same anisotropic fractal domain pattern. Such domain patterns arise from a competition of uniaxial ferromagnetic exchange interaction favoring collinear domains in the easy axis without domain walls and dipolar interactions at the surfaces of the material adding stray-field energy. The latter is minimized by nucleation of closure domains at the surface at the expense of additional domain walls, whose orientation is defined by the anisotropy within the ab plane. Thus, the nested domains are present in a region below the surface and form a fractal tree structure along the c axis, also known as branching domains [START_REF] Hubert | Magnetic Domains: The Analysis of Magnetic Microstructures[END_REF]. Additional measurements on the polycrystalline sample B confirm that the fractal pattern indeed belongs to such closure domains. Details can be found in the Supplemental Material.

Moreover, we find characteristic hints for the DMI in the material. As already mentioned, lamellar stripe domains appear in two orientations within the ab plane. Examples are shown in Figs. 2(c) and 2(d). Note that these two images have been filtered for enhanced contrast of the smaller domains. The nested domains within these stripes partly appear with an arrowhead shape. The direction defined by the arrows along the stripe domain walls (highlighted by yellow dashed lines) defines a certain chirality, which is solely set by the in-plane orientation of the domain wall, as schematically shown in Figs. 2(c) and 2(d) by the red loops. This reflects the D 2d symmetry of the crystal; namely, in order to transform from one loop to the other, one has to apply the combination of a 90 • rotation and an inversion, like for the chirality of helices and the nontopological bubbles observed by LTEM in thin-plate samples [30]. This very peculiar feature of the domain pattern is so far unique to Mn 1.4 PtSn and, to the best of our knowledge, has not been reported before for any other fractal magnetic domain pattern. It may be related to the Dzyaloshinskii-Moriya interaction, which is responsible for the existence of antiskyrmions in the material in the first place [27].

B. Domain structure in applied field

Next, we discuss the magnetic-field response of the magnetic texture of Mn 1.4 PtSn. Figure 3(a) shows a series of SANS patterns collected at different field magnitudes applied parallel to the c axis at T = 250 K. For all patterns, the B = 0.57 T scattering (the fully polarized state) was subtracted as background in analogy to Fig. 1(c). The azimuthal intensity profiles were extracted from each SANS pattern and are plotted in Fig. 3(b). The pattern of B = 0.09 T looks very similar to the SANS pattern at zero field; namely, it has the same anisotropic cruciform scattering distribution with the same intensity. The pattern recorded at B = 0.21 T retains the anisotropy with approximately two times lower overall intensity. The SANS pattern at B = 0.33 T demonstrates very low intensity, which is seen only in the vicinity of the center Q ≈ 0, where Q denotes the momentum transfer defined as the difference between the momentum of the scattered neutrons k f and the momentum of the incident neutrons k i , Q = k fk i . Nevertheless, the characteristic cross shape remains quite distinguishable in the pattern. At a higher field of 0.45 T, only a very weak isotropic scattering is observed at small momenta in the vicinity of the direct beam, which indicates a transformation from rectangular towards isotropic domains. Not only is the symmetry of the diffuse scattering preserved in increased magnetic field up to B = 0.33 T, but also the radial I (Q) profiles approximately retain the initial slope, as evidenced in Fig. 3(c), where the profiles are shown for the same set of fields. The data collected at higher fields up to 1.4 T did not reveal any scattering, which confirms that the sample is uniformly magnetized already at 0.57 T.

There are two possible scenarios of the magnetic-structure polarization process that would cause the observed smooth decrease in the intensity of the anisotropic diffuse scattering. The first one implies that in the applied magnetic field the rectangular-domain texture is gradually dissolved into the homogeneous ferromagnetic background. In other words, the sample breaks into coexisting domains of the fully polarized state, growing in volume with an increasing field, and the volume occupied by the densely packed small rectangular domains. In this case, the intensity of the SANS should decrease in accord with the modulated-texture volume, I = I 0 (1 -M z /M s ), where M z /M s is the normalized net magnetization and I 0 is the intensity in zero field. In the opposite scenario, the modulated magnetic texture occupies the entire volume in finite applied fields, but the magnitude of the modulated component of the local magnetization (its in-plane projection) is reduced in favor of the homogeneous M z component. Since the SANS intensity I ∝ M x,y (x, y) 2 , where M x,y (x, y) is the magnetization component modulated in the basal plane, the field dependence of I should read

I = I 0 [1 -(M z /M s ) 2 ].
The integral intensities (integrated along the stripes) of the diffuse scattering were extracted from the SANS patterns, 4(c), the nested domains within the antiparallel magnetized stripe domains (shown in green) disappear, yet the edges of those obey a sawtooth shape. In turn, in the stripe domains magnetized parallel to the field, the number of nested domains increases. Between B = 250 and 350 mT, the sawtooth shape of the domain walls is lost, and the nested domains appear with both a more rounded shape and less ordering, shown in Figs. 4(d) to 4(f). For further increasing field magnitudes, the antiparallel magnetized domains start to disappear, and only a few bubble domains or very large antiskyrmions are left over for B > 400 mT [see Fig. 4(h)]. The last of those switches into the field-polarized state when B = 450 mT is reached, consistent with the isothermal magnetization curve, taking into account the limited field of view of the MFM. Overall, there is perfect agreement between the real-space images and the behavior of the diffuse scattering pattern described before.

C. Magnetic texture at T < T SR

Finally, it is important to understand how the magnetic texture changes with temperature. The crucial point is whether or not the rectangular domain structure persists at any T < T C , including temperatures below the spin-reorientation (SR) transition T SR = 170 K. The SR transition in Mn 1. 4 PtSn can be detected by a step in the temperature-dependent magnetic susceptibility and by a kink in the resistivity [38,39]. Powder neutron diffraction measurements showed that the local (on the scale of the unit cell) magnetic structure of Mn 1.4 PtSn is collinear ferromagnetic above T SR and becomes canted (noncollinear) ferromagnetic below T SR [38,[START_REF] Kumar | [END_REF]. The correlations between the local (within the unit cell) magnetic configuration and the topology of the large-scale magnetic texture seemed controversial. On the one hand, the magnetotransport measurements of bulk single crystals revealed a topological Hall effect (THE) below T SR [38], which is widely associated with the skyrmion phase in other materials [54][55][56][57][58][59][60] (antiskyrmions are expected to give rise to a THE similar to that of skyrmions [6]). On the other hand, the LTEM measurements [27][28][29][30] demonstrated that the antiskyrmions nucleate only at T > T SR , which suggests that the THE is related to the local noncollinear structure.

Again, we first describe the SANS measurements. Figure 5(a) shows SANS patterns (no background subtraction) collected after zero-field cooling to two temperatures above T SR , namely, T = 280 and 180 K, as well as to two temperatures below T SR , namely, T = 160 K and T = 90 K. The corresponding azimuthal profiles and the radial profiles of the intensity are plotted in Figs. 5(b) and 5(c), respectively. The patterns at 280 and 180 K exhibit the same anisotropy. Despite the fact that the magnetic moment is reduced at higher temperatures due to thermal fluctuations (which reduces the intensity of magnetic scattering at elevated temperatures), the intensity at 280 K is significantly higher. At T = 160 K, which is just below T SR , the stripes of intensity can still be distinguished but have much weaker intensity than at T = 180 K. Far below T SR at 90 K, the cross-shaped scattering disappears completely. The remaining diamond-shaped scattering is similar to the pattern at the field-polarized state at 250 K [Fig. 1(b)]. Finally, in Fig. 5(d), the scattering intensity of the 100 streaks is plotted as a function of temperature. It decreases upon cooling with a kink at T = T SR . This shows that the fractal magnetic domain pattern is inherent in the high-temperature phase with the locally collinear magnetic order. However, it does not transform to the homogeneous state immediately below the SR transition. Instead, traces of the anisotropic scattering are present over a 20-30 K wide region below T SR , which correlates with the gradual change in the spin canting within the unit cell [38,[START_REF] Kumar | [END_REF].

The loss of the fractal self-affinity as well as the absence of lamellar stripe domains in zero field is apparent from the MFM measurements obtained below at T SR both T = 140 and 80 K, which we show in Figs. 6(a) and 6(c), respectively. This is also supported by the fitting of the low-temperature SANS data (Fig. S4 in the Supplemental Material [37]), which is described by the exponent D that is close to simple Porod scattering. Moreover, also the strong anisotropic pinning of the domain walls to two perpendicular directions within the ab plane is lost. Interestingly, in higher fields, again, round-shaped domains appear before the field-polarized state is reached [see Figs. 6(b) and6(d)]. In comparison to the reported LTEM measurements [27][28][29][30], where antiskyrmions were present only above T SR , it is very likely that the domains here are (closure) bubble domains rather than antiskyrmions.

IV. DISCUSSION AND CONCLUSIONS

To conclude, we used a combination of SANS and MFM to study the bulk magnetic structure of Mn 1. 4 PtSn and showed that it differs drastically from what was previously reported from LTEM measurements of thin-plate samples. The bulk Mn 1.4 PtSn does not support antiskyrmions or any other type of regular long-periodic single-q or multi-q structures but develops ferromagnetic lamellar stripe domains combined with an anisotropic fractal surface domain pattern that has a characteristic scale with a lower boundary of ∼48 nm and an upper boundary of ∼3 μm defined by the width of the lamellar stripe domains. This magnetic pattern gives rise to an anisotropic diffuse intensity distribution in SANS and, to the best of our knowledge, was previously observed only in the low-temperature phase of Nd 2 Fe 14 B. Yet it differs from the latter in the presence of characteristic hints of the DMI inherent in the D 2d symmetry of the crystal, which manifest in the orientation of arrowhead-shaped nested domains at the domain walls of the lamellar stripe domains. Our measurements showed that the magnetic texture of bulk Mn 1.4 PtSn is polarized by the applied magnetic field in a multistep process. During the first step, the spins gradually cant towards the field direction, keeping the overall domain pattern unaffected. During the second step, the fractal domain pattern softens, and the nested domains transform into an assembly of bubble domains. Finally, in the third step, only the bubble domains persist and switch individually into the field-polarized state. The latter two steps resemble the metamagnetic phases of the dense antiskyrmion lattice and the isolated antiskyrmions in the ferromagnetic background, respectively, observed in the thin plates [27][28][29][30]. Like the antiskyrmions in the thin-plate geometry, the fractal magnetic pattern of the bulk Mn 1.4 PtSn appears for T > T SR and shows an enhanced stability at elevated temperatures, which further demonstrates the intimate connection between the magnetic structure in the bulk and in the thin plates.

To the best of our knowledge, Mn 1.4 PtSn is therefore the first known material where the magnetic texture can be unambiguously tuned between ferromagnetic domains with an anisotropic fractal closure domain pattern in zero field or bubble domains in high field in bulk samples and helices or antiskyrmions in the thin-plate geometry. A sizable anisotropic DMI allowed in the D 2d symmetry, if present, will result in a modulated texture with a period defined by the ratio between the exchange interaction J and the DMI constant D, λ ∝ J/D, independent of the sample thickness. Contrary to the previous interpretations of the experiments on the thin plates, the observed complex multiscale domain-wall structure of bulk Mn 1.4 PtSn suggests that the DMI plays only a minor role in this material. The other relevant magnetic energy terms include the second-order uniaxial and fourthorder in-plane magnetocrystalline anisotropies, as well as the sample thickness-dependent dipole-dipole energy, the competition of which is known to influence the width of domain walls [START_REF] Hubert | Magnetic Domains: The Analysis of Magnetic Microstructures[END_REF][61][62][START_REF] Yu | Proc. Natl. Acad. Sci. USA[END_REF]. Thus, our findings highlight the importance of the dipolar interaction as an essential ingredient to describe the magnetic texture of Mn 1.4 PtSn. This was also realized to important for explaining all the observations in recent LTEM experiments [29,30].

Moreover, we may speculate that new materials may be (anti)skyrmion hosts in the thin-plate geometry even if they have not been identified as such in bulk experiments. Possible candidates would be uniaxial materials with fractal closure domains in the bulk and with D 2d symmetry. Since a noncentrosymmetric crystal symmetry is the only necessary condition for the possible existence of (anti)skyrmions, the range of materials could be even larger. Vice versa, like for Mn 1.4 PtSn, materials that support (anti)skyrmions in the thinplate geometry could show more complicated domain patterns in the bulk. For example, this could be the case for Cr 11 Ge 19 , which hosts biskyrmions in thin-plate geometry [START_REF] Takagi | [END_REF].

Note added. Recently, we became aware of a thicknessdependent study in the range up to 4 μm of the magnetic texture in Mn 1.4 PtSn [65]. The authors explained the crucial role of dipolar forces in the material by rigorous simulations, which fully agree with the conclusions drawn in our study.

FIG. 1 .

 1 FIG. 1. The SANS patterns of Mn 1.4 PtSn at 250 K. (a) The SANS pattern at zero field. The sample orientation is depicted by white arrows. (b) The scattering in the field-saturated state at 0.57 T. (c) The result of the subtraction of the SANS map recorded at 0.57 T from the map at 0 T. (d) The comparison of the intensity profiles for the momenta along [100] and [110]. (e) The intensity profiles as a function of the azimuthal angle φ. (f) The radial intensity profile of the background-subtracted data (symbols) and the fit by the power function (solid line).

FIG. 2 .

 2 FIG. 2. The magnetic domain pattern of Mn 1.4 PtSn at room temperature. (a) MFM phase image showing the domain pattern in the ab plane at zero field and (b) its fast Fourier transform. (c) and (d) depict the zoomed area marked in (a) by the turquoise and orange squares, respectively. They are filtered for enhanced contrast of the smaller domains. The red loops highlight the chiral sense of the pattern of triangular-shaped nested domains at the domain walls (yellow dashed line) of the lamellar stripe domains. The numbers written in the bars correspond to the length of the bars. Note that the reciprocal-space scale in (b) is much smaller than the momentum range covered in the SANS patterns.

FIG. 3 .

 3 FIG. 3. Magnetic field dependence of the SANS signal at T = 250 K. (a) A series of SANS patterns (after background subtraction) collected in different magnetic fields applied along the c axis. (b) The azimuthal profiles of the scattering extracted from each pattern. (c) The radial intensity profiles at the same fields. (d) The integral intensity of the magnetic scattering as a function of the applied field (symbols) and the magnetization M(H ) curve measured at the same temperature and field orientation. The dashed lines are the approximations by parabolic and linear functions (see the text). The black arrow marks the crossover between the two field-polarizing regimes.

FIG. 4 .

 4 FIG. 4. Magnetic field dependence of the domain pattern in MFM at T = 240 K. Sample magnetization parallel and antiparallel to the external field is shown in purple and green, respectively. The frame size is equal for all images; the span of the color scale has been adapted individually.

FIG. 5 .

 5 FIG. 5. Temperature dependence of the SANS signal at zero field. (a) A series of SANS patterns (no background subtraction) collected at different temperatures in zero-field cooling. (b) The azimuthal profiles of the scattering extracted from each patter. (c) The radial intensity profiles at the same temperatures. (d) The integral intensity of the magnetic scattering as a function of T . The black arrow marks the spin-reorientation transition.

FIG. 6 .

 6 FIG. 6. Magnetic domain pattern in MFM below T SR at (a) and (b) T = 140 K and (c) and (d) T = 80 K both (a) and (c) in zero field and (b) and (d) in high field. Sample magnetization parallel and antiparallel to the external field is shown in purple and green, respectively. The span of the color scale has been adapted individually.

Fig. S2 .

 S2 Fig. S2. The magnetic domain pattern of Mn1.4Pt0.9Pd0.1Sn polycrystal at room temperature. (a) EBSD measurement showing in blue crystallites with their c-axis approximately normal to the surface of the sample. The inset shows the orientation of the unit cell. The contours of the c-axis oriented grains are shown in red. (b) MFM image at the same position with the contours of the c-axis oriented grains shown in red. (c) Larger overview image. Note the dependency of bending direction of the sawtooth shaped domains on the in-plane orientation. Two areas are highlighted by red circles.

FigI

  Fig. S3. A SANS pattern of the (HHL) reciprocal plane recorded at T = 250 K and zero field.

A. K. Nayak, V. Kumar, T. Ma, P. Werner, E. Pippel, R. Sahoo, F. Damay, U. K. Rössler, C. Felser, and S. S. P. Parkin, Nature (London) 548, 561 (2017).

ACKNOWLEDGMENTS A.S.S. thanks S. E. Nikitin for many stimulating discussions. B.E.Z.C. thanks U. Burkhardt and S. Kostmann for electron backscatter diffraction measurements and polishing of the polycrystalline sample. This project was funded by the German Research Foundation (DFG) under Grants No. FE 633/30-1, No. IN 209/9-1, No. EN 434/38-1, and No. MI 2004/3-1, as well as Grants No. EN 434/40-1 and No. IN 209/7-1 as part of the Priority Program SPP 2137 "Skyrmionics"; via Projects C03 and C05 of the Collaborative Research Center SFB 1143 (Project-id 247310070) at TU Dresden; and the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter-ct.qmat (EXC 2147, Project-id 390858490). A.S.S. and B.E.Z.C. acknowledge support from the International Max Planck Research School for Chemistry and Physics of Quantum Materials (IMPRS-CPQM).

Anisotropic fractal magnetic domain pattern in bulk Mn 1. 4 PtSn -Supplemental information A. S. Sukhanov, 1, 2 B. E. Zuniga Cespedes, 1, 3 P. Vir, 1 A. S. Cameron, 2 A. Heinemann, 4 N. Martin, 5 G. Chaboussant, 5 V. Kumar, 6 P. Milde, 3 L. M. Eng, 3, 7 C. Felser, 1, 7 and D. S. Inosov 2, 7

1 Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany 2 Institut für Festkörper-und Materialphysik, Technische Universität Dresden, D-01069 Dresden, Germany

3 Institute of Applied Physics, Technische Universität Dresden, D-01069 Dresden, Germany 4 German Engineering Materials Science Centre (GEMS) at Heinz Maier-Leibnitz Zentrum (MLZ), Helmholtz-Zentrum Geesthacht GmbH, D-85747 Garching, Germany Supplemental information showing a photograph of the sample used for small-angle neutron scattering measurements, complementary magnetic force microscopy measurements on a polycrystal of Mn1.4Pt0.9Pd0.1Sn, an additional SANS pattern for the c-axis perpendicular to the incident neutron beam, and the analysis of the SANS intensity profile at a low temperature. Polycrystalline ingots Mn 1.4 Pt 0.9 Pd 0.1 Sn were prepared by arc-melting stoichiometric amounts of the constituent elements in a high-purity argon atmosphere. Details of the procedure and structural characterization are given in Ref. 1 .

A. Sample used for SANS measurements

The surface of a polycrystalline sample with crystallite sizes in the order of tens of micrometers was mechanically polished. Further, we used electron backscatter diffraction (EBSD) to identify grains with their c-axis oriented approximately normal to the surface, shown in blue in Fig. S2(a) with the angle between surface normal and c-axis measuring up to 10 • . Later, topographic features where used to identify the same location in the magnetic force microscope (MFM).

In Fig. S2(b) we show the same sample area as measured by MFM. The grain boundaries extracted from the EBSD measurement are shown in red. Apparently, magnetic domains observed in the ab-plane are very different from the domains in grains with other orientations. Thus, the shape of the grains observed by EBSD are also easily recognized in the MFM images.

In the ab-plane (blue grains), again the same anisotropic fractal domain pattern as for the Mn 1.4 PtSn single crystal is visible. For the other grains, we see a side view (actually the angle is not necessarily 90 • ) of the same pattern. There, the nested domains can easily be identified as they do not propagate through the whole crystallite but appear with an anisotropic sawtooth shape. The bending direction of this shape again depends on the in-plane orientation and reflects the D 2d symmetry of the crystal, as shown in Fig. S2(c). Also, the nested domains form a fractal tree structure along the c-axis. This proves that indeed the fractal domain pattern seen in the ab-plane consists of closure domains.

C. Absence of SANS intensity for the out-of-plane momenta

Figure S3 shows a SANS pattern obtained when the incident neutron beam is perpendicular to the crystallographic [001] direction of Mn 1.4 PtSn. For this, the sample was rotated by 90 • around the vertical [110] axis. Thus, the pattern shows the intensity of SANS scattering in the (HHL) reciprocal plane. As can be seen, the obtained scattering distribution is featureless and matches the nearly isotropic background scattering observed in the (HK0) plane at a high magnetic field [Fig. 1(b) of the main text], in which the sample is fully polarized. This confirms that the anisotropic magnetic diffuse scattering discussed in the main text is present only in the basal plane of the material.