Gilles Daigre

Patrick Gougeon
email: patrick.gougeon@univ-rennes1.fr

Philippe Gall

Odile Merdrignac-Conanec

Rabih Al

Rahal Al Orabi

Regis Gautier

Anne Dauscher

Christophe Candolfi
email: christophe.candolfi@univ-lorraine.fr

Bertrand Lenoir

Odile Connanec-Merdrignac

Régis Gautier

Unravelling the Beneficial Influence of Ag insertion on the Thermoelectric Properties of the Cluster Compound K2Mo15Se19

Keywords: Thermoelectric, molybdenum clusters, semiconductors, thermal conductivity, single crystal

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In 1971, R. Chevrel, M. Sergent and J. Prigent discovered the "Chevrel phases" of generic chemical formula MxMo6X8 (M = rare-earth, transition metals, Na, Ca, Sr, Ba, Sn, Pb; X = S, Se, Te), the crystal structure of which is built up by octahedral Mo6 clusters. [START_REF] Chevrel | Sur de nouvelles phases sulfurées ternaires du molybdène[END_REF] These compounds exhibit many interesting physical properties such as high-field superconductivity in PbMo6S8 or the coexistence of superconductivity and ferromagnetic order in HoMo6Se8. 2 The inherent metallic character of the electrical conduction in these compounds originates from the nature of the top of the valence bands, the presence of inter-cluster interactions and the flexibility of the electron count, that is, of the charge transfer between the Mo6 clusters and the M cations.

Following these pioneering works, condensed molybdenum-based clusters Mo9 and Mo12 were obtained by increasing the metal-to-chalcogen ratio. [START_REF] Gougeon | Ag3.6Mo9Se11 Premier Composé à Clusters Mo9 dans des Motifs Mo9Se11[END_REF][START_REF] Gougeon | Crystal Structure and Electrical Properties of the First Compound Containing Uniquely Mo12Se14 Cluster Units[END_REF][START_REF] Gautier | Crystal and Electronic Structures, and Electrical Properties of Rb2Mo12Se14 Containing Trioctahedral Mo12 Clusters[END_REF] The condensation process is realized by sharing Mo3 opposite triangular faces of the Mo6 octahedra whose ultimate stage leads to the uniaxial infinite chain of face-faced octahedra |Mo 6/2 | ∞ observed in the quasi-1D

M2Mo6X6 compounds (M = Na, Rb, Cs, Tl, In and X = S, Se, Te). [START_REF] Tarascon | Physical properties of several M2Mo6X6 compounds (M = GROUP IA METAL; X = Se, Te)[END_REF] Of note, the nearly 1D character of the crystal structure of these compounds gives rise to exotic superconductivity and possibly to novel types of fermionic excitations due to topologically non-trivial electronic band structures. [START_REF] Petrovic | A disorder-enhanced quasi-one-dimensional superconductor[END_REF][START_REF] Gannon | Lattice dynamics of the cluster chain compounds M2Mo6Se6 (M = K, Rb, Cs, In, and Tl)[END_REF][START_REF] Mitra | Dimensional crossover in the quasi-one-dimensional superconductor Tl2Mo6Se6[END_REF][START_REF] Liu | Predicted Realization of Cubic Dirac Fermion in Quasi-One-Dimensional Transition-Metal Monochalcogenides[END_REF] So far, the intermediate Mo9, Mo12, Mo15, Mo18, Mo21, Mo24, Mo30 and Mo36 clusters have been observed in various compounds. [START_REF] Gougeon | Ag3.6Mo9Se11 Premier Composé à Clusters Mo9 dans des Motifs Mo9Se11[END_REF][START_REF] Gougeon | Crystal Structure and Electrical Properties of the First Compound Containing Uniquely Mo12Se14 Cluster Units[END_REF][START_REF] Gautier | Crystal and Electronic Structures, and Electrical Properties of Rb2Mo12Se14 Containing Trioctahedral Mo12 Clusters[END_REF][START_REF] Gougeon | Structure of Rb3Mo15Se17 Containing the New Mo15 Clusters[END_REF][START_REF] Picard | Rb2n(Mo9S11)(Mo6nS6n+2) (n = 1 to 4): A Novel Family of Superconducting Molybdenum Cluster Compounds[END_REF][START_REF] Picard | Single-Crystal Structure of Cs5Mo21S23[END_REF] However, the thermoelectric properties of some of these ternary and quaternary molybdenum chalcogenides have only been assessed recently. [START_REF] Zhou | Promising Thermoelectric Properties in AgxMo9Se11 Compounds (3.4 ≤ x ≤ 3.9)[END_REF][START_REF] Zhou | Comprehensive Study of the Low-Temperature Transport and Thermodynamic Properties of the Cluster Compounds AgxMo9Se11 (3.41 ≤ x ≤ 3.78)[END_REF][START_REF] Gougeon | Crystal and Electronic Structures, and Thermoelectric Properties of the Novel Cluster Compound Ag3In2Mo15Se19[END_REF][START_REF] Rahal | X-ray Characterization, Electronic Band Structure, and Thermoelectric Properties of the Cluster Compound Ag2Tl2Mo9Se11[END_REF][START_REF] Rahal | Cu Insertion Into the Mo12 Cluster Compound Cs2Mo12Se14: Synthesis, Crystal and Electronic Structures, and Physical Properties[END_REF][START_REF] Daigre | Crystal Structure and High-Temperature Transport Properties of the New Cluster Compound Rb2Mo15Se19[END_REF][START_REF] Masschelein | Influence of S and Te substitutions on the thermoelectric properties of the cluster compound Ag3.8Mo9Se11[END_REF][START_REF] Colin | Optimization of Bulk Thermoelectrics: Influence of Cu Insertion in Ag3.6Mo9Se11[END_REF][START_REF] Gougeon | Crystal Structure, and Transport Properties of the Hexagonal Mo9 Cluster Compound Ag3RbMo9Se11[END_REF][START_REF] Gougeon | Electronic Band Structure and Transport Properties of the Cluster Compound Ag3Tl2Mo15Se19[END_REF] Their inherent structural complexity, arising from a high number of atoms per unit cell and the presence of cations in the inter-cluster voids, is the key ingredient leading to very low lattice thermal conductivity 𝜅 𝑝ℎ .

Combined with electrical properties that can gradually evolve from metallic to semiconductinglike by inserting additional cations, this property can potentially yield high dimensionless thermoelectric figures of merit 𝑍𝑇 = 𝛼 2 𝑇/𝜌(𝜅 𝑒 + 𝜅 𝑝ℎ ) which determine the efficiency of a thermoelectric material at an absolute temperature 𝑇. [START_REF] Zhou | Promising Thermoelectric Properties in AgxMo9Se11 Compounds (3.4 ≤ x ≤ 3.9)[END_REF][START_REF] Zhou | Comprehensive Study of the Low-Temperature Transport and Thermodynamic Properties of the Cluster Compounds AgxMo9Se11 (3.41 ≤ x ≤ 3.78)[END_REF][START_REF] Gougeon | Crystal and Electronic Structures, and Thermoelectric Properties of the Novel Cluster Compound Ag3In2Mo15Se19[END_REF][START_REF] Rahal | X-ray Characterization, Electronic Band Structure, and Thermoelectric Properties of the Cluster Compound Ag2Tl2Mo9Se11[END_REF][START_REF] Rahal | Cu Insertion Into the Mo12 Cluster Compound Cs2Mo12Se14: Synthesis, Crystal and Electronic Structures, and Physical Properties[END_REF][START_REF] Daigre | Crystal Structure and High-Temperature Transport Properties of the New Cluster Compound Rb2Mo15Se19[END_REF][START_REF] Masschelein | Influence of S and Te substitutions on the thermoelectric properties of the cluster compound Ag3.8Mo9Se11[END_REF][START_REF] Colin | Optimization of Bulk Thermoelectrics: Influence of Cu Insertion in Ag3.6Mo9Se11[END_REF][START_REF] Gougeon | Crystal Structure, and Transport Properties of the Hexagonal Mo9 Cluster Compound Ag3RbMo9Se11[END_REF][START_REF] Gougeon | Electronic Band Structure and Transport Properties of the Cluster Compound Ag3Tl2Mo15Se19[END_REF] The main challenge then lies in achieving concomitantly high thermopower 𝛼, low electrical resistivity 𝜌, and low electronic thermal conductivity 𝜅 𝑒 .

First studies performed on the Chevrel phases revealed their potential for hightemperature thermoelectric applications with a maximum ZT of 0.6 at 1150 K for Cu2FeMo6Se8, rivaling those obtained in the state-of-the-art Si-Ge solid solutions. [START_REF] Caillat | Potential of Chevrel phases for thermoelectric applications[END_REF][START_REF]Thermoelectrics and Its Energy Harvesting[END_REF] Later on, initial investigations of the thermoelectric properties of the AgxMo9Se11 (3.4 ≤ x ≤ 3.8) compounds revealed equivalent ZT values at 800 K (ZT of 0.65 for x = 3.8) that notably arise from their very low lattice thermal conductivity approaching the amorphous limit at 800 K (0.5 W m -1 K - 1 ). [START_REF] Zhou | Promising Thermoelectric Properties in AgxMo9Se11 Compounds (3.4 ≤ x ≤ 3.9)[END_REF][START_REF] Zhou | Comprehensive Study of the Low-Temperature Transport and Thermodynamic Properties of the Cluster Compounds AgxMo9Se11 (3.41 ≤ x ≤ 3.78)[END_REF][START_REF] Colin | Optimization of Bulk Thermoelectrics: Influence of Cu Insertion in Ag3.6Mo9Se11[END_REF] The physical origin of this glass-like thermal transport is related to the large voids separating the Mo9Se i 11Se a 6 bioctahedral clusters in which Ag + cations occupy four independent crystallographic sites and show large anisotropic thermal displacement parameters. The polymorph compounds Ag2Tl2Mo9Se11 and Ag3RbMo9Se11 that crystallize in the hexagonal space groups 𝑅3 ̅ 𝑐 and P63/m, respectively, also combine very low 𝜅 𝑝ℎ values and semiconducting behavior yielding peak ZT values of 0.6 and 0.4 at 800 K, respectively. [START_REF] Rahal | X-ray Characterization, Electronic Band Structure, and Thermoelectric Properties of the Cluster Compound Ag2Tl2Mo9Se11[END_REF][START_REF] Gougeon | Crystal Structure, and Transport Properties of the Hexagonal Mo9 Cluster Compound Ag3RbMo9Se11[END_REF] The M2Mo15Se19 (M = K, Ba, In, Tl, Rb) compounds are another family investigated for their thermoelectric properties. [START_REF] Gougeon | Crystal and Electronic Structures, and Thermoelectric Properties of the Novel Cluster Compound Ag3In2Mo15Se19[END_REF][START_REF] Daigre | Crystal Structure and High-Temperature Transport Properties of the New Cluster Compound Rb2Mo15Se19[END_REF][START_REF] Gougeon | Electronic Band Structure and Transport Properties of the Cluster Compound Ag3Tl2Mo15Se19[END_REF] Their crystal structure contains both Mo6Se i 8Se a 6 and Mo9Se i 11Se a 6 cluster units in equal proportion that delineates large voids where the M cations reside. In agreement with electronic band structure calculations, 26 metallic electron counts (MEC) indicate that these materials are metallic, assuming a monovalent character of the M cations. Driving these metallic properties towards semiconducting-like properties can be realized in filled variants by inserting additional cations such as Ag. This strategy has been successfully applied for M = In and Tl resulting in higher thermoelectric performances than in Ag-free compounds with peak ZT values of 0.45 and 0.20 at 1100 and 800K, respectively. [START_REF] Gougeon | Crystal and Electronic Structures, and Thermoelectric Properties of the Novel Cluster Compound Ag3In2Mo15Se19[END_REF][START_REF] Gougeon | Electronic Band Structure and Transport Properties of the Cluster Compound Ag3Tl2Mo15Se19[END_REF] Following these encouraging results, we explore herein the transport properties of the isostructural compounds K2Mo15Se19 and Ag3K2Mo15Se19 to further elucidate the influence of the nature of the M cations on the thermoelectric properties. The experimental results are compared with those reported on the In and Tl compounds outlined above and complemented by calculations of the electronic density of states.

RESULTS AND DISCUSSION

The two compounds K2Mo15Se19 and Ag3K2Mo15Se19 are isostructural to In2Mo15Se19 and Ag3In2Mo15Se19, respectively, that both crystallize in the space group 𝑅3 ̅ 𝑐 (Tables 1 and2).

Their crystal structures are based on the two cluster units Mo6Se8Se6 and Mo9Se11Se6, the threedimensional arrangement of which is shown in Figure 1. These two units share ligands via the Mo1-Se2 and Se1-Mo2 bonds to ensure the three-dimensional cohesion of the crystal structure (Figure 2). Compared to the K2Mo15Se19 compound, the insertion of Ag atoms results in distorted Se sites forming trigonal bipyramids located between two consecutive K sites and in a modification of the K environment (Figures 3a and3b). A clear shift of the K atoms towards the Se5 atoms is indeed observed with a significant decrease in the distance K-Se5 from 3.6760 (15) Å in K2Mo15Se19 to 3.260(2) Å in Ag2.2K2Mo15Se19. In contrast, the Se3 and Se4 atoms move away from K with K-Se3 and K-Se4 distances of 4.062(1) Å and 3.674(2) Å in Ag2.2K2Mo15Se19 instead of 3.7891(7) Å and 3.4256(15) Å in K2Mo15Se19.

Ag insertion leads to variations in the Mo-Mo distances in both clusters due to the increase in the cationic charge transfer. In the Mo6 cluster (Table 3), a shortening of the inter-triangular distance Mo1-Mo1 from 2.7675(3) Å in K2Mo15Se19 to 2.7146(4) Å in Ag2.2K2Mo15Se19 is observed upon increasing the cationic charge. In contrast, the intra-triangular Mo1-Mo1 distances remain practically unchanged. In the Mo9 cluster, in addition to the decrease in the inter-triangular Mo2-Mo3 distances (2.7138(2) Å to 2.6873(2) Å), the intra-angular Mo3-Mo3 distance increases from 2.6821(3) Å in K2Mo15Se19 to 2.7158(5) Å in Ag2.2K2Mo15Se19. This modification is accompanied by a shortening of the intra-triangular Mo2-Mo2 distances from 2.6682(3) Å to 2.6424(4) Å. All these variations in the interatomic distances are consistent with the theoretical calculations (see below) carried out on the host structure K2Mo15Se19.

The PXRD patterns of both polycrystalline specimens, shown in Figure 4, were successfully indexed by the structure model derived from single-crystal X-ray diffraction data.

These data indicate the absence of secondary phases within experimental uncertainty. Rietveld refinements against the diffraction data for Ag3K2Mo15Se19 showed that the occupancy factor of the Ag atom is 0.493 (9), in very good agreement with the nominal chemical composition that corresponds to an occupancy factor of 0.5. The crystallographic parameters determined from these refinements are given in Table S1 in Supporting Information. The atomic coordinates, equivalent isotropic displacement parameters and selected interatomic distances are listed in Table S2 andS3, respectively.

The good chemical homogeneity of the two samples is further confirmed by elemental Xray mapping (Figures S4 and S5 in Supporting Information) indicating that Ag and K are homogeneously distributed. In the Ag3K2Mo15Se19 compound, these experiments further indicate the presence of very small Ag-rich or K-rich areas, suggesting that local, weak compositional fluctuations in the Ag/K ratio exist in this sample. The possibility that the overall cation content slightly varies spatially is in agreement with the single-crystal X-ray diffraction data evidencing an under-stoichiometric Ag concentration in the single-crystals studied.

Nevertheless, as shown by these images, these Ag-or K-rich areas are very small and are thus not expected to significantly impact the measured transport properties. Fracture images collected on both samples evidence some differences in the microstructure of both samples (Figure S6 in Supporting Information). While the Ag3K2Mo15Se19 compound is composed of micron-sized particles homogeneously distributed, the Ag-free compound is rather characterized by a coexistence of similar large grains with smaller ones, suggesting a broader size distribution than in Ag3K2Mo15Se19. The corresponding elemental X-ray mappings (Figures S7 and S8 in Supporting Information) show that this difference in the microstructure does not affect the homogeneous distribution of Ag and K in both polycrystalline samples.

The metallic electron count (MEC), that is, the number of electrons available for the formation of Mo-Mo bonds, optimizes metal-metal bonding in the Mo9Se11 and Mo6Se8 clusters when equal to 36 and 24, respectively. [START_REF] Gougeon | Crystal and Electronic Structures, and Thermoelectric Properties of the Novel Cluster Compound Ag3In2Mo15Se19[END_REF] Assuming the absence of significant interaction between these clusters, the optimum MEC for the Mo15Se19 subnetwork is thus equal to 60. The electronic DOS and COHP curves calculated for different Mo-Mo bonds confirm this analysis.

The Fermi level is located almost at the top of the valence bands, predominantly centered on the Mo atoms. The small contribution of K states to the occupied bands confirms the ionic interaction with the transfer of 4s electrons from K to the Mo15Se19 subnetwork (Figure 5). The COHP curves calculated for the Mo-Mo bonds in the Mo6 and Mo9 clusters show that the vacant bands at the top of the valence bands have mostly a weakly bonding or weakly anti-bonding character (Mo3-Mo3). Hence, these vacant bands can be considered as non-bonding as a first approximation. The COHP for the Mo1-Mo2 inter-cluster, shown in Figure 6, confirms the weak interaction between these patterns. A band gap of about 0.5 eV separates the valence bands from the anti-wear strips. Within a rigid-band model (that is, independent of the electron count), an increase in the MEC up to 60 should therefore be possible without significantly altering the architecture of K2Mo15Se19.

For Ag3K2Mo15Se19, each inserted Ag atom transfers its valence electrons to the Mo-Se framework which increases the overall MEC of the Mo15Se19 clusters to 57. The variations in the Mo-Mo distances observed in single-crystal X-ray diffraction data (Table 3) are in agreement with those expected in view of the COHP curves, considering the occupation of the bands located just above the Fermi level in K2Mo15Se19. Indeed, the observed shortening of the distances Mo1-Mo1, Mo2-Mo2 and Mo2-Mo3 is consistent with the Mo-Mo bonding character that binds bands above the Fermi level in K2Mo15Se19 (Figures 7 and8). In contrast, the antibonding character of the Mo3-Mo3 and the intra-triangular Mo1-Mo1 bonds explains the observed increase in these distances upon inserting Ag.

According to the above-mentioned considerations of the MEC in these two compounds, the insertion of Ag into K2Mo15Se19 should drive this compound towards a more heavily-doped semiconducting state. This expectation should therefore be synonymous with an increase in the thermopower 𝛼 in Ag3K2Mo15Se19 with respect to K2Mo15Se19. A comparison of the temperature dependences of 𝛼, shown in Figure 9a, confirms this simple picture with a significant increase in the 𝛼 values in Ag3K2Mo15Se19 over the entire temperature range.

However, a concomitant increase in 𝜌 that may be expected due to a decrease in the carrier concentration is not observed (Figure 9b). In contrast, Ag3K2Mo15Se19 shows lower 𝜌 values compared to K2Mo15Se19, resulting in higher power factor compared to the Ag-free compound (Figure S9 in supporting Information). This trend is not due to differences in the relative density of the two polycrystalline samples since both consolidated pellets exhibit similar geometric densities. This difference may be related to the different microstructures of the two samples evidenced by fracture images. The broader distribution of grain size suggested by these images in K2Mo15Se19 may result in lower carrier mobilities resulting in increased 𝜌 values.

Alternatively to microstructure effects, a decrease in the electron-phonon coupling strength induced by the addition of Ag could also explain higher hole mobilities in Ag3K2Mo15Se19 compared to K2Mo15Se19, as suggested recently in the Cs2Mo12Se14 cluster compound upon Cu insertion. [START_REF] Rahal | Cu Insertion Into the Mo12 Cluster Compound Cs2Mo12Se14: Synthesis, Crystal and Electronic Structures, and Physical Properties[END_REF] A detailed analysis of this possibility based on Hall effect measurements is however complicated in the present compounds due to the high hole concentrations giving rise to small Hall signals difficult to resolve experimentally, should it be measured at low or high temperatures. Indeed, as documented for several other Mo-based cluster compounds, the Hall signal is often composed of electron-like and hole-like contributions which tend to cancel out. 14- 23 The total thermal conductivity 𝜅, shown in Figure 9c, exhibits a similar linear temperature dependence in both compounds, varying upon warming from 1.0 and 1.2 W m -1 K -1 at 300 K to 1.6 and 2.0 W m -1 K -1 at 800 K in the Ag3K2Mo15Se19 and K2Mo15Se19 compounds, respectively. The electronic thermal conductivity 𝜅 𝑒 has been estimated using the Wiedemann-Franz law 𝜅 𝑒 = 𝐿𝑇/𝜌 where 𝐿 is the Lorenz number (Figure S10 in Supporting Information).

In order to take into account possible variations in 𝐿 in this temperature range, the temperature dependence of 𝐿 has been calculated assuming a single-parabolic band model with acoustic phonon scattering. The subtraction of 𝜅 𝑒 from 𝜅 leaves the lattice contribution 𝜅 𝑝ℎ , shown in Figure 9c as a function of temperature for both compounds. The insertion of Ag leads to a substantial reduction in the heat transport from 1.05 W m -1 K -1 in K2Mo15Se19 to 0.45 W m -1 K - 1 in Ag3K2Mo15Se19 at 800 K. This strong decrease in 𝜅 𝑝ℎ is a result of an increased complexity in the unit cell and of the probable presence of additional low-energy optical modes related to the large thermal motion of the Ag atoms. The addition of Ag helps to bring the heat transport down to its theoretical minimum estimated by the model developed by Cahill and Pohl where the high-temperature limit of the minimum thermal conductivity 𝜅 𝑚𝑖𝑛 is expressed as 27

𝜅 𝑚𝑖𝑛 = 1 2 ( 𝜋 6 ) 1/3 𝑘 𝐵 𝑉 -2/3 (2𝑣 𝑇 + 𝑣 𝐿 ) (1)
In this expression, 𝑘 𝐵 is the Boltzmann constant, 𝑉 is the atomic volume and 𝑣 𝑇 and 𝑣 𝐿 are the transverse and longitudinal sound velocities. In the present case, room-temperature measurements of 𝑣 𝑇 and 𝑣 𝐿 by a pulse-echo method yields 𝜅 𝑚𝑖𝑛 ≈ 0.45 W m -1 K -1 for both compounds.

The temperature dependence of the dimensionless thermoelectric figure of merit ZT, shown in Figure 9d, evidences the overall beneficial influence of Ag on the thermoelectric properties of K2Mo15Se19. The concomitant increase in the power factor 𝛼 2 /𝜌 and decrease in 𝜅 𝑝ℎ driven by the insertion of Ag results in a nearly eightfold increase in the ZT values with a peak value of 0.18 at 800 K. This maximum value is similar to that achieved in the Tl-containing analogue (0.19 at 800 K) but lower than that obtained in the In-containing compound (0.26 at 800 K). [START_REF] Gougeon | Crystal and Electronic Structures, and Thermoelectric Properties of the Novel Cluster Compound Ag3In2Mo15Se19[END_REF][START_REF] Gougeon | Electronic Band Structure and Transport Properties of the Cluster Compound Ag3Tl2Mo15Se19[END_REF] Although all these compounds seem similar according to their respective MEC, these results show that the nature of the transport properties are sensitive to the nature of the M cation.

The fact that these different elements are not electronically equivalent in these compounds may have several origins. First, the MEC count relies on the assumption that the M cations exhibit a +1 valence state. In the AgxMo9Se11 compounds, combined high-resolution fluorescencedetection X-ray absorption spectroscopy (HERFD-XAS) and resonant inelastic X-ray scattering (RIXS) measurements have evidenced the presence of sub-monovalent Ag atoms. 28 The presence of a similar property in the Ag3M2Mo15Se19 compounds would explain the differences observed in their transport properties. In addition, the actual charge of the Ag and M atoms in these structures may likely vary depending on the nature and atomic size of the M cations and on the actual concentrations of both Ag and M. Alternatively, these differences may be due to slight but systematic variations in the valence bands as a function of the M cations. In particular, these modifications might change the balance between the electron-and hole-like contributions usually observed in the Hall signal which, in turn, would alter their impact on the thermopower values and hence, on the ZT values. Because both mechanisms could be at play in these compounds, further experimental investigations with HERFD-XAS and RIXS would be valuable to systematically probe the valence state of the Ag and M cations.

CONCLUSION

The novel reduced molybdenum selenides K2Mo15Se19 and Ag3K2Mo15Se19 were synthesized by solid-state reaction at 1300°C in sealed Mo crucibles. As in In2Mo15Se19, the crystal structure contains an equal proportion of octahedral Mo6 and bioctahedral Mo9 clusters, forming Mo6Se i 8Se a 6 and Mo9Se i 11Se a 6 cluster units, separated from each other by large voids. These voids are filled up by eleven-coordinated K atoms in K2Mo15Se19 and by five-coordinated Ag atoms in Ag3K2Mo15Se19. In agreement with simple metallic electron count and electronic band structure calculations, K2Mo15Se19 is a p-type metal with moderate thermopower values. Upon inserting Ag, a clear evolution of these properties towards a heavily-doped semiconducting state is observed. In addition to influencing the electronic properties, the presence of Ag further lowers the phonon transport close to the amorphous limit. Very low-temperature thermodynamic measurements and spectroscopic probes will be of interest to establish in detail the microscopic origin of this behavior. The comparison of the transport properties measured herein with those reported for the In and Tl-containing analogues suggests that the nature of M cation is an important parameter to tune the thermoelectric performances. Future investigations of the transport properties of these compounds with other M atoms will be helpful to better understand its role and to develop structure-properties relationships in this family of cluster compounds.

Supporting Information.

Experimental and computational details, details of the crystallographic data collection and powder X-ray structural analysis, final atomic coordinates and equivalent isotropic displacement parameters, selected interatomic distances for polycrystalline Ag3K2Mo15Se19 determined from profile matching against the PXRD data, temperature dependence of the

Table of Contents Graphic

This work reports a detailed study of the influence of Ag insertion on the thermoelectric properties of the Mo-based cluster compound K2Mo15Se19 that yields enhanced thermoelectric properties at high temperatures.

Figure 1 .

 1 Figure 1. Views of the crystal structures of (a) K2Mo15Se19 and (b) Ag2.2K2Mo15Se19 projected

Figure 2 .

 2 Figure 2. Inter-unit linkage of the Mo9Se11Se6 and Mo6Se8Se6 cluster units. Thermal

Figure 3 .

 3 Figure 3. a) Se environment of the K + cations in K2Mo15Se19. b) Se environment of the Ag +

Figure 4 .

 4 Figure 4. Profile matching refinement of the powder X-ray diffraction patterns of K2Mo15Se19

Figure 5 .

 5 Figure 5. Total and partial densities of states as a function of the energy in K2Mo15Se19.

Figure 6 .

 6 Figure 6. COHP curves calculated for the Mo-Mo intra-bonds in the Mo6 cluster for

Figure 7 .

 7 Figure 7. COHP curves calculated for the Mo-Mo intra-bonds in the Mo9 cluster for

Figure 8 .

 8 Figure 8. COHP curves calculated for the inter-cluster bonds Mo1-Mo2 for K2Mo15Se19.

Figure 9 .

 9 Figure 9. Temperature dependence of the a) electrical resistivity, b) thermopower, c) total

7 Figure 9

 79 Figure 2

Table 1 .

 1 Gougeon, P.; Halet, J.-F.; Gautier, R. Towards the prediction of the transport properties of cluster-based molybdenum chalcogenides. J. Mater. Chem. C 2017, 5, 12097-12104. Single-crystal data collection and structure refinements of K2Mo15Se19 and

	(27) Cahill, D. G.; Watson, S. K.; Pohl, R. O. Lower limit to the thermal conductivity of
	disordered crystals. Phys. Rev. B 1992, 46, 6131-6140.
	(28) Butorin, S. M.; Kvashnina, K. O.; Klintenberg, M.; Kavcic, M.; Zitnik, M.; Bucar, K.;
	Gougeon, P.; Gall, P.; Candolfi, C.; Lenoir, B. Effect of Ag Doping on Electronic Structure of
	Cluster Compounds AgxMo9Se11 (x = 3.4, 3.9). ACS Appl. Energy Mater. 2018, 1, 4032-4039.

Table 2 .

 2 Fractional atomic coordinates, equivalent isotropic thermal displacement parameters (in Å 2 ) and site occupancy factors for single-crystalline K2Mo15Se19 and Ag2.2K2Mo15Se19.

	Atom	x	y	z	Ueq	s.o.f
	Mo1	0.64652(2)	-0.51856(2)	0.35303(2)	0.00774(4) 1
	Mo2	0.84743(2)	-0.16372(2)	0.28925(2)	0.00774(4) 1
	Mo3	0.84074(3)	0.0000	0.2500	0.00727(5) 1
	Se1	0.62840(3)	-0.37968(3)	0.31684(2)	0.00935(4) 1
	Se2	0.65235(3)	-0.30839(3)	0.38094(2)	0.01032(5) 1
	Se3	0.69207(3)	-0.30793(3)	0.2500	0.01105(6) 1
	Se4	0.6667	-0.6667	0.38756(2)	0.01267(8) 1
	Se5	1.0000	0.0000	0.32386(2)	0.01081(7) 1
	K	1.0000	0.0000	0.38697(2)	0.0314(3)	1
	Atom	x	y	z	Ueq	s.o.f
	Mo1	0.65070(3)	-0.51996(3)	0.35272(2)	0.00546(4) 1
	Mo2	0.85270(3)	-0.15840(3)	0.28920(2)	0.00581(5) 1
	Mo3	0.84259(3)	0.0000	0.2500	0.00480(5) 1
	Se1	0.63359(3)	-0.38357(3)	0.31594(2)	0.00793(6) 1
	Se2	0.64789(3)	-0.30520(4)	0.37892(2)	0.00943(6) 1
	Se3	0.70133(4)	-0.29867(4)	0.2500	0.00858(7) 1
	Se4	0.6667	-0.6667	0.38847(2)	0.01002(9) 1
	Se5	1.0000	0.0000	0.32432(2)	0.01029(9) 1
	K	1.0000	0.0000	0.38101(4)	0.0400(4)	1
	Ag	0.70336(14)	0.79923(10)	0.08127(3)	0.0314(4)	0.3697(12)

thermal diffusivity for both samples, temperature dependence of the thermal conductivity 𝜅 measured perpendicular (low temperature) and parallel (high temperature) to the pressing direction for K2Mo15Se19 and Ag3K2Mo15Se19, temperature dependence of the specific heat 𝐶 𝑝 for K2Mo15Se19 and Ag3K2Mo15Se19, elemental X-ray mapping for K2Mo15Se19 and Ag3K2Mo15Se19, fracture images for K2Mo15Se19 and Ag3K2Mo15Se19, elemental fracture images and their corresponding elemental X-ray mapping for K2Mo15Se19 and Ag3K2Mo15Se19, temperature dependence of the power factor, temperature dependence of the electronic thermal conductivity.

AUTHOR INFORMATION

Corresponding Authors *christophe.candolfi@univ-lorraine.fr *patrick.gougeon@univ-rennes1.fr

ORCID

Notes

The authors declare no competing financial interest.

Conflicts of interest

There are no conflicts to declare.


Jérome Long
email: jerome.long@umontpellier.fr

Dr Ivan V Basalov

Dr Konstantin A Lyssenko

Anton V Cherkasov

Dr Ekaterina Mamontova

Prof. Dr Yannick Guari

Joulia Larionova

Dr Alexander A Trifonov

Jérôme Long

Dr J Long

Dr A Cherkasov

Synthesis, Structure, Magnetic and Photoluminescent Properties of Dysprosium(III) Schiff Base Single-Molecule Magnets: Investigation of the Relaxation of the Magnetization

Keywords: Lanthanides, Schiff bases, Magnetism, Single Molecule Magnets, Luminescence

come   L'archive ouverte pluridisciplinaire

Introduction

Lanthanide-based Single-Molecule Magnets (SMMs) are an exciting family of coordination or organometallic complexes exhibiting a slow relaxation of their magnetization, signifying that they can retain their magnetization in the absence of a magnetic field. [1] This feature allows them to be frequently considered as pertinent candidates for future applications in data storage, spintronics or quantum computing. [1a, 2] These tremendous expectations however encounter difficulties associated with the relatively low maximum temperature (also known as blocking temperature) at which the magnetic information can be preserved. The physical foundation of such phenomenon is mainly correlated with the anisotropic barrier opposing the reversal of the magnetization aligned to the anisotropy axis of the complex. In mononuclear lanthanide SMMs, the control of the anisotropy may be achieved through an important axial crystal-field generated by the ligands over a specific lanthanide ion. Such acquaintanceship between 4f ion and ligands could be chemically optimized in order to design complexes with targeted coordination environments, with the aim to maximize the magnetic anisotropy and reduce the rate of the Quantum Tunneling of the Magnetization (QTM) relaxation, [3] two necessary conditions for the blocking of the magnetization. Besides QTM, intricate spin-lattice relaxations (Raman, direct) can also create underbarrier pathways. [4] For instance, the role of molecular vibrations on the slow relaxation dynamics has been very recently recognized as a critical factor to enhance the overall properties. [4a, 4b, 5] Using these concepts, considerable advances have recently been achieved in the field with several mononuclear SMMs exhibiting giant anisotropic barriers of few thousands of cm 1 , [3b, 6] and magnetic hysteresis that could reach liquid nitrogen's boiling point. [4a, 6c] In this sense, simple electrostatic considerations could be exploited to design high anisotropic barriers SMMs. Thus, lanthanide ions with an oblate electronic 4f density (flattened spheroid), such as Dy 3+ , could be efficiently stabilized by an axial-crystal field. It has been first demonstrated by theoretical modelling [3b, 7] and then experimentally, that this could be achieved in linear complexes exhibiting two negatively charged ligands with short Ln 3+ -ligand distances along an axial direction that allows maximizing the crystal-field splitting, shortcutting the QTM [4a, 6c, 6d, 8] and reduce the metal-ligand vibrational modes. [5b] Additionally, the Ln 3+ -ligand distances in the equatorial plane should be as long as possible.

While organometallic chemistry ligands, such as cyclopentadienyl derivatives, appear particularly efficient to design highly axial systems, examples of Werner-type complexes based on ligands involving nitrogen or oxygen donors are still rather scarce owing to the difficulty to accurately control the coordination environment. [6a, 6e, 9] In this regard, Schiff bases involving phenoxide moieties are among the most popular ligands to obtain lanthanide SMMs, that could eventually benefit from air-stability, [1a, 1b, 1d, 10] due to their large tunability (electronic, steric etc...) and the possibility to implement additional functionalities, such as luminescence. [11] Consequently, an important effort has been done to rationally design high energy barrier SMMs involving such ligands. [6e, 12] With this in mind, we have recently reported two multifunctional dysprosium complexes based on unsymmetrical bulky tridentate N,N,O  Schiff base ligands, 4-di-tert-butyl-6-((quinolin-8ylimino)methyl)phenolate and 2,4-di-tert-butyl-6-(((pyridin-2ylmethyl)imino)methyl)phenolate. They displayed a genuine SMM behaviour with relatively high energy barriers, which is also associated with a ligand-based luminescence. [13] Encouraged by these promising results, we pursued our effort on the optimization of Dy 3+ -Schiff base SMMs and focused on the influence of the pendant group, coordinated solvent molecules and counter anion on the coordination environment of the Dy 3+ and then on the magnetic properties. We report in this article the synthesis, crystal structures, magnetic and photoluminescence properties of three novel mononuclear dysprosium complexes based on two tridentate N,O,O  Schiff base ligands, which differ by the nature of pendant groups (the substituent by the ether oxygen (methyl vs. phenyl). Note that the steric hindrance imposed by tert-butyl groups of these ligands is favorable to generate mononuclear complexes, while the presence of different pendant groups permits to finely modify the environment of the dysprosium site and also slightly alter the emission wavelength. Moreover, the impact of the coordinated solvent molecules and the counter ions (Cl  vs. BPh4  ) on the coordination environment of the Dy 3+ ion and the direction of the anisotropic axes is also investigated. All compounds exhibit a slow relaxation of the magnetization associated with a ligandbased luminescence.

Results and Discussion

Synthesis and crystal structures. The synthetic strategy relies on the combination between the oblate electronic density of Dy 3+ ion with the unsymmetrical bulky tridentate ligands, HL1 (Phenol, 2,4- (3) complexes was synthesized using a salt metathesis approach (Scheme 1).

bis(1,1-dimethylethyl)- 6-[[(2-methoxy-5-methyl phenyl)imino]methyl]) or HL2 (Phenol, 2, 4-bis(1,1-dimethylethyl)-6-[[(2-methoxyphenyl)imino]methyl]),
The reactions of anhydrous DyCl3 with 2 equivalents of in situ prepared potassium phenolates KL1 or KL2 in THF at room temperature afford the bis(iminophenolate)chloro dysprosium [Dy(L1)2Cl(DME)] (2) or [Dy(L2)2Cl] (3) complexes which were isolated in 84 and 82 % yields respectively. Scheme 1. Synthesis of complexes 1-3.

The reaction of complex 2 with one equivalent of NaBPh4 in THF, followed by recrystallization from a THF:py:hexane mixture (1:1:2) resulted in the formation of the cationic complex [Dy(L1)2(py)2][B(Ph)4] (1) in 86 % yield. "One-pot" reaction of the in situ prepared potassium phenolate KL1 with DyCl3 and NaBPh4 (1:0.5:0.5 molar ratio) in THF at room temperature also allows the synthesis of 1 in 80 % yield. Unfortunately, the attempts to synthesize the cationic dysprosium complex coordinated by L2  ligand following the same synthetic protocol were unsuccessful.No product formation was observed when equimolar amounts of complex 3 and NaBPh4 were refluxed in THF at 70°C for 72 hours (Scheme 1).

X-ray analysis performed on single crystals indicates that 1 exists as a separated ion pair. It crystallizes in the triclinic space group (Table S1) with a unique [Dy(L1)2(py)2] + cationic moiety in the asymmetric unit. The coordination sphere of the Dy 3+ is composed by four oxygens and two nitrogens belonging to two L1  ligands and two nitrogen atoms from pyridine moieties giving a formal coordination number of eight for the Dy 3+ ion (Figure 1). The asymmetric unit also contains a solvate pyridine molecule and a tetraphenylborate anion which ensures the electroneutrality. The Dy-N distances are ranging between 2.488(3) and 2.592(3) Å while the Dy-O(methoxy) ones are equal to 2.476(2) and 2.506(2) Å. As expected, the shortest distances are observed for the Dy-O(phenoxide) bonds with values of 2.172(2) and 2.183(2) Å (Table 1). The bent angle O(phenoxide)-Dy-O(phenoxide) is equal to 124.55(9)°. The coordination geometry was quantitatively further analyzed with the SHAPE [14] software which indicates a distorted biaugmented trigonal prism geometry (Table S2) whereas the shortest intermolecular Dy 3+ -Dy 3+ distance found in the crystal is equal to 10.8104(4) Å (Figure 2, Table 1).

Complex 2 crystallizes in the P21/n space group. The asymmetric part of the unit cell in 2 contains one dysprosium complex and a DME solvate molecule located on an inversion centre giving the resulting formula [Dy(L1)2Cl(DME)]•0.5DME. In contrast to 1, the coordination sphere of the Dy 3+ in 2 along with two L2  ligands, contains one chloride and a monodentate DME ligands resulting also in a formal coordination number of eight (Figure 1). Similarly to 1, the shortest distances accounts for the Dy-O(phenoxide) with values of 2.185(6) and 2.223(5) Å while the Dy-Cl one is expectedly significantly larger and equal to 2.621(2) Å (Table 1). The O(phenoxide)-Dy-O(phenoxide) angle is noticeably larger than in 1 with a value of 144.6(2)°. The shortest interomolecular Dy 3+ -Dy 3+ distance in 2 is equal to 9.2237(5) Å (Figure 2). Finally, compound 3 crystallizes as a toluene solvate in the triclinic space group with one dysprosium complex in the asymmetric unit. 8) [13] The structure is reminiscent to that of 2 with the exception that the absence of a coordinated solvent molecule gives an heptacoordinated geometry for the Dy 3+ site (Figure 1), close to

1 2 3 1) 2)
3)

a distorted capped octahedron (Table S3). The two Dy-O(phenoxide) distances are equal to 2.139(2) and 2.143(2) Å. In contrast to 2, the bent angle O(phenoxide)-Dy-O(phenoxide) is much narrower with a value of 89.76(9)°. The shortest Dy 3+ -Dy 3+ distance is found equal to 7.8396(6) Å (Figure 2). In comparison with the related complexes based on tridentate N,N,O  ligands we recently reported [13] (denoted as 4 and 5, Table 1), the distances and the angles are summarized in Table 1.

Magnetic Properties.

The magnetic properties of the three complexes were investigated by SQUID magnetometry. Firstly, the direct current (dc) magnetic properties were analyzed.

At room temperature, the T values of 13.74, 14.55 and 13.32 cm 3 .K.mol 1 for 1, 2 and 3 respectively are in a relatively good agreement with the value of 14.17 cm 3 .K.mol 1 expected for a single Dy 3+ ion using the free-ion approximation (Figure 3).

Compounds 2 and 3 show a continuous decrease of T upon cooling originating from the thermal depopulation of the mJ levels.

In contrast, the T product for compound 1 remains nearly constant as the temperature is reduced and then exhibits a dramatic decrease at low temperature suggesting a larger crystal-field splitting with respect to 2 and 3. At 1.8 K, the magnetization values under a 70 kOe field are 5.82, 4.53 and 5.25 N for 1, 2 and 3 respectively (Figure 3). For complex 1, a clear inflection point could be observed at low field. Such trend was previously observed in others lanthanide based SMMs, [6b, 6d, 13, 16] and may reflect either the extreme field dependence of the relaxation rates [9b] , the flip of the Dy 3+ spins under an applied magnetic field. [16] Figure 3. Temperature dependence of T under an applied magnetic field of 1000 Oe for 1-3. Inset: Field dependence of the magnetization at 1.8 K.

Alternate currents (ac) measurements were then performed in order to characterize the occurrence of a SMM behaviour. Under a zero dc-field, the three complexes exhibit an important signal of the out-of-phase (") of the ac susceptibility indicating the presence of a slow relaxation of the magnetization (Figure 4, Figure S1). Nevertheless, important differences are readily observed. Hence, the frequency dependences of " exhibits a single temperature dependent peak for 1 and 3 whereas a peak associated with a plateau at high frequencies is observed for 2. Moreover, the temperature range of the slow relaxation greatly differs (Figure 1, Figure S1). Thus, out-of phase signals are observed up to 45 and 15 K for 2 and 3 respectively, while it reaches up 60 K for 1 (Figure S2). The Cole-Cole plots for 1 (Figure S3) confirm the occurrence of a single relaxation for 1 and could be fitted with a generalized Debye model, leading to low values of the  parameter (< 0.1) in the high temperature region while it significantly increases (up to 0.5) at low temperature (Table S4). Surprisingly, the Cole-Cole plots for 3 at low temperature could be only badly fitted with a single function suggesting a very wide distribution of relaxation times (Figure S3, Table S6). Although such phenomenon could have various origins, one can note a slight crystallographic disorder observed on one L2  ligand. As regards 2, the presence of a low temperature second relaxation process could be ultimately confirmed by the Cole-Cole plots (Figure S3) which could be fitted with a sum of two modified Debye functions with  parameters lower than 0.36) (Table S5).

In order to obtain further insights into the relaxation dynamics, the temperature dependence of the relaxation time, , was monitored for the three complexes. The classical deviation from the linearity observed in the ln vs. T 1 plot (Figure 5) indicates an overlap between different relaxation processes. Consequently, the fitting of the whole temperature range could be achieved using the following model:  1 = 0 1 exp(/kT) + CT n +  1 QTM (Eq. 1). [17] The first term accounts for a thermally activated process, while the second and third ones stand for two-phonon Raman and QTM, respectively. In order to avoid over-parameterization, the n coefficient was successively fixed to various values until getting the best correlation coefficient. The obtained fitting parameters could be found in Table 2 and T / K indicate that, for complex 1, the relaxation involves the three considered processes. Interestingly, the obtained value of  = 472 ± 25 cm 1 is found much larger than in our two related previous examples based on N,N,O  Schiff base ligands (Table 2). [13] In contrast, meaningless parameters are obtained for complex 2 using Eq. 1. Nevertheless, performing the fit taking only into account Raman and QTM processes (n being let free) yields to better results. The n value of 4.3 is close to the value of 5, which is sometimes observed for Kramers ion. [18] Due to the wide distribution of the relaxation times, the situation for complex 3 is more complicated and it was not possible to perform any pertinent fitting. Moreover, the presence of strong dipolar interactions caused by short intermolecular Dy 3+ -Dy 3+ distances (i.e. 7.840 Å) may also complicate the overall picture.

Nevertheless, it could be noticed that the relaxation time is found several order of magnitude lower with respect to complexes 1 and 2. As a consequence, dramatic differences in the zero-field relaxation dynamics could be observed. In order to shortcut the contribution of the QTM, the field dependence of the ac susceptibilities and in turn the relaxation time were monitored (Figures S4-S5). Upon applying a dc field larger than 500 Oe, the three complexes exhibit a relaxation time which remains constant in the investigated field range. A dc field value of 1000 Oe was therefore chosen as the optimum field for all samples. To our knowledge, the qualitative description of the dynamics of Raman process in SMMs is mainly based on physic concepts derived from EPR spectroscopy on simple inorganic salts. On one hand, some studies have reported that the fieldindependent character of the Raman process [19] while others have predicted a complex field dependence as (for Kramers ions). [START_REF] Van Vleck | [END_REF] Some recent studies have highlighted that while the first order Raman process is field independent, the second order Raman process implies a field-dependence. [21] Considering the field dependent character of the Raman process will require fitting the field dependence of the relaxation time with eight different parameters which will undoubtedly lead to over-parameterization and meaningless results. Besides, recent studies have also anticipated or reported that the Raman relaxation is independent on the magnetic field strength in SMMs based on Kramers ions. [9b, 22] Although it may not reflect the complex fielddependence of the Raman process, we have integrated the Raman contribution in the K constant with the Orbach process. Hence, the field dependence of the relaxation time (Figure S5) was modeled using:

(Eq. 2),

The increased values of B1 and B2 going from complexes 1 to 3 (Table S7) directly reflects the increase of the QTM rate. As a consequence, the frequency dependences of the ac susceptibilities under a dc field of 1000 Oe (Figure S6) validate the decrease of the QTM. It could be noticed that for 3, applying dc fields greatly shifts the slow relaxation temperature range for which maximum of " could be observed up to 14.5 K. The Cole-Cole plots (Figure S7) further corroborate the presence of a second relaxation for complex 2 at low temperature. Remarkably, the fitting of the Cole-Cole plots with either a generalized Debye model (complexes 1 and 3) or the sum of two modified Debye functions (complex 2) (Tables S8-S10) yield to weak values for the  parameter ( < 0.03) for the three complexes. This indicates that applying a dc-field causes a dramatic influence over the distribution of relaxation times with respect to the zerofield data. Such results imply that the large distribution of the relaxation times is somehow related to the QTM process and in some extent to the crystallographic disorder or an anisotropic displacement of the coordinated atoms in the coordination sphere of the Dy 3+ , as it was recently suggested. [23] Fitting of the temperature dependence for 2 and 3 could be carried out considering only a Raman process as  1 = CT n (Table S11, Figure S8). On the other hand, the fitting for 1 was performed with the following model with  1 = 0 1 exp(/kT) + CT n (Eq. 3)

(Figure S8, Table S11). As expected for a thermally activated process, the anisotropic barrier is found comparable, taken into account the uncertainties of the fitting, with respect to that obtained under a zero-dc field. Obviously, complex 1 exhibits the most interesting magnetic properties. In this regards, it has been recently highlighted that large  parameter values may result in large uncertainties for the corresponding relaxation times. [23] In order to qualitatively compare the anisotropic barriers, the uncertainties on the relaxation time  for compounds 1, 4 and 5 have been calculated 6 from the  parameters of the generalized Debye model using the CC-Fit2 software based on the log-normal distribution. [23] Figure S9 clearly shows the strong decrease of the  uncertainties for compound 1 for the data collected under a dc-field. Starting from this, we have reinvestigated the fitting of the relaxation times for 4 and 5 (Table 2, Figure S10). The slightly different obtained parameters with respect our previous study [13] could be rationalized from the different methods of the extraction of the relaxation times (i.e. using CC-Fit2). Similarly than for compound 1, the uncertainties related to  for 5 are found greatly reduced for the in-field data with respect to those obtained under a zerodc field, whereas this decrease is less obvious for 4 (Figure S10). Since the thermally activated process is field-independent, these results indicate that the in-field data should give a more accurate estimation of the anisotropic barriers, in accordance with the trend observed in zero-dc field. Consequently, while for 4 and 5, the  values are found comparable (within the uncertainties),

complex 1 shows clearly a greater barrier. Finally, the ability of lanthanide SMMs to maintain their magnetization constitutes definitely an important feature for future applications. Among the three new investigated complexes, 1 and 2 clearly exhibits the more probabilities to present a clear magnetic bistability. For comparison, the relaxation time for complex 1 at 2 K is found almost 70 times greater with respect to 3. The Zero-Field Cooled (ZFC) and Field-Cooled (FC) curves reveal distinct behaviours. While a clear maximum in the ZFC curve (one of the possible definition for the blocking temperature TB [24] ) is observed for 1 at 2.6 K, only a slight non-superposition between the ZFC and FC curves is detected for 2 (Figure S11). This suggests that 1 exhibits a higher blocking temperature. The divergence between the ZFC/FC curves occurs at 6.0 and 5.5 K for 1 and 2 respectively. This point could be described as an irreversible temperature (Tirr.) and reflects an out-of-equilibrium state frequently observed in lanthanide SMMs. [4a, 6c, 6d, 9a, 25] Moreover, the magnetic irreversibility is further confirmed by the opening in the hysteresis loops for 1 and 2 at 1.8 K (Figure 6). For complex 1 which clearly shows the best performances, the hysteresis loop is almost closed at 5 K in our experimental conditions (Figure S12). Magneto-structural correlations. Rationalization of the observed magnetic properties could be obtained with magneto-structural correlations. It is well known that dysprosium-based SMMs show a strong dependence of their slow relaxation features depending on the coordination environment of the lanthanide site [3b, 26] which could be modulated by nature of the pendant group of the ligands, the nature of the counter anion and the coordinated solvent molecules. [27] Firstly, compounds 1 and 2 are based on the same Schiff base L1  ligand bearing a methyl on the ether group. While 1 is a cationic complex [Dy(L1)2(py)2] + , 2 is a neutral complex [Dy(L1)2Cl(DME)] incorporating a coordinated chloride anion in the coordination sphere of the Dy 3+ ion. The O(phenoxide)-Dy-O(phenoxide) (abbreviated as O  -Dy-O  ) arrangement is much greater for 2 with respect to 1 (144.8 vs. 124.6°) but the Dy-O  are shorter in 1. The orientation of the anisotropic axes estimated from a simple electrostatic model with the Magellan [15] package shows that, for both complexes, these axes are almost collinear to the O  -Dy-O  sequence with deviation of 27.34/28.09° and 16.84/18.36° for 1 and 2, respectively (Figure 1). The fact that the anisotropic axis is only moderately tilted in 2, despite the presence of the coordinated Cl  , may be explained by the relatively long Dy-Cl distance of 2.623 Å that limits its electrostatic influence. However, the magnetic analysis suggests that the substitution of pyridine moieties by a chloride and DME solvent alters the relaxation dynamics. It would be tempting to correlate this with a modification in the metal-ligand vibrational modes that affects the Raman process but would require detailed far-infrared and/or Raman studies. [28] Secondly, compounds 2 and 3 present slightly different coordination environments which vary by the nature of the ether substituents (methoxy vs. phenoxy) of the Schiff base, as well as from the solvent molecule present in the coordination sphere of Dy 3+ . Due to the steric hindrance brought by the phenyl groups, the coordination geometry around the Dy 3+ ion for 3 is found reduced with an heptacoordinated geometry [Dy(L2)2Cl]. Hence, a dramatically weaker O  -Dy-O  angle of almost 90° is observed for 3. In that case, the anisotropic axis obtained from Magellan is oriented along the O  -Dy-Cl sequence (Figure 1) since this latter provides an angle of 158°, closer to the linearity. Despite the fact that 3 exhibits the shortest Dy-O  distances, the presence of a negatively charged phenoxide coordinated perpendicular to the anisotropic axis induces a strong transverse component. Due to the large distribution of relaxation time at zero-field, it was not possible to study in details the zero-field relaxation dynamics for 3. However and in the same way than for 2, the ac data obtained under a dc field suggest that it is dominated by a Raman process. Both the strong QTM and Raman relaxation explain the fact that, the three investigated compounds, 3 shows the weakest magnetic features.

The results obtained for complex 1 may be directly compared with the ones found for our two previously reported cationic complexes 4 and 5, based on slightly different N,N,O  Schiff base ligands, but for which the orientation of the anisotropic axes were found similar. [13] Indeed, the anisotropy barrier found for 1 is much greater (see Table 2). Although the O  -Dy-O  angles are found nearly similar (124.6° for 1 vs 128.5° for 4), a slightly shorter Dy-O  distance of 2.173(3) Å is observed in 1, with respect to the Dy-O  distances ranging from 2.190(6) to 2.196(2) Å observed in 4 and 5. Visibly, this 0.02 Å -5000 -2500 0 2500 5000

-4 -2 0 2 4 1 2 M / N H / Oe
difference in bond length involving the negatively charged donor atom may affect the crystal-field splitting and highly enhance the magnetic axiality, which explains the important improvement of the energy barrier. [3b] Such increase in the anisotropic barriers with comparable bond shortening magnitude has been previously evidenced in the dysprosium metallocenium family SMMs with enlargement up to 20 %. [5b, 29] In the case of Schiffbase phenoxide complexes, the highest measured anisotropic barrier of 665 cm 1 to our knowledge shows a shortest Dy-O  of 2.126 Å associated with a O  -Dy-O  angle of 144.7 °.

[6e] This clearly shows that the bond distance and to a lesser extent the O  -Dy-O  angle have to be carefully controlled in order to achieve large energy barrier systems.

Photoluminescence. Schiff base ligands are also promising to implement photoluminescence properties through the ligandbased luminescence or through the enhanced Ln 3+ emission thanks to the antenna effect and therefore to design bifunctional SMM systems. [11] The photoluminescent properties were therefore investigated in solid-state for all complexes. The room temperature emission spectra, excited at 370 nm, show a broad emission band centered at 563, 583 and 544 nm for complexes 1, 2 and 3, respectively (Figure 7) while the excitation spectra (Figure S13) exhibit a large band around 370-380 nm. The broadness of the emission band clearly indicates a ligand-based luminescence. This is confirmed by the photoluminescence spectra of HL1 and HL2 which show a comparable profile with a maximum emission wavelength at about 570 nm (Figure S14). Although based on the same L1  ligand, the differences in the emission wavelengths between 1 and 2 may be ascribed to modifications in the ligand-ligand interactions within the crystal structures. Noticeably, the three compounds do not show dysprosium-based luminescence indicating that L1  and L2  ligands are not active as antenna for lanthanide excitation. Such behavior was also observed for complexes 4 and 5. [13]

Conclusion

Three new mononuclear dysprosium Schiff-base complexes with a tunable coordination environment were synthesized by the combination of bulky unsymmetrical tridentate Schiff-base ligands with coordinative solvents and counter anions. The control of the coordination environment may be achieved by playing on : i) the nature of the substituents of both, the phenol ring and ether groups, ii) the use of two different counter-anions, namely coordinative and small Cl  ion or non-coordinative and bulky BPh4  , and iii) the coordination (or not) of solvent molecules through adjustment of the experimental conditions. The three reported complexes exhibit a zero-field slow relaxation of the magnetization with distinct relaxation dynamics. Hence, using the L1  ligand, two dysprosium complexes differing mainly by the presence of a coordinated chloride in the coordination sphere of the Dy 3+ ion have been obtained. The cationic complex 1 shows a genuine SMM behavior with out-of-phase signals observed up to 60 K and a fair energy barrier of 472 cm 1 .

In comparison with the previously reported similar complexes and based on related Schiff base ligands presenting closed coordination environment and similar orientation of the anisotropic axis, the shortening of the Dy-O(phenoxide) induces an enhancement of the height of the energy barrier. On the other hand, the introduction of a coordinated chloride in the coordination sphere in complexes 2 and 3 strongly affects the relaxation dynamics that appears to follow a Raman temperature dependence. Additionally, the greater steric hindrance of the phenyl group in L2  decreases severely the O-Dy-O angle. Moreover, all the complexes exhibit a ligand-centered luminescence. The great flexibility in the nature of the substituents of both, phenol and ether groups of the Schiff base ligands associated with the careful use of the counter anions and the coordinated solvents is highly promising to design genuine luminescent SMMs with high anisotropic barriers.

Experimental Section

Materials and Methods.

All experiments were performed in evacuated tubes or in inert atmosphere, using standard Schlenk-flask or glove-box techniques, with rigorous exclusion of traces of moisture and air. After drying over KOH, THF was purified by distillation from sodium/benzophenone ketyl, hexane and toluene by distillation from sodium/triglyme benzophenone ketyl prior to use. Pyridine was dried over KH and was purified by distillation prior to use. L1H and L2H were synthesized according to literature procedures. [30] IR spectra were recorded as Nujol mulls on a Bruker-Vertex 70 spectrophotometer. The N, C, H elemental analyses were carried out in the microanalytical laboratory of the IOMC by means of a Carlo Erba Model 1106 elemental analyser with an accepted tolerance of 0.4 unit on carbon (C), hydrogen (H), and nitrogen (N). Lanthanide metal analysis was carried out by complexonometric titration. [31]

Synthesis of the complexes Synthesis of [Dy(L1)2(py)2][B(Ph)4]•py (1).

Method A: A mixture of HL1 (0.200 g, 0.566 mmol) and KH (0.029 g, 0.725 mmol) in THF (30 mL) was stirred at room temperature for 1 h and the resulting suspension was filtered. The clear yellow solution was added to a suspension of DyCl3 (0.076 g, 0.283 mmol) in THF (10 mL) and the reaction mixture was stirred another 1 h. After that NaBPh4 (0.097 g, 0.283 mmol) was added to the solution and the reaction mixture was stirred overnight at room temperature.

Synthesis of [Dy(L2)2Cl]•2.5(C7H8) (3).

A mixture of HL2 (0.200 g, 0.498 mmol) and KH (0.026 g, 0.646 mmol) in THF (30 mL) was stirred at room temperature for 1 h and the resulting suspension was filtered. The clear yellow solution was added to a suspension of DyCl3 (0.067 g, 0.249 mmol) in THF (10 mL) and the reaction mixture was stirred overnight at room temperature. The solution was filtered, the volatiles were removed in vacuum and the solid residue was dissolved in toluene. Slow concentration of the solution at room temperature resulted in the formation of 3 as yellow crystals. The mother liquid was decanted and the crystals were washed with cold hexane and dried in vacuum for 30 min. Complex 3 was isolated in 82% yield (0.251 g). Elemental analysis calcd. (%) for C71.50H80ClDyN2O4: C,69.85; H, 6.65; N, 2.27; Dy, 13.20; found (%): C,69.47; H, 6.32; N, 2.01; Dy, 13.48. IR (Nujol, KBr) ν/cm -1 : 480 (s), 520 (m), 610 (s), 660 (s), 730 (s), 770 (s), 840 (s), 880 (m), 920 (m), 980 (m), 1010 (s), 1050 (s), 1070 (s), 1155 (s), 1210 (s), 1260 (s), 1310 (s), 1415 (s), 1540 (s), 1580 (s), 1625 (s).

X-Ray crystallography

X-ray diffraction data for 1-3 were collected on Bruker Apex II (1, 3) and Bruker D8 Quest (2) diffractometers (graphite monochromator, ω-scan technique) using MoKα-radiation (0.71073 Å). The intensity data were integrated by SAINT program [32] and were corrected for absorption and decay using SADABS. [33] All structures were solved by direct methods and were refined by full-matrix least squares on F2 for all data using SHELX. [34] All non-hydrogen atoms in 1-3 were found from Fourier syntheses of electron density and were refined anisotropically. All hydrogen atoms were placed in calculated positions and were refined as riding atoms with relative isotropic displacement parameters U(H)iso = 1.2Ueq (U(H)iso = 1.5Ueq for methyl groups). The structure of complex 2 was refined as a 2-component twin with TWIN 0 0 -1 0 -1 0 -1 0 0 and BASF 0.38249. CCDC-1973040 (1), 1973041 (2) and 1973042 (3) contains the supplementary crystallographic data for this paper. These data are provided free of charge by The Cambridge Crystallographic Data Centre: ccdc.cam.ac.uk/structures. The crystallographic data and structure refinement details for 1-3 are given in Table S1.

Magnetic Measurements

Magnetic susceptibility data were collected with a Quantum Design MPMS-XL SQUID magnetometer working in the range 1.8-350 K with the magnetic field up to 7 Tesla. The samples were prepared in a glove box. The data were corrected for the sample holder and the diamagnetic contributions calculated from the Pascal's constants. The AC magnetic susceptibility measurements were carried out in the presence of a 3 Oe oscillating field in zero or applied external DC field.

Photoluminescence measurements

The emission and excitation spectra were recorded at 77 K and 295 K using a spectrofluorimeter Edinburgh FLS-920. The excitation source was a 450 W Xe arc lamp. The emission spectra were corrected for detection and optical spectral response of the spectrofluorimeter. Low temperature measurements (77 K) were performed using a liquid nitrogen dewar (quartz). The solid-state photoluminescence for HL1 and HL2 have been performed using an Ocean Optics USB2000 with an LED (365 nm) as the excitation source.

  containing the donor atoms N,O,O  . Incorporation of bulky tertbutyl groups into the ortho position to the phenolate oxygen allows limiting the coordination of "parasitic" ligands that would decrease the axiality, while variation of the substituent on the ether oxygen (Me vs. Ph) may affect the symmetry of the dysprosium

Figure 1 .

 1 Figure 1. Molecular structure for complexes 1-3. Colour code: orange, Dy; blue, N; grey, C; green, Cl; Hydrogen atoms, [B(Ph)4]  and solvate molecules have been omitted for clarity. The purple lines represent the anisotropic axes for the ground doublet obtained with MAGELLAN.

Figure 2 .

 2 Figure 2. Perspective views of the crystal packing for 1-3 showing the coordination polyhedra.

Figure 4 .

 4 Figure 4. Frequency dependence of " for compounds 1-3 under a zero dcfield.

Figure 5 .

 5 Figure 5. Temperature dependence of the relaxation time, , for complexes 1-3 under a zero dc-field. The solid lines represent the fit.

Figure 6 .

 6 Figure 6. Hysteresis loops at 1.8 K for 1 and 2 with an average sweep rate of 15 Oe.s 1 .

Figure 7 .

 7 Figure 7. Room temperature normalized emission spectra for complexes 1-3 obtained under an excitation at exc. = 370 nm. The asterisk sign indicates excitation second order.

Table 1 .

 1 Selected bond lengths and angles in complexes 1

-5.

	Compound	Dy-O  phenoxide distances (Å)	O Dy-Cl distances (Å)	Dy-Dy (Å) intermolecular distance	Ref.
	1	2.172(2) 2.183(2)	124.55(9)	-	10.8104(4)	This work
	2	2.185(6) 2.223(5)	144.6(2)	2.621(2)	9.2237(5)	This work
	3	2.139(2) 2.143(2)	89.76(9)	2.6369(9)	7.8396(6)	This work
	4	2.190(6)	128.5(2)	-	13.9590

 -Dy-O  angle (°) [13] 5 2.193(2) 2.196(2) 121.20(4) -10.6582(

Table 2 .

 2 Fit parameters of the temperature dependence of the relaxation time for 1,2, 4 and 5.

	Compound	 (cm 1 )	0 (s)	n	C (s 1 .K n )	QTM (ms)
	1 (0 Oe)	472 ± 25	(2 ± 1)  10 10	5.35*	(6.2 ± 0.1)  10 6	20 ± 3
	2 (0 Oe)	-	-	4.3 ± 0.2	0.0012 ± 0.0008	2.6 ± 0.2
			(4.1 ±	3*	0.0157 ±	14 ±
	4 (0 Oe)	272 ± 5	0.6) 		0.0008	2
			10 8
			(6.6 ±	3*	0.0231 ±	24 ±
	5 (0 Oe)	294 ± 4	0.8) 		0.0009	7
			10 9
	*fixed parameter

  The solution was filtered, the volatiles were removed in vacuum and the solid residue was redissolved in a THF:Py:Hexane mixture (1:1:2). Slow concentration of the solution at room temperature resulted in the formation of 1 as yellow crystals. The mother liquid was decanted and the crystals were washed with cold hexane and dried in vacuum for 30 min. THF (10 mL) and the reaction mixture was stirred overnight at room temperature. The solution was filtered, the volatiles were removed in vacuum and the solid residue was dissolved in DME. Slow concentration of the solution at room temperature resulted in the formation of 2 as yellow crystals. The mother liquid was decanted and the crystals were washed with cold hexane and dried in vacuum for 30 min. Complex 2 was isolated in 84% yield (0.247 g). Elemental analysis calcd.

					Complex 1 was isolated in 80%
	yield (0.322 g). Elemental analysis calcd. (%) for C85H95BDyN5O4: C,
	71.69; H, 6.73; N, 4.91; Dy, 11.41. found (%): C, 71.99; H, 6.48; N, 5.18;
	Dy, 11.25. IR (Nujol, KBr) ν/cm -1 : 490 (s), 540 (w), 570 (w), 630 (s), 780
	(s), 800 (s), 840 (s), 880 (s), 985 (m), 1030 (s), 1070 (s), 1160 (s), 1200
	(m), 1230 (s), 1320 (s), 1420 (s), 1580 (s), 1600 (s) 1625 (s).
	Method B: NaBPh4 (0.061 g, 0.180 mmol) was added to a solution of 1
	(0.178 g, 0.171 mmol) in THF (10 mL) and the reaction mixture was
	stirred at room temperature for 15 h. The solution was filtered, the
	volatiles were removed in vacuum and the solid residue was redissolved
	in a THF:Py:Hexane mixture (1:1:2). Slow concentration of the solution at
	room temperature resulted in the formation of 1 (0.209 g) in 86 % yield.
	Synthesis of [Dy(L1)2Cl(DME)]•0.5DME (2). A mixture of HL1 (0.200 g,
	0.566 mmol) and KH (0.029 g, 0.725 mmol) in THF (30 mL) was stirred at
	room temperature for 1 h and the resulting suspension was filtered. The
	clear yellow solution was added to a suspension of DyCl3 (0.076 g, 0.283
	mmol) in
	1.0 units	1
	0.5 intensity / arb.	2 3
	0.0 Normalized							*
	400	450	500	550	600	650	700	750
			Wavelength / nm

(%) for C52H75ClDyN2O7:

C, 60.16; H, 7.28; N, 2.70; Dy, 15.65; found (%): C, 60.50; H, 7.44; N, 2.36; Dy, 15.38. (Nujol, KBr)

ν/cm -1 : 500 (s), 530 (m), 610 (s), 660 (s), 710 (s), 770 (s), 840 (s), 880 (m), 920 (m), 980 (m), 1000 (s), 1050 (s), 1070 (s), 1155 (s), 1210 (s), 1260 (s), 1310 (s), 1415 (s), 1540 (s), 1620 (s).

Acknowledgements

The authors thank the University of Montpellier, CNRS for financial support, Plateforme of Analysis and Characterisations (PAC) of ICGM for magnetic measurements. The Russian coauthors thank the Russian Science Foundation (grant 17-73-30036).

Conflict of Interest

The authors declare no conflicts of interest.


Jérôme Long

Alexander N Selikhov

Konstantin A Lyssenko

Yannick Guari

Joulia Larionova

Alexander A Trifonov

New -carbazolyl Dy(III) half-sandwich complex showing a Single Molecule Magnet behavior

We report the synthesis, structure and magnetic

The carbazolyl ligand exhibits an unprecedented  5 -interaction with the magnetically anisotropic dysprosium(III) ion resulting in a genuine zero-field singlemolecule magnet behavior.

Lanthanide coordination complexes have recently emerged in materials science owing to their intriguing Single-Molecule Magnet (SMM) behavior which opens exciting potentialities in information storage or spin-based computing. 1 Some lanthanides complexes are indeed able to exhibit a slow relaxation of their magnetization associated with a magnetic bistability at the molecular scale below a blocking temperature. [START_REF] Giansiracusa | Correlating blocking temperatures with relaxation mechanisms in monometallic single-molecule magnets with high energy barriers (Ueff > 600 K)[END_REF] This phenomenon originates from the electronic structure of a specific lanthanide ion in a particular crystal-field that allows the appearance of an anisotropic barrier opposing two antiparallel directions of magnetic moment related to the ± m J states. 3 Among the lanthanide series, the Dy 3+ Kramers ion exhibiting an oblate 4f electronic density, unambiguously gives the best SMM performances. Hence, following theoretical modeling predictions 3a, 4 in association with electrostatic considerations, [START_REF] Rinehart | Exploiting single-ion anisotropy in the design of f-element single-molecule magnets[END_REF] major advances have been achieved recently by engineering a high axial crystal-field for Dy 3+ through designing mononuclear complexes with two negatively charged ligands along the axial direction with short bond lengths and weak coordinated species in the equatorial plane. Although coordination chemistry ligands have been used in this purpose, 6 organometallic ligands such as cyclopentadienyl (Cp) derivatives gave exceptional magnetic features in dysprosium metallocene complexes 7 with magnetic hysteresis that could even reach 80 K. [START_REF] Guo | Magnetic hysteresis up to 80 kelvin in a dysprosium metallocene single-molecule magnet[END_REF] Nevertheless, the use of other carbon-based organometallic ligands, such as cyclooctatetraene (COT) or systems with greater hapticity could hardly compete with the Cp derivatives in terms of SMM's performance. This could be ascribed to their increased hapticity which provides a larger binding site, more suitable to provide an equatorial field. 9 As a consequence, the employment of rigid  5 -ligands constitutes the most appealing strategy to design high blocking temperatures SMMs. In particular, several studies lead to the improvement of SMM performances by substituting some Cp positions to increase the hysteresis temperature, 7b, 8 or by introducing an heteroatom in the Cp backbone to shortcut the molecular vibration and provide larger crystal-fields. [START_REF] Kotrle | Are Inorganic Single-Molecule Magnets a Possibility? A Theoretical Insight into Dysprosium Double-Deckers with Inorganic Ring Systems[END_REF] Thus, other  5 -organometallic ligands, such as monophosphonyl [START_REF] Evans | Bis-Monophospholyl Dysprosium Cation Showing Magnetic Hysteresis at 48 K[END_REF] or dicarbollide ligands [START_REF] Jin | Dysprosiacarboranes as Organometallic Single-Molecule Magnets[END_REF] were used. However, the SMM hallmarks were found less outstanding in comparison with authentic dysprosium metallocene complexes due to the difficulty to achieve a linear angle or the generation of onresonance vibrational modes. The magnetic relaxation being extremely sensitive to subtle effects, new examples of original  5ligands are therefore highly needed to understand the parameters affecting the relaxation and draw a general picture.

With this in mind, carbazole-based ligands constitute a tempting alternative to Cp derivatives. Indeed, these heterocyclic ligands exhibit a diversity in their coordination modes since they could act either as monoanionic -donor amido ligand but are also able to form -complexes involving the five-membered pyrrole ring, while benefiting from a strong rigid character arising from multiple aromatic rings. [START_REF] Kays | Extremely bulky amide ligands in main group chemistry[END_REF] They also show a great tunabilty in terms of substituent allowing to tune their steric hindrance and electronic features. Moreover, introducing novel functionalities, such as luminescence could be achieved since the rigid plane biphenyl core with wide band gap and high luminescent efficiency presents great opportunities for the synthesis of new emitters, [START_REF] Kong | Design Strategy for High-Performance Dendritic Carbazole-Containing Alkynylplatinum(II) Complexes and Their Application in Solution-Processable Organic Light-Emitting Devices[END_REF] and in turn for the design of luminescent SMMs. 15 In this sense, while most of the carbazolyl complexes involves divalent lanthanide ions, 16 we have recently reported that simple carbazolyl with a -donor interaction could be used to design Dy(III) SMMs. [START_REF] Long | Single-molecule magnet behavior in luminescent carbazolyl Dy(III) octahedral complexes with a quasi linear N-Dy-N angle[END_REF] However, examples of -carbazolyl complexes remain scarce and are strictly limited to divalent lanthanide ions. 18 We would like also to emphasize that examples of Dy complexes with Dy/carbanion interactions are also limited. [START_REF] Guo | An NCN-pincer ligand dysprosium single-ion magnet showing magnetic relaxation via the second excited state[END_REF] We report in this communication the synthesis, structure and magnetic investigations of a half-sandwich heteroleptic dysprosium complex showing an unprecedented  5 -coordination mode of the carbazolyl ligand resulting in the appearance of an axialcrystal field and a zero-field SMM behavior. tBu 4 CarbH and[Dy(o-Me 2 N-C 6 H 4 CH 2 ) 3 ] in toluene at 80° C (25 min.) affords the heteroleptic complex [Dy(tBu 4 Carb)(o-Me 2 N-C 6 H 4 CH 2 ) 2 ]•C 7 H 8 (1) (Scheme 1) in 82% yield after recrystallization from hot hexane. Single crystals of 1 suitable for X-Ray analysis were obtained by slow concentration of the mother liquor at room temperature. Complex 1 is a bright yellow crystalline solid, oxygen-and moisture-sensitive. It is readily soluble in THF, Et 2 O and aromatic solvents, sparingly soluble in hexane.

Analysis by single-crystal X-ray diffraction indicates that 1 crystallizes in the monoclinic P2 1 /c space group, with a unique complex in the asymmetric unit and a toluene solvate (Table S1). The compound could be described as a heteroleptic half-sandwich complex. The coordination environment of the Dy 3+ ion consists in a η 5 -coordinated carbazolyl ligand, as well as two nitrogens and two negatively charged carbons from two bidentate o-Me 2 N-C 6 H 4 CH 2 ligands (Figure 1a). In contrast to our recently reported dysprosium complexes based on an unsubstituted carbazole acting as a simple amido ligand, [START_REF] Long | Single-molecule magnet behavior in luminescent carbazolyl Dy(III) octahedral complexes with a quasi linear N-Dy-N angle[END_REF] the introduction of bulky tertbutyl groups forces the -coordination mode of the (tBu 4 Carb) ligand.

Hence, the Dy-(tBu 4 Carb) cent. bond length is equal to 2.418(2) Å, which appears greater in comparison to the distances found in dysprosium metallocene with cyclopentadienyl derivatives. [7][START_REF] Guo | Magnetic hysteresis up to 80 kelvin in a dysprosium metallocene single-molecule magnet[END_REF][START_REF] Day | Cyclopentadienyl Ligands in Lanthanide Single-Molecule Magnets: One Ring To Rule Them All?[END_REF] For comparison, the Dy-Cp* and Dy-Cp iPr5 distances are equal to 2.296(1) and 2.284(1) Å, respectively, in the complex [Dy(Cp iPr5 )(Cp*)] + . [START_REF] Guo | Magnetic hysteresis up to 80 kelvin in a dysprosium metallocene single-molecule magnet[END_REF] In 1, the Dy-C distances involving o-Me 2 N-C 6 H 4 CH 2 are comparable to the Dy-(tBu 4 Carb) cent one with values of 2.414(4) and 2.423(4) Å, while the Dy-N bond lengths are significantly longer (2.596(4) and 2.607(4) Å). It is especially worth noting the difference in the coordination type of the tBu 4 Carb ligand with Dy 3+ and Ln 2+ . 18a In [Ln(tBu 4 Carb) 2 ] complexes (Ln = Sm, Eu, Yb, Ca), the coordination of carbazolyl ligands to Ln 2+ ions features a strong contribution of η 3 -mode into η 5 metal-ligand bonding giving a displacement of the Ln 2+ ion with respect to the centroid of the five-membered ring. In contrast for 1, typical η 5 coordination mode occurred with a symmetric localization of the Dy 3+ ion above the centroid of the pyrrolyl ring (Figure 1b). The C35-Dy-C44 angle strongly deviates from linearity with a value of 138.5(1)° while the C44-Dy-(tBu 4 Carb) cent and C35-Dy-(tBu 4 Carb) cent angles are much weaker and equal to 108.22(9) and 112.03(9)°, respectively. The shortest distance between the two centroids of the aromatic cycles of the bidentate o-Me 2 N-C 6 H 4 CH 2 ligands is equal to 3.792 Å, pointing out an intramolecular -stacking interaction. Analysis of the crystal packing indicates that the shortest intermolecular Dy-Dy distance is equal to 10.1740(7) Å, suggesting that the complexes are relatively well isolated (Figure S1).

The magnetic properties were investigated in both, static and dynamic modes by using a SQUID MPMS-XL. At room temperature, the T value of 14.03 cm 3 .K.mol 1 for 1 is in an excellent accordance with the value of 14.17 cm 3 .K.mol 1 , expected for a unique Dy 3+ ion using the free-ion approximation (Figure S2).

Reducing the temperature induces a monotonous decrease of T, reflecting the thermal depopulation of the  m J levels. Below 10 K, a dramatic T decrease is observed to reach the value of 5.24 cm 3 .K.mol 1 at 1.8 K. The field dependence of the magnetization monitored at 1.8 K shows the characteristic unsaturated curve with a value of 5.13 N under a 70 kOe field. Besides, a clear inflection point could be observed at low field and was previously observed in other lanthanide based SMMs. 6b, 6e, 17, 21 Such phenomenon may express either the extreme field dependence of the relaxation rates 6h or the flip of the Dy 3+ spins under an applied magnetic field. [START_REF] Long | Single-molecule magnet behavior in luminescent carbazolyl Dy(III) octahedral complexes with a quasi linear N-Dy-N angle[END_REF] At low temperature, a clear opening in the hysteresis loop could be evidenced (Figure S3), suggesting the occurrence of a slow relaxation of the magnetization.

Such fact was further corroborated by using alternate current (ac) measurements with the aim to analyze the relaxation dynamic. Under a zero dc-field, 1 exhibits a clear frequency dependence of the in-phase (') and out-of-phase (") components of the magnetic susceptibility (Figure 2), pointing out a SMM behavior.

A single frequency peak of " that shifts towards higher frequency as the temperature increases could be noticed (Figure 2), while these out-of-phase signals could be observed up to 45 K (Figure S4). The related Cole-Cole plots (Figure S5), fitted with a generalized Debye model, give moderate  parameter values (< 0.18; Table S2). This latter being directly associated to the distribution of relaxation times, the program CC-FIT2, recently developed by Reta and Chilton,[START_REF] Reta | Uncertainty estimates for magnetic relaxation times and magnetic relaxation parameters[END_REF] was utilized to extract the relaxation time () values and the corresponding uncertainties from the underlying distribution function.

The temperature dependence of the relaxation time (Figure 3) reveals an overlap between different relaxation processes. Attempts to fit the data were performed by considering the following a) b)

equation:  1 =  0 1 exp(/kT) + CT n +  1
QTM (Eq. 1), [START_REF] Meihaus | Influence of pyrazolate vs Nheterocyclic carbene ligands on the slow magnetic relaxation of homoleptic trischelate lanthanide(III) and uranium(III) complexes[END_REF] for which the first term accounts for a thermally activated process, while the second and third ones stand for two-phonon Raman and QTM, respectively. By taking into account the simple extracted  values or the distribution of relaxation time (CC-FIT2), small  barriers and/or large uncertainties were obtained. This suggests that the thermally activated Orbach process is not dominant or even not involved in the relaxation in the investigated temperature range. The fitting was therefore performed considering only a Raman and QTM processes  1 = CT n +  1 QTM (Eq. 2) and gives the parameters found in Table 1. For comparison, the parameters obtained from CCFIT2 are reported in Table S3.

At low temperature, the relaxation time starts to become temperature independent indicating a significant QTM contribution. This latter could be shortcut by applying dc magnetic fields. Consequently, the field dependence of the ac susceptibilities was investigated for various fields up to 6000 Oe (Figure S6). The corresponding field dependence of the relaxation time could be modeled with,  1 = DH 4 T + B 1 /(1+B 2 H²) + K (Eq. 3), for which the first term accounts for the direct process (for Kramers-ion), the second one for the QTM, while the K constant accounts for Raman and thermally activated processes (Figure S7, Table S4). A maximum increase of the relaxation time is observed for an optimum field of 1000 Oe. When measured under this dc field, out-of-phase peaks could be observed up to 27 K confirming the decrease of the QTM (Figure S8). The Cole-Cole plots (Figure S9), fitted with a general Debye model, give reduced values of the  parameter (< 0.06; Table S5) with respect to the zero-field data and smaller uncertainties related to the relaxation time (Figure 3). Attempts to fit the temperature dependence of the relaxation time considering only a Raman process was performed (Figure S10, Table S3), considering that the direct process should be inoperative for such weak values of magnetic field. However, a better fit could be obtained by adding a thermally activated process as  1 =  0 1 exp(/kT) + CT n (Eq. 4) (Figure 3, Table 1). To avoid over-parameterization, the n parameter was successively fixed to different values until getting the best fitting coefficient. In contrast to the zero-field data, the shortcut of the QTM reveals the Orbach process in a higher temperature range.

Magneto-structural correlations could be achieved by determining the orientation of the anisotropic axis for the ground Kramers doublet of 1 by using the MAGELLAN software. [START_REF] Chilton | An electrostatic model for the determination of magnetic anisotropy in dysprosium complexes[END_REF] The negative charge on the tBu 4 Carb ligand was delocalized on the five atoms of the heterocycle, whereas two negative charges were ascribed on each bonded carbons of the o-Me 2 N-C 6 H 4 CH 2 ligands. It turns out that the η 5 -carbazolyl ligand imposes the direction of the anisotropic axis, which is found to pass almost trough the centroid of the five-membered heterocycle (deviation of about 5°, Figure S11). As a consequence, it appears that the C35-Dy-C44 sequence showing comparable Dy-ligand distances but an angle of 138.5°, which strongly deviates from linearity, is not favorable to dominate the electrostatic contribution. However, these negatively charged carbons localized almost perpendicular to the anisotropic axis most likely create a transverse component explaining the occurrence of the substantial QTM contribution. This latter precludes the observation of a thermally activated process under a zero-dc field. The relaxation is therefore dominated by both Raman and QTM. However, applying dc fields causes a shift of the ac signals towards higher temperatures and reveals a thermally activated relaxation. The uncertainties were determined from the CC-FIT2 software. [START_REF] Reta | Uncertainty estimates for magnetic relaxation times and magnetic relaxation parameters[END_REF] The red solid lines correspond to the fit with Eq. 2 (0 Oe) and Eq. 4 (1000 Oe).

 (cm 1 ) 0 (s) n C (s 1 .K n ) QTM (s) 1 (0 Oe) - - 2.7  0.1 0.7  0.3 0.00057  0.00002 1 ( 1000
We have reported in this communication the synthesis and structure of a new heteroleptic Dy(III) complex based on carbazolyl and carbananions ligands. Remarkably, a η 5coordinated mode carbazolyl ligand is observed for the first time with a lanthanide(III) ion. This coordination mode results in a complex with a relatively high axial crystal-field, able to stabilize the oblate electronic density of Dy(III), which leads to a genuine SMM behavior. While the relaxation in zero-field occurs through a combination of Raman and QTM processes due to the presence of coordinated ligands in the equatorial plane, the application of dc field suppresses the QTM and reveals Raman and thermally activated relaxations. Such carbazolyl ligands may therefore be considered as promising alternatives to usual Cp ligands to design high-energy barriers SMMs.

ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge on the ACS Publications website. Experimental procedures, additional structural and magnetic data could be found in the PDF.

Scheme 1 :

 1 Scheme 1: Synthesis of 1. The alkane elimination reaction of equimolar amounts of tBu 4 CarbH and [Dy(o-Me 2 N-C 6 H 4 CH 2 ) 3 ] in toluene at 80° C (25 min.) affords the heteroleptic complex [Dy(tBu 4 Carb)(o-Me 2 N-C 6 H 4 CH 2 ) 2 ]•C 7 H 8 (1) (Scheme 1) in 82% yield after recrystallization from hot hexane. Single crystals of 1 suitable for X-Ray analysis were obtained by slow concentration of the mother liquor at room temperature. Complex 1 is a bright yellow crystalline solid, oxygen-and moisture-sensitive. It is readily soluble in THF, Et 2 O and aromatic solvents, sparingly soluble in hexane.Analysis by single-crystal X-ray diffraction indicates that 1 crystallizes in the monoclinic P2 1 /c space group, with a unique complex in the asymmetric unit and a toluene solvate (TableS1). The compound could be described as a heteroleptic half-sandwich complex. The coordination environment of the Dy 3+ ion consists in a η 5 -coordinated carbazolyl ligand, as well as two nitrogens and two negatively charged carbons from two bidentate o-Me 2 N-C 6 H 4 CH 2 ligands (Figure1a). In contrast to our recently reported dysprosium complexes based on an unsubstituted carbazole acting as a simple amido ligand,[START_REF] Long | Single-molecule magnet behavior in luminescent carbazolyl Dy(III) octahedral complexes with a quasi linear N-Dy-N angle[END_REF] the introduction of bulky tertbutyl

Figure 1 .

 1 Figure 1. a) Molecular structure of 1. Color code: orange, Dy; grey, C; blue, N. Hydrogen atoms have been omitted for clarity. The dashed green bond indicates the Dy•••(tBu 4 Carb) centre interaction. b) Top view of the molecular structure of 1.

Figure 2 .

 2 Figure 2. Frequency dependence of the out-of phase (") susceptibilities for 1 under a zero dc-field.

Figure 3 .

 3 Figure 3. Temperature dependence of the relaxation time, , for 1.

Table 1 :

 1 Fit parameters of the temperature dependence of the relaxation time for 1.

	Com-
	pound

AUTHOR INFORMATION

Corresponding Author *E-mail: jerome.long@umontpellier.fr *E-mail: trif@iomc.ras.ru Author Contributions ‡All the authors contributed equally.

Notes

The authors declare no competing financial interests.

ACKNOWLEDGMENT

The financial support of the Russian Science Foundation is highly acknowledged (Project № 17-73-30036). The French authors thank the University of Montpellier, CNRS and PAC of ICGM.