Interplay between crystal and magnetic structures in YFe2(HαD1−α)4.2 compounds studied by neutron diffraction

Author’s Accepted Manuscript Interplay between crystal and magnetic structures in YFe2(HαD1-α)4.2 compounds studied by neutron diffraction V. Paul-Boncour, M. Guillot, O. Isnard, B. Ouladdiaf, A. Hoser, T. Hansen, N. Stusser www.elsevier.com/locate/yjssc

PII: DOI: Reference:

S0022-4596(16)30346-2 http://dx.doi.org/10.1016/j.jssc.2016.09.002 YJSSC19518

To appear in: Journal of Solid State Chemistry Received date: 15 July 2016 Revised date: 31 August 2016 Accepted date: 1 September 2016 Cite this article as: V. Paul-Boncour, M. Guillot, O. Isnard, B. Ouladdiaf, A. Hoser, T. Hansen and N. Stusser, Interplay between crystal and magnetic structures in YFe2(HαD1-α)4.2 compounds studied by neutron diffraction, Journal of Solid State Chemistry, http://dx.doi.org/10.1016/j.jssc.2016.09.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Interplay between crystal and magnetic structures in YFe2(HaD1a)4.2

compounds studied by neutron diffraction

V. Paul-Boncour1*, M. Guillot2, O. Isnard3,4, B. Ouladdiaf5, A. Hoser6, T. Hansen5, N. Stusser6 1

Université de Paris Est, ICMPE, CNRS-UPEC, UMR7182, 2-8 rue Henri Dunant, 94320 Thiais – France 2 LCNMI, CNRS, BP166, 38042 Grenoble Cedex 9, France 3 CNRS, Institut Néel, 38042 Grenoble, France 4 Univ. Grenoble Alpes, Inst. Néel, 38042 Grenoble, France 5 Institut Laue Langevin, 71 avenue des Martyrs, 38042 Grenoble Cedex 9, France 6 Hahn-Meitner-Institut Berlin GmbH Glienicker Str. 100, D-141 09 Berlin, Germany *

Corresponding author. Tel.: +33.1.49.78.12.07; fax: +33.1.49.78.12.03.

[email protected],

Abstract We report a detailed magnetic structure investigation of YFe2(HaD1-a)4.2 (a=0, 0.64, 1) compounds presenting a strong (H,D) isotope effect by neutron diffraction and Mössbauer spectroscopy analysis. They crystallize in the same monoclinic structure (Pc space group) with 8 inequivalent Fe sites having different H(D) environment. At low temperature, the compounds are ferromagnetic (FM) and show an easy magnetization axis perpendicular to the b axis and only slightly tilted away from the c axis. Upon heating, they display a first order transition from a ferromagnetic towards an antiferromagnetic (AFM) structure at TM0 which is sensitive to the H/D isotope nature. The AFM cell is described by doubling the crystal cell along the monoclinic b axis. It presents an unusual coexistence of non magnetic Fe layer sandwiched by two thicker ferromagnetic Fe layers which are antiparallel to each other. This FM-AFM transition is driven by the loss of ordered moment on one Fe site (Fe7) through an itinerant electron metamagnetic (IEM) behaviour. The key role of the Fe7 position is assigned to both its hydrogen rich atomic environment and its geometric position. Above TM0 a field induced metamagnetic transition is observed from the AFM towards the FM structure accompanied by a cell volume increase. Both thermal and magnetic field dependence of the magnetic structure are found strongly related to the anisotropic cell distortion induced by (H,D) order in interstitial sites.

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Graphical Abstract Representation of the FM-AFM magnetic structures of YFe2D4.2 deuteride.

Keywords: Laves Phases; Metal hydride, Isotope effect, Neutron diffraction, Magnetic structure, Magnetic transition

1. Introduction Insertion of light elements can strongly modify the magnetic properties of rare earth and transition metal intermetallic compounds [1-5]. These modifications are often related to the changes of cell volume and electronic properties due to the inserted atoms. The change of crystal structure induced by hydrogen insertion can also influence significantly the magnetic properties. For example a strong interplay has been observed between the structural and magnetic properties of RMn2 hydrides and deuterides (R=Y, Rare Earth) leading to complex magnetic phase diagrams [6-10]. Hydrogen induces a lowering of crystal symmetry (tetragonal, cubic or rhombohedral) below a given structural ordering transition temperature (TO-D). The magnetic ordering temperatures were found very close to TO-D, and this was explained by the release of magnetic frustrations on the Mn magnetic sublattice. The study of YFe2 Laves phase deuterides and hydrides, which present various crystal structures versus D or H content, is also a very interesting case to understand how the lowering of crystal symmetry induced by D or H absorption can strongly influence their magnetic structures [11]. YFe2 crystallizes in a C15 type cubic structure (Fd-3m space group (s.g.)). At room temperature, hydrogen or deuterium insertion in YFe2 leads to the formation of several YFe2(HaD1-a)x compounds (1.2 ≤ x ≤ 5), crystallizing in different structures derived from the parent cubic C15 structure (cubic, tetragonal, rhombohedral, monoclinic or orthorhombic). These structural distortions are in some cases accompanied by superstructures: for example a doubling of the cubic cell parameter was observed for x=1.75 [12,13]. This lowering of crystal symmetry is related to the long range order of H or D atoms in particular interstitial sites. Upon heating, these compounds undergo order-disorder (O-D) transitions from the ordered structures towards disordered C15 cubic structure with statistical occupation of H or D atoms in tetrahedral Y2Fe2 (96g) and YFe3 (32e) interstitial sites [12]. These structural transitions occurs at an order-disorder temperature TO-D, which decreases from 460 K for x=1.3 to 360 K for x=4.2 [12,13]. A detailed study of YFe2D4.2 by X-ray (XRD), synchrotron (SR) and neutron powder diffraction (NPD) versus temperature has shown that the deuterium order occurs in several steps: a first order transition from cubic (Fd-3m s.g.) to rhombohedral (R-3m s.g.) structure with the coexistence of the two phases between 360 and 340 K and a second order transition from 2

rhombohedral to monoclinic structure below 330 K [14-16]. The room temperature XRD and SR patterns of YFe2D4.2 were first refined in a monoclinic structure in a C2/m s.g. with 1 Y site and 3 Fe sites. However the NPD pattern at 300 K revealed additional peaks due to a further lowering of crystal symmetry in a primitive Pc space group with a doubling of the monoclinic b parameter. A full determination of the nuclear structure of YFe2D4.2 was finally solved in this monoclinic structure with 4 Y, 8 Fe and 18 interstitial D sites in 2a Wyckoff positions, using high resolution neutron powder diffraction with a time of flight spectrometer [15]. The study of the magnetic properties of YFe2Dx deuterides has revealed for 1.2 ≤ x ≤ 3.5 a ferromagnetic (FM) behaviour with a decrease of the Curie temperature TC from 720 to 363 K upon increasing x and an increase of the average moment from 2.9 to 4 µB/f.u. at 4.2 K [17]. YFe2D5 behaves as a Pauli paramagnet with a small spontaneous magnetization of 0.4 µB/f.u.[18]. YFe2D4.2 is ferromagnetic at low temperature. Upon heating, it undergoes a transition towards an antiferromagnetic (AFM) structure at TM0 and becomes paramagnetic above TN [15]. More unusual has been the discovery that replacing H by D in this compound induces a very large change of the magnetic properties [14,19]. A huge shift of 47 K (50%) of the transition temperature T M0 has been observed between YFe2D4.2 (TM0=84 K) and YFe2H4.2 (TM0=131 K) [14,20,21]. As the hydride has a larger cell volume than the deuteride, this difference of T M0 was attributed to a magnetovolumic effect [14]. The strong dependence of TM0 versus the cell volume variation was confirmed by applying an external pressure [16,21]. The suppression of the ferromagnetic order was observed for pressures above 0.56 and 1.25 GPa for the deuteride and the hydride respectively. Above TM0, the magnetization curves of YFe2(HaD1-a) compounds display a metamagnetic behaviour, with a linear increase of the transition field versus temperature and similar dBtrans/dT slopes for 0 ≤ α ≤ 1. A large variation of the magnetic entropy was also observed at TM0 revealing interesting magnetocaloric effects [20]. In order to clarify the origin of this FM-AFM transition at TM0 and its large sensitivity to isotope effect, it is important to have a clear description of the FM and AFM magnetic structures for both deuteride and hydride. But until now, only the evolution of the magnetic peak intensities of YFe2D4.2 and YFe2(H0.64D0.36)4.2 compounds measured by neutron diffraction has been published [14]. In addition, since the nuclear structure of YFe2D4.2 was at this time not fully solved, the discussion on the magnetic transition was performed using the small monoclinic cell (determined by XRD and described in the C2/m s.g.) which contains only three non-equivalent Fe sites instead of the eight non-equivalent Fe sites described in the Pc s.g. [15]. At last, the nuclear and magnetic structures of the YFe2H4.2 hydride, necessary to understand the isotope effect, were until now not investigated by neutron diffraction. Therefore, to determine the ferromagnetic and antiferromagnetic structures of YFe2(HaD1-a)4.2 compounds (a=0, 0.64 and 1), a detailed study of their NPD patterns versus temperature has been 3

undertaken, taking into account the complete nuclear structure previously solved for YFe2D4.2 [15]. New NPD experiments have been performed on YFe2H4.2 with a high intensity diffractometer in order to obtain a sufficient signal/noise ratio despite the large incoherent scattering factor of hydrogen. In addition, neutron diffraction experiments versus applied magnetic field have been performed for YFe2D4.2 at selected temperatures to explain the metamagnetic behaviour observed in the magnetization curves above the FM-AFM transition. These results will be discussed in term of correlation between the crystal and magnetic structures refined in this work and using also previous Mössbauer spectroscopy results. Finally, a structural and magnetic phase diagram will be presented for YFe2Dx versus D content to highlight the strong interplay between crystal and magnetic structures in this system.

2. Experimental The preparation of the YFe2 intermetallic compounds, and of the YFe2(HaD1-a)4.2 (a= 0, 0.64, 1) compounds are described in ref [22]. The total H and D content was estimated by a volumetric method and found to be 4.2±0.2 (H+D)/f.u.. The samples were quenched into liquid nitrogen and slowly heated under air up to room temperature in order to passivize the surface and avoid H or D desorption, which can occur when the samples are kept for a long time at ambient temperature. The powder samples were introduced in vanadium sample holder for the neutron diffraction experiments at zero field. Neutron powder diffraction (NPD) patterns of YFe2D4.2 and YFe2(H0.64D0.36)4.2 have been recorded at 10 and 300 K on the high resolution 3T2 spectrometer at the Laboratoire Léon Brillouin (LLB, CEA, Saclay, France) with l= 1.225 Å (angular range 15 ° ≤ 2q ≤ 125 ° and a step of 0.05 °). NPD patterns of YFe2D4.2, YFe2(H0.64D0.36)4.2 and YFe2H4.2 compounds were measured at temperatures between 1.8 and 300 K on G4.1 spectrometer (LLB, Saclay) with l=2.4266 Å which allow to measure the magnetic peaks at low angle with high resolution (angular range 2° ≤ 2q ≤ 82° and a step of 0.01 °). The NPD patterns of the hydride were measured at temperatures between 2 and 300 K on high intensity two axis diffractometer D20 at the Institut Laue Langevin (ILL) in Grenoble with l=1.870 Å, the angular range was 4-145° and the step 0.1°. NPD measurements have been performed for YFe2D4.2 under applied field up to 120 kG using a vertical field cryo-magnet on E6 focusing diffractometer at Helmoltz Zentrum Berlin (HZB) in Germany. The powder sample introduced in an aluminum cylindrical sample container was frozen with deuterated alcohol to avoid preferred orientation of grains under high magnetic field. In addition, to avoid the presence of additional Bragg peaks due to the crystallization of pure ethanol or methanol 4

at low temperature, the alcohol was constituted by a mixture of deuterated ethanol and methanol which introduces only an amorphous contribution upon cooling. The selected wavelength was 2.454 Å and the angular range 3 ° ≤ 2q ≤ 113 ° with a step of 0.15 °. To facilitate the comparison of the NPD patterns obtained on diffractometers with different wavelengths, all the NPD patterns will be presented versus Q (4.π.sin(θ)/l) instead of 2θ. All the NPD patterns were refined using the Fullprof code [23,24]. The Wigner-Seitz cells were calculated with the BLOKJE code from Gelato [25] with a metallic radius of 1.81 Å for the Y atoms, 1.26 Å for the Fe atoms and 0.4 Å for D atoms.

3. Results and analysis 3.1 Crystal structure at 300 K Refined NPD patterns (Table 1) of YFe2(HaD1-a)4.2 compounds (a= 0, 0.64 and 1) measured on G4.1 at 300 K are compared in figure 1. The influence of H/D isotope is clearly seen: the signal/background intensity ratio decreases significantly upon H for D substitution due to the large incoherent scattering cross section of hydrogen compared to the deuterium one (sincoh (H) = 80.27(6) barn and sincoh (D) =2.05(3) barn). The intensities of the Bragg peaks are also different due to the opposite signs of the coherent scattering length of hydrogen isotopes (bcoh. (H) = -3.741(1) fm and bcoh. (D) =6.671(4) fm). The NPD pattern of YFe2D4.2 was previously refined in the monoclinic Pc s.g. taking into account the doubling of the b parameter [15,26]. The cell parameters refined from the NPD patterns are compared with those obtained by XRD at 300 K in the same Pc s.g. in table 1. The D atoms are located in 18 different tetrahedral interstitial sites (15 Y2Fe2 and 3 YFe3) as reported in table 2 and represented in figure S1 (Supplementary material). The NPD pattern of YFe2(H0.64D0.36)4.2 was refined with only the contribution of Y and Fe metal atoms. The H/D ratio was chosen to obtain an average value = 0, and no H or D contribution due to a preferential H or D insertion in the tetrahedral site was observed (see refined 3T2 pattern in figure S2). The NPD pattern was refined with a mixture of 78 wt% of the YFe2(H0.64D0.36)4.2 monoclinic phase and 22 wt% of the YFe2(H0.64D0.36)3.5 rhombohedral phase. The presence of the rhombohedral phase with x=3.5 is due to a partial (H,D) desorption which has occurred because the sample was kept a long time at room temperature. The refined monoclinic cell parameters are reported in table 1. The XRD and NPD patterns of YFe2H4.2 were refined with only one single monoclinic phase. The NPD pattern of YFe2H4.2 (Figure S3), measured on D20 in order to have a reasonable signal/noise intensity, was well refined with the same nuclear structure as YFe2D4.2 (same H atomic positions and 5

occupancy factors than for D atoms) (table 2) and larger cell parameters (table 1). The cell volume increase (+0.8%) has been attributed to the larger amplitude of vibration at zero point energy (ZPE) of the interstitial hydrogen atoms compared to the deuterium one [14]. The calculated Fe-D(H) and Fe-Fe distances (dmin–dmax range and average value for each site) are reported in table 3 for a= 0 and 1. Wigner Seitz cells (WSc) were calculated for each Fe site. The average numbers of D(H) neighbours around each Fe site (ND and NH) have been calculated taking into account the refined occupancy factor Nocc of each interstitial atom. Fe1 is surrounded by an average of 3.75 interstital atoms (forming a D or H tetrahedron) whereas the seven other Fe sites are surrounded by an average of 4.6 - 4.9 D(H) atoms (forming D or H trigonal bipyramids) (figure S4 in supplementary material). Note that these non integer values are related to the partial occupancy of some interstitial sites by H or D atoms. For full site occupancy, Fe1 would be surrounded by 4 D(H) atoms and the other Fe sites by 5 D(H) atoms. The Fe-D(H) distances are ranging between 1.62(1.63) and 1.88(1.89) Å depending on the Fe site, with an average value around 1.75(1.76) Å. These values are larger than for YFe2D1.3 [27], but smaller than observed for other iron rich deuterides as R2Fe17D5 compounds (Fe- D(H) = 1.9-2.0 Å) [28,29]. All the D-D (H-H) distances are larger than 2 Å, as expected from the Switendick criteria [30] so that simultaneous occupancy of two nearest neighbour deuterium sites have been excluded by deuterium or hydrogen order [31]. Each Y atom is surrounded by about 8 D(H) neighbours at distances ranging between 2.08 and 2.47 Å, 12 Fe neighbours at distances between 3.02 and 3.45 Å and 4 Y neighbours at distances between 3.37 and 3.48 Å. The Y-D values are smaller than the R-D distances varying between 2.32 and 3.38 Å of the above mentioned R2Fe17Dx compounds [28,29,32]. This indicates that the YFe2(H1-aDa)4.2 crystal structure can be considered as compact.

3.2. Structural evolution versus temperature The evolution of the monoclinic cell parameters of YFe2H4.2 versus temperature is displayed in figure 2 and compared to the M(T) magnetization. There is a sharp contraction of the a, b, c and V cell parameters at TM0=131±1 K. Upon heating, the relative cell parameter variation is around -0.2% for a and c parameters, whereas it remains smaller for b and β (< -0.1 %). The cell volume contraction at TM0 (DV/V= -0.43 %) is smaller than in YFe2D4.2 (DV/V= -0.65 %). As the temperature increases, the cell parameters decrease slightly up to 170 K. A significant change is observed at higher temperature with an increase of a, c and β parameters and a continuous decrease of b which can be attributed to the reduction of the monoclinic distortion. This evolution is qualitatively similar to that observed for YFe2D4.2 [15], but the structural transitions are shifted to higher temperature.

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3.3. Magnetic structures at zero field The evolution of the strongest FM (Q» 1.35 Å-1, d» 4.65 Å) and AFM (Q» 0.27Å-1, d» 6 Å) peak intensities versus temperature is compared for the three YFe2(H1-aDa)4.2 compounds with different isotopic ratio a = 0, 0.64 and 1 measured on G4.1 in figure 3(a). For YFe2(H0.64D0.36)4.2 only the lines belonging to the monoclinic phase were analyzed. The cell volume variation, added in this figure, shows the coincidence between the crossing of the FM-AFM line intensities and the cell volume contraction for each compound. This figure clearly demonstrates that the H for D isotope substitution induces an increase of TM0 and TN transition temperatures. The variation of TM0, TN and TAFM (the temperature at which the AFM line intensity is the largest) is displayed versus H content in figure 3(b). A linear increase of TM0 and TAFM is observed versus a, whereas this increase is non linear for TN. Indeed the TN-TM0 difference decreases from 52 K to 35 K for a varying between 0 and 1. TM0 was found to increase also linearly versus the cell volume confirming that the FM-AFM transition is driven by a magnetovolume effect [14,33]. To understand the origin of the FM-AFM transition and the non linear variation of TN(a), we need to solve both the ferromagnetic and antiferromagnetic structures of the deuteride and the hydride. Due to the complexity of the crystal structure some constrains were introduced to refine the magnetic structure from NPD patterns. The atomic positions and occupation numbers of Y, Fe and D(H) atoms were fixed as refined in the paramagnetic range at 300 K, as no significant change of the nuclear structure has been observed at 200, 96 and 60 K [15]. The small negative induced magnetic moment of Y (~ -0.4 µB/atom) observed by spin polarized band structure calculations [17] was considered as negligible compared to that of Fe. Due to the small number of magnetic peaks (4 peaks for FM and 2 peaks for AFM structures) it was not possible to fit the NPD patterns by refining independently eight different Fe moments. Therefore, we have in a first step assumed an average Fe moment <µFe> for all Fe sites. We will then consider previous Mössbauer results published on YFe2D4.2 to discuss the distribution of local Fe moments in the deuteride [34]. 3.3.1. Ferromagnetic structure The NPD patterns of YFe2D4.2 at 10 K (3T2) and YFe2H4.2 at 2 K (D20) were refined taking into account the previous assumptions. Due to the strong anisotropy of the monoclinic structure, a spherical description of the magnetic structure has been used. The theta angle (q) and the phi angle (j) are defined as the angles between the Fe moment and the c and b axis respectively (see insert in figure 4a). Different magnetic models have been tried to take into account all the possible Fe moment orientations. The best refinement of YFe2D4.2 NPD pattern (figure. 4(a)) is obtained for <µFe> = 1.82(11) µB, q= 16±5° and j=90°. Similar magnetic structure is found for YFe2H4.2 with <µFe>= 7

2.09(7) µB, q= 13.8±5° and j=90° (figure 4(b)). The refined values of the Fe moments are close to those deduced from the saturation magnetization at 4.2 K [14] (µFe=1.86(2) µB and 2.06(2) µB for a= 0 and 1 respectively) confirming a larger mean Fe moment for the hydride as expected from larger Fe-Fe distances [17]. The Fe moments are parallel to the basal plane i.e. perpendicular to the monoclinic b axis. The values of q indicate a small canting from the c axis as represented in the inset of figure 4. The refinement results are reported in Table 4 and compared with that in AFM and PM (paramagnetic) states at selected temperatures. The cell parameters are larger in the FM state than in the PM state ( measured at 150 and 200 K for the deuteride and the hydride respectively). A schematic description of the FM structure is shown in figure 5(a) and (c). In figure 5(a) one can observe chains of Fe atoms almost aligned along the b axis (Fe7-Fe4-Fe6-Fe3-Fe7 chains for x» 0.5 and z» 0.25 or 0.75). Each of these Fe pairs participates to one edge of a Fe4 tetrahedra whereas the Fe1 and Fe8 atoms form vertex which rely two corresponding tetrahedra. The Mössbauer spectrum of YFe2D4.2 at 4.2 K has been previously refined with 8 sextets of equal intensity with BHF hyperfine fields varying between 147.6 to 279.6 kG and an average value of 206.8 kG [34]. Assuming that corresponds to <µFe>= 1.82 µB, this yields a conversion factor A=113.6 kG/µB. Using this conversion factor, the local Fe moments are found to vary between 1.30 µB and 2.46 µB (Table S1, appendix). These minimum and maximum values are comparable with those obtained by ab-initio calculations for YFe2H4 described in the small monoclinic cell described in C2/m s.g. (µFe(4b)=1.48 µB, µFe(2a)= 2.22 and 2.46µB) [17]. These calculations showed that without hydrogen, the mean Fe moment was around 2.45 µB due to cell volume expansion, but was significantly reduced by the presence of strong Fe-H chemical bonding above 4 H/f.u.. Therefore, it was assumed that the smaller local Fe moments correspond to the Fe sites with larger number of D neighbours (N D). Then for two Fe sites with close ND number it was supposed that a larger volume of Wigner-Seitz cell corresponds to a larger Isomer Shift (IS), as it is generally done to assign Mössbauer sextets to crystallographic sites [34-36]. A proposed assignment of the Fe moments issued from Mössbauer data with the different crystallographic Fe sites is detailed in table S1 taking into account these different parameters (ND and WSc volume). These Fe moments are also reported in table 2 and compared with the refined average µFe value obtained by NPD at 10 K. This leads to three Fe sites (Fe7, Fe4 and Fe3) with small Fe moments (1.3-1.42 µB), two Fe sites (Fe5, Fe8) with intermediate Fe moments (1.6, 1.7 µB) and three sites (Fe2, Fe6 and Fe1) with large Fe moments (2.33-2.46 µB).

3.3.2. Antiferromagnetic structure The 57Fe Mössbauer spectra of both deuteride and hydride showed a mixture of doublets and sextets between TM0 and TN, indicating the coexistence of ordered and non ordered Fe moments [14,37]. We have therefore supposed that the FM-AFM transition can be related to the loss of magnetic order of at

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least one Fe site and to the change of orientation of other Fe moments. This assumption is supported by a similar type of FM-AFM transition observed for Hf1-xTaxFe2 Laves phases compounds (x≤ 0.2) [38-41]. Hf0.8Ta0.2Fe2 crystallizes in a C14 hexagonal structure with two inequivalent Fe sites (2a and 6h sites) and its ground state is ferromagnetic with µ(Fe-2a)=1.41 µB and µ(Fe-6h)=1.48 µB. Upon heating a transition toward an AFM structure is observed at 200 K: the ordered moment of Fe-2a atom is suppressed and the magnetic moment of the Fe-6h atoms remain parallel in the (0 0 1) plane and become antiparallel between two successive planes. The additional AFM magnetic peaks observed for TM0 ≤ T < TN in YFe2(HaD1-a)4.2 NPD patterns have been indexed with a (0, 1/2, 0) magnetic propagation vector [19]. The AFM magnetic cell can therefore be described by doubling the monoclinic b parameter and generating 4 positions for each of the 8 inequivalent Fe sites with the symmetry operations reported in table S2 (supplementary material). 32 Fe atom positions were generated in the AFM cell and sorted by increasing y coordinate values lying along the b axis (Table 5). Assuming that the Fe moment of one given Fe site can vanish at the transition and that half the Fe moments of their closest Fe neighbours change of sign, it is possible to build eight different arrangements for the AFM structure (Table 5). Only the solutions 1 and 8, assuming that µFe=0 at Fe7 or Fe6 site, lead to an equivalent number of positive and negative signs for the other Fe moments and a good refinement of the NPD pattern. The other 2 to 7 solutions can easily be ruled out since they do not correspond to the AFM behaviour observed from macroscopic data analysis. In addition, the assumption that both Fe6 and Fe7 atoms loss their moments at TM0 (solution 9) did not allow to refine the NPD pattern either. The geometric condition is therefore an important criterion to choose the appropriate Fe site: both Fe6 and Fe7 sites contain two atoms with almost the same value of y coordinate, and form Fe layers perpendicular to the b axis i.e. to the high symmetry direction in the chemical structure. Therefore the AFM structure built from simple FM layers may be easily created when the Fe atoms located on Fe6 or Fe7 position lose their magnetic moments. The best fit is obtained for the solution 1, corresponding to Fe7 site which has also a smaller Fe moment (1.30 µB) compared to Fe 6 (2.40 µB). Note that the Fe7 moment magnitude is also close to that of Fe-2a moment in Hf0.8Ta0.2Fe2 which loses its moment at the FM-AFM transition [41]. The refinement results of the NPD pattern of YFe2D4.2 at 95 K and YFe2H4.2 at 135 K are given in table 4 and plot in figure 6. The AFM structure and a zoom around the Fe7 atom are represented in figure 5(b) and (d). The easy magnetization axis is perpendicular to the b axis, a result in agreement with the anisotropy of the Fe sublattice in the FM ground state. This AFM structure is constituted by ferromagnetic layers with Fe moments parallel to the (a, c) plane and a thickness of about 11.5 Å, separated by a non magnetic layer. The ferromagnetic layers are oriented antiparallel above and below the (010) plane containing the Fe7 atoms, forming a two dimensional magnetic network as presented in figure 5(b). Like in the ferromagnetic state, a distribution of Fe moment magnitudes should also exist in these intermediate ferromagnetic layers, but the broadening of the Mössbauer spectra did not

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allow to refine each sextets with three independent parameters (IS, quadrupolar splitting and B HF) and propose a correspondence between the Fe sites and the local Fe moment. Coming back to the Pc space group symmetry retained by the nuclear structure, we recall that the glide mirror c is perpendicular to the b axis and located at coordinates (x 0 z). The observed AFM structure bears witness that the polar magnetic vectors are respecting the c symmetry operator without any time reversal, the magnetic space group being Pc. Two features are remarkable in such magnetic structure: i) the coexistence of large Fe moments on the blocks (<µFe> =1.75 µB) and of zero moment on the Fe7 sites, and ii) the very small if not zero value expected for the molecular field experienced at the Fe7 position due to the opposite coupling of the layers located above and below. One can wonder why the Fe7 position plays such unique role among the Fe atomic sites that is determinant to establish such AFM layered structure made of antiparallel coupled ferromagnetic blocks? A remarkable feature is the absence of ordered magnetic moment on these Fe7 positions. In addition due to its weak moment in the FM state, the Fe7 moment should become more easily disordered through a first order itinerant electron metamagnetic (IEM) transition [14,16], which explain the also the metamagnetic behaviour observed above TM0. Each Fe7 atom is surrounded by 6 Fe atoms: 2 Fe1 (d1=2.734 and d’1= 2.792 Å), 2 Fe2 (d2=2.737 and d’2=3.007 Å), 1 Fe3 (d3=2.726 Å) and 1 Fe4 (d4=2.807 Å) and is located at the contact point of two tetrahedra (figure. 5(c)). The interatomic distances between these 6 neighbour atoms located below and above the (010) plane are varying between 4.74 and 5.83 Å. In addition according to the Mössbauer result analysis the Fe1 and Fe2 should have large local Fe moments (µFe > 2.3 µB) and the Fe3 and Fe4 smaller and comparable Fe moments (1.3-1.4 µB). The second question is why such distribution of nearest neighbour number and distance stabilize preferentially an anti-parallel alignment i.e. negative values of Fe-Fe exchange interactions for layers located above and below the (a, c) plane containing the Fe7 atoms? It is difficult to calculate all the exchange interactions for each Fe-Fe pairs in this structure which contains 8 different Fe sites, but some general assumption can be made using previous calculations of the exchange interactions in Y-Fe compounds [42]. In YFe2, three positive exchange parameters between Fe-Fe pairs were calculated using a Monte Carlo simulation: J01 =15.2 meV (6 Fe at 2.604 Å), J02 =1.14 meV (12 Fe at 4.509 Å) and J03 =1.34 meV (12 Fe at 5.206 Å). It was also shown that in accordance with the mean field theory, the Curie temperature T C of the Y-Fe compounds is proportional to , where is the total exchange interaction averaged over the different Fe sites (112 meV for YFe2). For YFe3, Y2Fe17 and YFe12, which contains three or four inequivalent Fe sites and therefore a larger Fe-Fe distance distribution than in YFe2, several negative values of Fe-Fe pairs exchange parameters have been reported in particular for the second (dFe-Fe=3.6-4.6 Å) and third (dFeFe=4.7-5.4

Å) Fe shells [42]. This resulted to a decrease of and TC despite their larger ratio of

Fe/Y atoms. From the variation of TC versus D content in YFe2Dx deuterides one can estimate the corresponding exchange parameter . For YFe2D4.2, should be around 17 meV for TM0=84 K. 10

In addition, the large distribution of Fe-Fe distances should induce a large number of negative values in second and third Fe shells like for other Y-Fe alloys [42]. In the absence of ordered Fe moment on the Fe7 site in the AFM state, only J02 and J03 parameters will contribute to the average interaction between its Fe neighbours separated by distances between 4.74 to 5.83 Å. In this case, the average FeFe interaction will be negative and the AFM order stabilized. On the other hand, in the sandwiched Fe layers, the Fe atoms are separated by distances between 2.5 and 3.05 Å, the exchange interaction parameter J01 should remain positive and larger than J02 and J03, leading to a positive value of and a FM coupling.

3.3.3. Magnetic structure evolution versus temperature The NPD patterns have been refined in the previously described FM and AFM structures for both hydride and deuteride from 2 K to TN and the mean Fe moments plot versus temperature in figure 7. The amplitude of the Fe moment in the FM phase decreases smoothly from 2 K to about 65 and 120 K for the deuteride and the hydride respectively. Then, there is a two phase range with coexistence of both FM and AFM phases (70-90 K for the deuteride and 120-135 K for the hydride), where the refined Fe moment of the FM phase decreases and that of the AFM phase increases. This FM-AFM transformation is accompanied by a sharp cell volume decrease (figures 2 and 3), mainly due to a contraction of a and c parameters, in agreement with the reduction of the Fe moments oriented in the (a, c) plane. The FM-AFM transition implies at the same time the vanishing of the ordered Fe7 moment and the rotation of 180° of half the other Fe moments. From a symmetry point of view it means that the glide mirror observed at (x 0 z) has undergone a time inversion when passing from the AFM to the FM magnetic structure upon cooling, thus enabling the Fe7 position to carry a magnetic moment within the (a, c) plane. NPD can give only an average picture, but locally this transformation should also occur with a distribution of Fe moments as observed by Mössbauer spectroscopy. At 90 K (deuteride) and 135 K (hydride), the transformation to AFM state is completed and the intensity of the Fe moment decreases progressively up to TN. This reduction is accompanied by a smooth decrease of the unit cell volume, related to the reduction of the mean Fe moment in each Fe layer. The b unit cell parameter presents a pronounced Invar like behaviour. The magnetization curve of YFe2H4.2 (figure 2) shows a sharp magnetization decrease at TM0 in agreement with the NPD results, but no significant change at TN. This implies that the decrease of the Fe moment amplitude occurs exactly in the same ways in the two ferromagnetic blocks carrying Fe magnetic moments of opposite direction, and vanishing at TN. The reduction of the Fe moment versus temperature can be interpreted as the progressive weakening of the Fe interactions in each ferromagnetic layer. In this case, what was interpreted as a Néel temperature can be also explained by a reduced Curie temperature for each FM block. Thin film studies have shown that the ordering temperature decreases as one of the physical dimension is reduced [43,44]. 11

The <µFe> moment variation between TAFM (temperature where the AFM peak is maximum) and TN can be fitted according to the following equation simulating a ferromagnetic saturation magnetization decrease versus temperature [45,46]: µ (T)/µ (T ) = A. (1 − exp

!"!#$% "!& *) t

(1)

with t= 12.7(5) K for the hydride and 24.6(9) K for the deuteride.

The non linear variation of TN versus a can be attributed to the competition between the ferromagnetic interactions inside the FM blocks and the thermal disorder. Under an applied pressure larger than 1 GPa, the AFM structure becomes the ground state with TN=90 K [16]. This value is larger than the difference TM0-TN = 52 K, observed for YFe2D4.2 at ambient pressure. Taking into account the data obtained also for YFe2D4.2 at 1 GPa and YFe2(H0.64D0.36)4.2, TN can be related to TAFM by a second order polynomial: T+ = 92.7 + 0.37. T + 0.0011 T

(2)

Above TN there is no longer magnetic peak, but the background increases with temperature at low angle, suggesting the existence of short range order ferromagnetic interactions. As expected, the paramagnetic state corresponds to the magnetic space group, Pc *1’. Note that above TN, the M(B) curves are described by a linear behaviour but with a remaining spontaneous magnetization: Mspont= 0.6 µB/f.u. at 170 K and 0.14 µB/f.u. at 290 K for YFe2D4.2.

3.4. Field dependence of magnetic structure of YFe2D4.2 in the range TM0
results confirm the first order character of the field induced transition from an AFM toward a FM state through an itinerant electron metamagnetic behaviour observed in MT(B) curves above TM0.

4. Discussion It is worth to observe that both hydride and deuteride crystallize in the same monoclinic structure and that the main structural difference between these two phases is related to a volume effect. In YFe2D4.2 and YFe2H4.2 the tetrahedral Fe4 sites formed by four Fe at the corner are too small to be filled (r < 0.4 Å) [47], and only 19 % of the Y2Fe2 and 10 % of the YFe3 available interstitial sites are filled due the repulsive interactions between the H-H or D-D atoms (dH-H ³2.1 Å) [30]. This partial H(D) filling induces a relaxation of Y and Fe metal atom positions and the monoclinic cell distortion. Previous band structure calculations performed on YFe2H4.25, assuming the same crystal structure than YFe2D4.2, have shown that at 0 K the monoclinic structure is more stable than the disordered cubic type C15 one [48]. The calculated heats of formation are DH=-1.76 kJ mole/at. and -1.23 kJ mole/at. for the monoclinic and cubic structures respectively. The present study shows the influence of the monoclinic crystal structure on the magnetic structures of YFe2(HaD1-a)4.2 compounds: i) the anisotropic orientation of the Fe moments perpendicular to the monoclinic b axis in both FM and AFM structures, ii) the doubling of the magnetic cell along the b axis in the AFM structure, iii) the anisotropic cell volume contraction in the basal plane at the FMAFM transition, iv) the influence of the number of H, D neighbours on the Fe7 IEM behaviour and the distribution of local Fe moment observed by Mössbauer spectroscopy, v) the influence of the cell volume changes induced by isotope substitution on the transition temperatures. These correlations, which have not been observed experimentally for the YFe2Dx deuterides with lower D content, can be explained by the coincidence of particular structural and electronic properties occurring for x=4.2, which are detailed below. To lighten this discussion both structural and magnetic transition temperatures have been reported versus deuterium content in figure 10. The Curie temperatures TC of the YFe2Dx compounds with x < 3.5 are above the corresponding structural order-disorder transition TO-D, whereas these two temperatures are crossing each other for x= 3.5. Then, for x > 3.5 the magnetic ordering temperatures become lower than TO-D [12,27,49-51]. Therefore, for x=4.2 the lowering of crystal symmetry induced by D order directly influences the magnetic structure of the deuteride, since the magnetic transitions are below TO-D (340-360 K). The unique Fe site in YFe2 is split in 8 different sites with various D(H) environment. As a consequence, the magnetic ordering temperatures of YFe2D4.2, TM0 and TN, are smaller than the magnetic ordering temperature of 200 K expected from a linear extrapolation of TC versus D content for x=4.2. The low value of TM0 can be attributed to the existence of the FM-AFM

13

transition: the mean Fe moment <µFe> is still large in the FM phase before the transition (1.75 µB), and a significantly higher TC should be expected in absence of this transition. On the other hand, band structure calculations [17] have shown that the ferromagnetic order of YFe2Hx hydrides is stabilized by the increase of the cell volume but destabilized by the insertion of H atoms, as the H electrons contribute to the filling of the conduction band and the formation of Fe-H bonds. The competition of these two effects was clearly seen on the evolution of the mean Fe magnetic moment measured at 4.2 K and calculated at 0 K:< µFe> is maximum at x=3.5 and decreases for larger H content. YFe2(HαD1-α)4.2 compounds are just located at the H or D concentration, where the opposite volume and electronic effects are crossing. For this reason, the Fe moment becomes more delocalized than in YFe2 and one Fe site adopts an itinerant electron metamagnetic behaviour, leading to the observed FM-AFM transition. This YFe2(HαD1-α)4.2 system is therefore a particularly interesting case to observe both geometric and electronic influence of H or D insertion on the magnetic properties of intermetallic compounds. It is also a rare situation, where the H for D substitution, so strongly modifies the magnetic transition temperatures. YMn2D4.3, which differs from YFe2D4.2 by the nature of the transition metal, presents also a strong interplay between the magnetic and hydrogen order. YMn2D4.3 undergoes an order-disorder transition from rhombohedral to cubic structure above 330-360 K, i.e. in the same temperature range than YFe2D4.2. This rhombohedral distortion (R-3m s. g.) is related to the ordering of D atoms into 3 over 6 available interstitial Y2Mn2 tetrahedral sites [6,8] and the Mn 16d crystallographic site is split into two inequivalent Mn sites (1a and 3b). Rhombohedral YMn2D4.3 is antiferromagnetic with a stacking sequence of (++--) ferromagnetic 111 planes and a Mn moment of 3.2 µB. Both rhombohedral splitting and antiferromagnetic peaks disappear at the same temperature at ambient pressure showing a coincidence between TN and TO-D. However, the deuterium and magnetic orders can be decoupled under applied pressure, with a decrease of TN and an increase of TO-D above 2 GPa [52]. This demonstrates that the rhombohedral-cubic structural transition is related to the D-D interactions and not to the AFM order as could be expected for a magnetostrictive effect. On the other hand the AFM structure is stabilized by the rhombohedral distortion, and the decrease of T N under pressure is due to the reduction of the Mn-Mn distances. Therefore, although the magnetic structures of YMn2D4.3 and YFe2D4.2 compounds are different, in both cases the magnetic order is a consequence of the lowering of crystal symmetry induced by deuterium order. In conclusion, the opposite influence of hydrogen or deuterium insertion in YMn2 and YFe2 on their magnetic ordering temperatures (augmentation/ reduction) can be mainly attributed to the modification of their density of states by additional H electrons. For YMn2H(D)x compounds both the cell volume increase and the addition of H electrons favor the onset of magnetism whereas in YFe2H(D)x the cell volume increase and the H electron insertion have opposite effects on the Fe magnetic interactions and the magnetism is destabilized for large H(D) content. 14

5. Conclusions YFe2H4.2 hydride crystallizes in the same monoclinic crystal structure than YFe2D4.2 with a 0.8 % larger cell volume at 300 K. In this monoclinic structure, which is due to deuterium order in 18 interstitial sites, there are 8 inequivalent Fe sites surrounded by different number of D neighbours and a broad Fe-Fe distance distribution. At low temperature the compounds are ferromagnetic, with a distribution of Fe moments (µFe =1.30 to 2.46 µB), and a larger mean Fe moment for the hydride (2.09 µB) compared to the deuteride (1.82 µB) attributed by its larger cell volume. Upon heating these compounds undergoes a FM-AFM transition observed for the Fe sublattice at TM0= 84 K for YFe2D4.2 and TM0= 130 K for YFe2H4.2. This confirms the existence of a huge H/D isotopic effect in YFe2(H,D)4.2 compounds and demonstrates the sensitivity of the Fe magnetism to slight volume changes. In both AFM and FM magnetic structures, the easy magnetization direction is perpendicular to the b axis. The AFM structure cell is described by doubling the nuclear cell along the b axis. The FM-AFM transition is attributed to the itinerant electron metamagnetic behaviour of one of the Fe site (Fe7) and is controlled by both geometric and electronic effects induced by H or D absorption. The neutron diffraction pattern characteristic of the AFM state is fitted with a Fe7 position carrying no magnetic moments since this atomic position is sandwiched by two blocks of (010) Fe planes carrying magnetic moments of equal magnitude but of opposite directions. Isothermal neutron powder diffraction study under applied magnetic field revealed the occurrence of a field induced transition from AFM to FM magnetic structure. This magnetic order change is accompanied by a large magnetovolumic effect at the transition field corresponding to a step in the magnetization curves. The strong interplay between the crystal and magnetic structure in this system has been related to the influence of interstitial hydrogen isotopes on both geometric and electronic properties.

Acknowledgments The authors thank the Intitut Laue Langevin (ILL, Grenoble, France), the Laboratoire Léon Brillouin (LLB, Saclay, France) as well as the HZB (Berlin, Germany) for the allocated beam time to perform the experiments. The experiments at HZB have been supported by the European Commission under the 6th Framework Programme through the Key Action: Strengthening the European Research Area, Research Infrastructures. Contract n°: RII3-CT-2003-505925 (NMI3). We are also thankful to G. André, retired from LLB, for his help as local contact on G4.1 spectrometer. We thank also G. Wiesinger and L. Bessais for the discussions on Mössbauer spectroscopy analysis.

References

15

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Table 1. XRD and NPD monoclinic cell parameters of YFe2(H1-aDa)4.2 compounds at room temperature in Pc space group. YFe2D4.2 Method

XRD

Instrument

YFe2(H0.64D0.36)4.2 NPD

XRD

3T2

NPD

YFe2H4.2 XRD

3T2

NPD D20

a (Ǻ)

5.508(3)

5.5075(3)

5.526(7)

5.5166(2)

5.5204(2)

5.5275(3)

b (Ǻ)

11.468(6)

11.4651(8)

11.482(10)

11.479(2)

11.505(2)

11.5257(6)

c (Ǻ)

9.429(3)

9.4211(5)

9.429(7)

9.4342(2)

9.4511(2)

9.4665(4)

122.38(2)

122.47(1)

122.45(1)

122.36(1)

122.35(2)

122.33(3)

503.3(4)

501.90(5)

504.74(8)

504.62(1)

507.08(1)

509.61(4)

Biso Y (Å )

2.91(6)

0.75(5)

1.0(1)

0.81(4)

1.24(5)

0.80(6)

2

2.85(7)

0.51(3)

1.1(1)

0.82(3)

1.26(6)

0.65(4)

b (°) 3

V (Å ) 2

Biso Fe (Å ) Biso D/H (Å2) RBragg (%)

1.76(5) 7.5

8.2

9.7 18

6.7

0.85(8) 6.8

7.4

RWp (%)

13.6

13.8

7.5

19

12.2

17.0

9.4

Table 2. Atomic positions in Pc space group for YFe2D4.2 [15] and YFe2H4.2 refined at 300 K. The corresponding cell parameters, Biso, RBragg and RWP factors are in table 1. The values of µFe are proposed from NPD refinement or according to previous Mössbauer results for the deuteride at 4.2 K. Name

site

x

y

z

NOcc

µFe (µB)

µFe (µB)

NPD

Mössbauer

Y1

2a

0.1318(10)

0.1188(5)

0.8683(6)

1

Y2

2a

0.8798(11)

0.3710(5)

0.6361(6)

1

Y3

2a

0.1384(10)

0.3753(4)

0.3694(6)

1

Y4

2a

0.8708(11)

0.1253(5)

0.1334(7)

1

Fe1

2a

0.4949(8)

0.12676(36)

0.4899(5)

1

1.82

2.46

Fe2

2a

0.0169(8)

0.12494(45)

0.5164(4)

1

1.82

2.33

Fe3

2a

0.5019(8)

0.24097(29)

0.2597(4)

1

1.82

1.42

Fe4

2a

0.5009(8)

0.24118(34)

0.7432(5)

1

1.82

1.33

Fe5

2a

-0.0146(8)

0.37900(45)

-0.0060(5)

1

1.82

1.61

Fe6

2a

0.4905(7)

0.50382(35)

0.2481(5)

1

1.82

2.40

Fe7

2a

0.4898(8)

0.99634(36)

0.7392(5)

1

1.82

1.30

Fe8

2a

0.4997(9)

0.37190(39)

0.0001(6)

1

1.82

1.70

D1

2a

0.5516(13)

0.6238(6)

0.8501(8)

0.845(12)

D2

2a

0.4856(12)

0.6325(5)

0.1419(6)

0.974(13)

D3

2a

0.4476(11)

0.1290(5)

0.1346(6)

1

D4

2a

0.8555(11)

0.2774(5)

0.8160(7)

0.913(10)

D5

2a

0.1422(13)

0.0078(5)

0.6469(7)

1

D6

2a

0.1528(11)

0.2744(5)

0.1726(7)

1

D7

2a

0.1477(12)

0.7814(5)

0.1740(7)

1

D8

2a

0.8601(14)

0.4767(6)

0.8362(8)

1

D9

2a

0.8785(11)

0.9757(5)

0.8561(7)

0.920(12)

D10

2a

0.2851(14)

0.4566(6)

0.8152(8)

0.835(14)

D11

2a

0.6582(9)

0.1301(5)

0.7137(6)

1

D12

2a

0.7193(11)

0.7077(4)

0.6965(7)

1

D13

2a

0.5338(10)

0.2370(4)

0.9298(6)

1

D14

2a

0.1604(14)

0.8291(5)

0.9064(8)

0.861(13)

D15

2a

0.8275(14)

0.5708(5)

0.5940(8)

0.897(12)

D16

2a

0.5316(11)

0.9786(4)

0.4425(6)

0.958(10)

D17

2a

0.3068(12)

0.5416(5)

0.5473(7)

0.960(10)

D18

2a

0.7449(10) 0.2069(5) 0.4695(7) Total H, D (atom /f.u.) (a) D should be replaced by H for the hydride.

0.931(10)

(a)

20

4.27 (5)

Table 3. Number of D(H) atoms around each Fe atom, Fe-D(H) and Fe-Fe distances (range and average value) of YFe2D4.2 (top) and YFe2H4.2 (below). WSc=Wigner-Seitz cell. Fe site

Fe1 Fe2 Fe3 Fe4 Fe5 Fe6 Fe7 Fe8

ND(H)

3.75(5) 4.71(5) 4.78(5) 4.89(5) 4.77(5) 4.61(5) 4.88(5) 4.69(5)

D, H

Fe-D(H) dmin- dmax (Å)

Fe-D(H) Average d (Å)

Fe-Fe dmin- dmax (Å)

Fe-Fe Average d (Å)

WSc

D

1.65-1.80

1.75(8)

2.55-2.80

2.72(9)

13.51

H

1.66-1.81

1.76(8)

2.56-2.81

2.73(9)

D

1.62-1.72

1.68(5)

2.71-3.00

2.81(11)

H

1.62-1.73

1.69(5)

2.72-3.04

2.82(11)

D

1.66-1.74

1.70(4)

2.55-3.04

2.85(18)

H

1.67-1.75

1.71(8)

2.56-3.05

2.86(18)

D

1.65-1.74

1.70(5)

2.71-2.92

2.82(10)

H

1.65-1.75

1.71(5)

2.72-2.94

2.83(10)

D

1.69-1.86

1.78(9)

2.71-3.04

2.86(11)

H

1.70-1.87

1.79(9)

2.72-3.05

2.87(11)

D

1.63-1.78

1.71(8)

2.75-3.01

2.86(10)

H

1.64-1.78

1.72(8)

2.76-3.03

2.87(10)

D

1.63-1.88

1.77(9)

2.73-3.01

2.80(11)

H

1.64-1.88

1.78(9)

2.74-3.03

2.81(11)

D

1.66-1.83

1.74(8)

2.71-2.86

2.80(6)

H

1.67-1.83

1.75(8)

2.72-2.88

2.81(6)

21

(Å3)

13.11 13.34 13.37 13.82 13.61 13.23 13.86

Table 4: Monoclinic cell parameters and magnetic moments obtained from the refinement of the NPD patterns of YFe2D4.2 and YFe2H4.2 at selected temperatures in the FM, AFM and PM states. q and j represent the angles between the Fe moment and the c axis and b axis respectively. YFe2D4.2 T(K)

10

YFe2H4.2 95

150

2

135

200

3T2

D20

G41

D20

5.4941(2)

5.5283(3)

Instrument

3T2

G41

a (Ǻ)

5.5070(1)

5.4874(5)

b (Ǻ)

11.4962 (3) 11.4725(2) 11.4797(4) 11.5433(4) 211.537(7) 11.5282(5)

c (Ǻ)

9.4294 (2)

b (°) 3

V (Å )

9.3984 (8)

9.4020(3)

9.4691(3)

5.523(2) 9.453(3)

5.5174(2) 9.4477(3)

122.273 (2) 122.242(8) 122.218(2) 122.253(2) 122.21(1)

122.21(1)

504.68(2)

508.45(3)

Magnetic

500.44(9)

501.69(3)

511.03(3)

AFM

PM

FM

FM

509.7( 3) AFM

PM

order

a

<µFe> (µB)a 1.82(11)

1.76(3)

0

2.09(7)

1.74(3)

0

µFe7 (µB)

1.82(11)

0

0

2.09(7)

0

0

q (°)

16 (5)

-

14(5)

-

j (°)

90

90

90

90

RBragg (%)

6.9

7.7

5.1

6.0

RMag (%)

6.5

6.1

4.7

9.3

6.9

All Fe sites except Fe7.

22

5.6

Table 5. List of the 32 Fe positions in the AFM structure sorted by increasing y values. Eight different possible magnetic configurations have been tested in the AFM structure assuming that one Fe site loss its order at the transition. They are listed and labeled from 1 to 8. The solution 9, where two Fe sites (Fe6 and Fe7) loss their moment at the transition has been added for comparison. atom Fe7b Fe2a Fe1a Fe3a Fe4a Fe8a Fe5a Fe6b Fe6a Fe5b Fe8b Fe4b Fe3b Fe1b Fe2b Fe7a Fe7d Fe2c Fe1c Fe3c Fe4c Fe8c Fe5c Fe6d Fe6c Fe5d Fe8d Fe4d Fe3d Fe1d Fe2d Fe7c S+ S <µFe> (µB) RBragg (%) Rmag (%)

Atomic positions x y z 0.4898 0.0018 0.2392 0.0169 0.0625 0.5164 0.4949 0.0634 0.4899 0.5019 0.1205 0.2597 0.5009 0.1206 0.7432 0.4997 0.1860 0.0001 0.9854 0.1895 0.9940 0.4905 0.2481 0.7481 0.4905 0.2519 0.2481 0.9854 0.3105 0.4940 0.4997 0.3141 0.5001 0.5009 0.3794 0.2432 0.5019 0.3795 0.7597 0.4949 0.4366 0.9899 0.0169 0.4375 0.0164 0.4898 0.4982 0.7392 0.4898 0.5018 0.2392 0.0169 0.5625 0.5164 0.4949 0.5634 0.4899 0.5019 0.6205 0.2597 0.5009 0.6206 0.7432 0.4997 0.6860 0.0001 0.9854 0.6895 0.9940 0.4905 0.7481 0.7481 0.4905 0.7519 0.2481 0.9854 0.8105 0.4940 0.4997 0.8141 0.5001 0.5009 0.8794 0.2432 0.5019 0.8795 0.7597 0.4949 0.9366 0.9899 0.0169 0.9375 0.0164 0.4898 0.9982 0.7392

1 0 + + + + + + + + + + + + + + 0 0 0 14 14 1.76(3) 7.7 6.1

2 0 + + + + + + + + + + + + 0 0 + + + + + + + + + + + + 0 24 4

Magnetic configuration tested 3 4 5 6 7 0 + 0 + + 0 + + + 0 + + + + 0 + + + + + + + + + + + + + + 0 + + + 0 + + 0 + 0 0 0 + 0 + + 0 + + + 0 + + + + 0 + + + + + + + + + + + + + + 0 + + + 0 + + 0 + 0 0 20 16 12 8 4 8 12 16 20 24

8 0 0 + + + + + + + + + + + + + + 0 0 14 14 1.74(3) 7.7 7.6 10 9 7.7 7.6 7.8 99 106 110 110 107 102 6.6

23

9 0 + + + + + + 0 0 0 0 + + + + + + 0 0 0 12 12 8.1 115

Fig1: Refined NPD patterns of YFe2(H1-aDa)4.2 compounds (α =0, 0.64 and 1) measured at 300 K on G4.1 spectrometer (l =2.4266 Å). (o = experimental, - calculated, - difference, | hkl positions) Fig 2: Evolution of the cell parameters of YFe2H4.2 compared to the magnetization (red).The vertical line corresponds to TM0 = 131 K. Fig 3. Evolution of a) the cell volume and relative magnetic line intensity of YFe2(H1-aDa)4.2 compounds and b) transition temperatures TM0, TAFM and TN versus H content. Fig 4. Rietveld refinement of the neutron powder diffraction pattern of a) YFe2D4.2 recorded at 10 K on 3T2 spectrometer (l =1.225 Å) and b) YFe2H4.2 recorded at 2 K on D20 spectrometer (l =1.870 Å). Inset in (a): orientation of the Fe moment in the (a, c) plane. Fig 5. Schematic representation of the magnetic structures of YFe2D(H)4.2 in a) ferromagnetic structure, b) antiferromagnetic structure, zoom on the Fe7 environment with nearest Fe and D neighbours in c) FM and d) AFM structure. Fig 6: Rietveld refinement of the neutron powder diffraction pattern of (a) YFe2D4.2 and (b) YFe2H4.2 recorded at 95 K and 135 K respectively on G4.1 spectrometer (l=1.225Ǻ). *diffraction corresponding to sample environment contribution.

Fig 7. Evolution of the refined Fe atomic moments versus temperature for YFe2D4.2 and YFe2H4.2 in both FM and AFM phases. Fig 8. Neutron powder diffraction patterns of YFe2D4.2 recorded on the E6 (HZB) spectrometer (λ = 2.454 Å) at 100 K and under various applied fields. Fig 9. (top) Integrated intensities of the AFM and FM peaks and (bottom) interplanar distances of the FM peak of YFe2D4.2 measured by NPD on the E6 instrument at T=100 K. The M(B) curve of YFe2D4.2 at 100 K has been added on the bottom figure for comparison. The dashed line corresponds to the inflexion point BTrans of the MT(B) curve. Fig 10: Crystal structure and magnetic phase diagram of YFe2Dx compounds. Highlights · · · · ·

YFe2(H,D)4.2 compounds undergoes a isotope sensitive FM-AFM transition at TM0 The FM structure is formed of Fe moments perpendicular to the monoclinic b axis AFM structure is formed by antiparallel Fe layers separated by non-magnetic Fe layer One Fe site among eight loses its moment at TM0 due to larger Fe-H bonding Magnetic properties are driven by the monoclinic distortion induced by D order

24

b

0.0

0.5

1.0

1.5

2.0

0

Ferromagnetic structure (FM)

*Graphical Abstract

<µFe> (µB)

FM

50

100 T (K)

AFM

TM0

150

PM

Refined mean Fe moment <µFe> of YFe2D4.2 deuteride in FM and AFM structures

Antiferromagnetic structure (AFM)

T

Fe7 atom loses its moment at TM0

2b

Figure10

Figure9

Figure8

Figure7

Figure6b

Figure6a

Figure5d

Figure5c

Figure5b

Figure5a

Figure4b

Figure4a

Figure3b

Figure3a

Figure2

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