Magnetic and Magnetocaloric Properties of the A2LnSbO6 Lanthanide Oxides on the Frustrated fcc Lattice

Frustrated lanthanide oxides are promising candidates for cryogen-free magnetic refrigeration due to their suppressed ordering temperatures and high magnetic moments. While much attention has been paid to the garnet and pyrochlore lattices, the magnetocaloric effect in frustrated face-centered cubic (fcc) lattices remains relatively unexplored. We previously showed that the frustrated fcc double perovskite Ba2GdSbO6 is a top-performing magnetocaloric material (per mol Gd) because of its small nearest-neighbor interaction between spins. Here we investigate different tuning parameters to maximize the magnetocaloric effect in the family of fcc lanthanide oxides, A2LnSbO6 (A = {Ba2+, Sr2+} and Ln = {Nd3+, Tb3+, Gd3+, Ho3+, Dy3+, Er3+}), including chemical pressure via the A site cation and the magnetic ground state via the lanthanide ion. Bulk magnetic measurements indicate a possible trend between magnetic short-range fluctuations and the field-temperature phase space of the magnetocaloric effect, determined by whether an ion is a Kramers or a non-Kramers ion. We report for the first time on the synthesis and magnetic characterization of the Ca2LnSbO6 series with tunable site disorder that can be used to control the deviations from Curie–Weiss behavior. Taken together, these results suggest fcc lanthanide oxides as tunable systems for magnetocaloric design.


■ INTRODUCTION
Cooling is a vital part of modern technology from satellite sensors to medical imaging to quantum computing. While cooling to T ≈ 2 K and T ≪ 2 K can be achieved using liquid He and 3-He, respectively, He is a depleting resource, and the search for alternatives based on magnetocaloric, mechanocaloric, and elastocaloric materials is an ongoing area of research. 1−4 Frustrated magnets have been identified as promising candidates for cryogen-free magnetic refrigeration due to their suppressed ordering temperatures and degenerate ground states. 5 Cooling is accomplished via the magnetocaloric effect (MCE) in which an applied magnetic field is used initially to order paramagnetic spins; once the field is removed, spins become disordered and the resulting magnetic entropy change is used to absorb heat. For a given change in field, ΔH, the adiabatic temperature change (ΔT) S of a material is proportional to its change in magnetic entropy at constant temperature ΔS m . 6 The lowest possible temperature is limited by the long-range magnetic ordering temperature, with reports of an enhanced MCE just above the magnetic ordering temperature in GdPO 4 7 and Gd(OH)F 2 . 8 Frustrated lanthanide oxides are well suited to magnetic refrigeration due to their large total angular momentum (high magnetic entropy) and high chemical stability compared to paramagnetic salts in traditional adiabatic refrigeration. 9 Due to the localized nature of the 4f electrons, the magnetic properties are highly dependent on competing superexchange, dipolar, and crystal electric field (CEF) interactions. For example, in the Ln 3 Mg 2 Sb 3 O 14 kagome family, Dy 3 Mg 2 Sb 3 O 14 is an Ising magnet that exhibits an emergent charge-ordered state at ∼0.3 K; 10 11 While the magnetocaloric effect has been studied in a variety of frustrating lattices, including the Shastry−Sutherland latttice (e.g., Ln 2 Be 2 GeO 7 ), 12 quasi-1D chains (e.g., Ca 4 LnO(BO 3 ) 3 ), 13 garnets (e.g., Ln 3 A 2 X 3 O 12 ), 14 and pyrochlores (e.g., Ln 2 B 2 O 7 , B = {Ti,Sn}), 15 the family of face-centered cubic (fcc) lanthanide oxides remains relatively unexplored. It is therefore important to obtain a holistic study of the magnetocaloric effect of the Ln fcc family in connection to its magnetic properties.
Systems of frustrated fcc magnetic sublattices can be formed using a double perovskite structure, A 2 BB′O 6 , in which the rock-salt ordering of the magnetic B and nonmagnetic B′ cations forms two networks of B−B and B′−B′ edge-sharing tetrahedra, 16 Figure 1a). The A site cation lies in the cavity between the BO 6 and B′O 6 octahedra and can result in either a cubic Fm3̅ m structure when the ionic radius is larger (e.g., for Ba 2+ ) and the fcc lattice is undistorted or the monoclinic P2 1 /n structure when the ionic radius is smaller (Sr 2+ or Ca 2+ ) 16 17 The magnetic ground states across the fcc family of double perovskites are exceedingly diverse depending on the B and B′ site cations. For example, the 3d transition metals Ni 2+ , high spin Mn 2+ , Ru 5+ , Co 3+ , and Os 7+ lead to ordered antiferromagnets at ∼10−50 K, 18−22 while Fe 3+ and Re 5+ / Re 6+ lead to spin glass states at ∼15−30 K. Notably, these spin glass effects are shown to persist when chemical pressure is tuned via the A site cation (e.g., Ba 2+ to Ca 2+ ), while the antiferromagnetic ordering temperature can be further suppressed in Co-based double perovskites for larger A site cations. 20,23 The B site cation Mo 5+ is reported to exhibit an exotic valence bond glass state, 17,24 and the rare-earth iridates Ba 2 LnIrO 6 all remain paramagnetic down to 2 K except for Pr 3+ . 25 Our previous work showed that, for Heisenberg spin systems, the magnetocaloric effect (per ion) is enhanced  (Fm3̅ m), A = Sr 2+ (P2 1 /n), and A = Ca 2+ (P2 1 /n). All Ln 3+ ions are distributed on an fcc lattice, which is composed of edge-sharing tetrahedra. The side-lengths of the tetrahedron for each compound, shown in the right part of the subfigure, are uniform for the cubic Ba compound and distorted for the monoclinic Sr and Ca compounds. The smaller ionic radius of Ca compared to Sr results in increased distortion, with side-length differences of ∼3.5% compared to 0.5%. (b) Combined Rietveld refinement of room-temperature PND (top panel) and PXRD data (bottom panel) for Ca 2 HoSbO 6 . The two peaks at d ≈ 4.63 and 4.76 Å, corresponding to the reflections (101)/(10 1̅ ) and (011), are much more suppressed in Ca 2 HoSbO 6 compared to Ca 2 NdSbO 6 , indicating only a small amount (∼8.3(2)% of all Ho) of Ln occupancy on the A site. (c) Volume of the unit cell and Goldschmidt tolerance factor of A 2 LnSbO 6 , where A = {Ba, Sr, Ca}, as a function of the Ln ionic radius normalized by the number of Ln ions per unit cell. Points correspond to the measured structural data, and the lines correspond to lines of best fit. when the system is frustrated, but its superexchange is minimal. 26 For example, the frustrated fcc Ba 2 GdSbO 6 has a nearest-neighbor (nn) superexchange J 1 of 10 mK and does not order down to 400 mK. fcc Ba 2 GdSbO 6 attains a magnetic entropy change ΔS m of −15.8(1) J/K/mol Gd compared to Gd 3 Ga 5 O 12 with J 1 = 100 mK and an entropy of −13.0 J/K/ mol Gd at 2 K and 7 T. The related compound Sr 2 GdNbO 6 with a lower symmetry and a distorted fcc lattice is similarly high performing, attaining −15.5 J/K/mol Gd near its ordering temperature of 3 K and 7 T, but orders at 3 K, highlighting that the d 0 versus d 10 electronic configuration of the nonmagnetic B site can play a role in the magnetic properties of fcc lanthanide oxides. 26,27 The fcc lanthanide oxides, A 2 LnBO 6 (A = {Ba 2+ , Sr 2+ }), are promising magnetocaloric materials because prior reports have shown a lack of ordering to 2 K and minimal correlations between spins or van Vleck paramagnetism. Karunadasa et al. studied A 2 LnSbO 6 , A = {Ba 2+ , Sr 2+ } and Ln = {Gd 3+ , Dy 3+ , Ho 3+ }, a subset of the materials studied in this work, and reported negative Curie−Weiss temperatures and postulated they were possible spin liquid candidates. 16 Subsequent lowtemperature neutron diffraction measurements, however, showed an absence of short-range correlations between Ln ions to 70 mK in the fcc Ba 2 HoSbO 6 and Ba 2 ErSbO 6 . Both compounds have been shown to be well described by van Vleck paramagnetism due to low-lying excited states. 28,29 In this report, we investigate the A 2 LnSbO 6 (A = {Ba 2+ , Sr 2+ } and Ln = {Nd 3+ , Tb 3+ , Gd 3+ , Ho 3+ , Dy 3+ , Er 3+ }) family to explore effects of lattice symmetry (tuned via chemical pressure) as well as single-ion anisotropy and the magnetic ground state (via a magnetic cation) on the magnetocaloric effect. We synthesize a new series of fcc materials, Ca 2 LnSbO 6 , and find that site-disorder can be tuned with slow cooling during synthesis. We find a trend between the deviations in the magnetic susceptibility of a material from Curie−Weiss behavior and the field-temperature phase space at which its magnetocaloric effect is maximized. Furthermore, we show that these magnetic properties are determined by whether the magnetic cations are Kramers versus non-Kramers ions. Taken together, these results indicate that the A 2 LnSbO 6 family of fcc magnets is a tunable system for magnetic refrigeration. for 12 h prior to weighing. Reactants were ground using a mortar and pestle and heated in air at 1400°C for 24 h for 2−4 cycles. Intermittent grindings between heatings were conducted. The Ba and Sr series were cooled to room temperature using furnace cooling, while the effect of "slow cooling" (1°C/min) was explored to eliminate site disorder in the Ca series.

■ EXPERIMENTAL METHODS
Structural Characterization. Room-temperature powder X-ray diffraction (XRD) measurements were conducted using a Bruker D8 Advance diffractometer (Cu Kα radiation, λ = 1.54 Å). Data were taken with a resolution of Δ(2θ) = 0.01°from 2θ = 15°to 2θ = 150°f or an overall collection time of 2−3 h. To minimize preferred orientation effects, the sample stage was rotated at 30 rpm during data collection. Additional high-resolution powder diffraction measurements were conducted for the Ca 2 LnSbO 6 samples at the I11 beamline at the Diamond Light Source using a position-sensitive detector at 100 K. Data were collected with λ = 0.826866 Å from 2θ = 8°to 2θ = 100°, with an overall collection time of 1 min. The powder sample was mounted in a 0.28 mm diameter borosilicate capillary. For Ca 2 HoSbO 6 , Ca 2 NdSbO 6 , and Ca 2 ErSbO 6 , high-resolution neutron powder diffraction measurements were conducted at room temperature using the POWGEN diffractometer at the Spallation Neutron Source (bank 1, 0.27 < λ < 1.33 Å with a center wavelength of 0.8 Å). Each (∼1 g) powder sample was mounted in a 6 mm diameter vanadium can, and data were collected to cover d = 0.1340−8.200 Å with 0.001 < Δd/d < 0.008 and an overall collection time of 2.5−3.25 h.
Powder X-ray diffraction (XRD) data were refined using the Rietveld method 30 in the Diffrac.Suite TOPAS5 program. 31 A pseudo-Voigt function was used to model peak shape, 32 and the background was fit using a 13-term Chebyshev polynomial. Except for Ca 2 LnSbO 6 (Ln = {Nd, Gd, Tb, Dy, Ho, Er}), where synchrotron XRD data or powder neutron diffraction data were available, all Debye−Waller factors were set to the literature-reported values from powder neutron diffraction. 16,33 Where available, joint Rietveld refinements were conducted on the powder neutron and powder X-ray diffraction data together. A cylindrical correction was used to correct for capillary absorption in the I11 data as well as a Lorentzian/Gaussian model to account for strain broadening effects on the peak shape. 34 Bulk Further details on the analysis of the magnetic measurements and calculations on the magnetocaloric effect can be found in the Supporting Information.

■ EXPERIMENTAL RESULTS
All compounds formed with the nominal Ln 3+ oxidation state. The following compounds have also been found to be stable but are not included in this report: Ba 2 YbSbO 6 , 35 Sr 2 YbSbO 6 , 36 and Ba 2 PrSbO 6 , 37 .
Structural Characterization. Ordered fcc Magnetic Sublattices: A = {Ba, Sr}. The X-ray diffraction of all A = Ba 2+ compounds are well fit to the cubic Fm3̅ m space group. 16,28,29 The Ln 3+ and Sb 5+ ions order in a rock-salt arrangement on octahedrally coordinated B sites with no observed B/B′ antisite disorder. Ba 2+ cations lie at cavities formed by the BO 6 octahedra, forming a double perovskite structure, Figure 1a). As in ref 38 Figure 1a). 16 The lower symmetry of the A = Sr 2+ crystal results in the reduction of coordination number of the A site from 12 to 8 and three independent O positions. Tables S2−S4 detail the crystal structure parameters for A 2 LnSbO 6 (Ln = {Nd−Er} and A = {Ba, Sr}). For both A = {Ba, Sr}, the rock-salt arrangement of Ln and Sb ions implies an fcc magnetic sublattice of edge-sharing tetrahedra.

Inorganic Chemistry
pubs.acs.org/IC Article {Sr, Ca} each tetrahedron is distorted, with ∼1.0−3.5% side-length differences (as discussed, Ca 2 LnSbO 6 (Ln = {Er, Ho}) are the only compounds in the Ca series with an ordered fcc magnetic sublattice). The volume of the unit cell and size of the Ln−Ln tetrahedra, for A = {Ba, Sr} and fcc Ca 2 HoSbO 6 and Ca 2 ErSbO 6 , scales linearly with the ionic radius of Ln 3+ , Figure 1c, as expected from a close-packing model of the structure. 39 Tunable Site-Disordered Magnetic Sublattices: A = Ca. All A = Ca materials were refined in the P2 1 /n space group, Tables 1 and S1, consistent with prior reports for Ca 2 NdSbO 6 and Ca 2 HoSbO 6 . 26,43,44 The diffraction patterns contain two PXRD/PND peaks at d ≈ 4.6− 4.8 Å, Figures 1b and S2, indicative of site disorder. Reports for A 2 BSbO 6 (A = {Sr 2+ , Ca 2+ }, B = {La 3+ , Sm 3+ }) show that these additional peaks correspond to (011) and (101)/(−101) in the monoclinic unit cell and emerge due to A site occupancy of the Ln 3+ ions. 45  To investigate the possibility of tunable site ordering, two additional heatings were conducted for Ln = {Dy, Ho}, with a slow-cooling rate of 1°C/min. Rietveld refinements after slow-cooling showed increased B site occupancy of x = 0.672(3) for Dy and x = 1.000 for Ho. Ca 2 TbSbO 6 was fired at 1400°C for three 24 h periods with a 1°C/min cooling rate but exhibited site disorder, with x = 0.215 (3), suggesting a slower rate may be necessary. An additional synthesis of Ca 2 ErSbO 6 carried out at a lower temperature (1300°C) with slow-cooling exhibited some (x = 0.937(1)) site disorder (see Table S1), suggesting that disorder may also depend on the synthesis temperature.
Crystal structure parameters for Ca 2 LnSbO 6 are provided in Table  1 for room temperature and Table S1 for 100 K. For the larger Ln = {Gd 3+ , Nd 3+ } ions, Ln 3+ is found almost exclusively on the A site in Ca 2 LnSbO 6 . 43,46 The possibility of A site ordering in Ca 2 GdSbO 6 has been addressed in ref 26. Superstructure peaks expected of a A site ordering are not evident in the high-resolution X-ray synchrotron data.
The Goldschmidt tolerance factor t was calculated to analyze the origin of site-disorder in the A = Ca series, Figure 1c). t predicts whether the ionic radii of the A site cation and B site cation are wellscaled for a cubic structure in which A site cations lie at the cavities of B−O octahedra. 47 It can be extended to double perovskites by computing an average B site ionic radius so that where r B,avg = 1/2r Sb + 1/2r Ln . 39  Since t ≈ 1 in stable perovskite structures, these results suggest that the Ln ions should lie preferentially on the B site. Additional factors may contribute to the observed A site occupancy, such as the entropic gain afforded by a disordered structure at high temperatures. Charge differences are unlikely to be responsible for the observed structure, as our calculations using a charge-based tolerance factor predict the B site ordered x = 1 structure to be the most stable. 48 Magnetic Characterization. Magnetic susceptibility χ measurements were conducted in an applied field of 0.1 T in both zero-field cooled (ZFC), Figure 2, and field-cooled (FC) conditions. None of the compounds exhibit features indicative of a long-range ordering transition down to 2 K. Ba 2 TbSbO 6 contains a shallow peak in χ at 3.5 K, which could be attributable to the onset of short-range fluctuations. There is no irreversibility observed in the ZFC/FC measurements with the exception of Ba 2 TbSbO 6 below 10 K, Figure S9, for which a 0.1% deviation is observed. None of the χ-curves exhibit ordering features or anomalies except for Ba 2 TbSbO 6 , which has a shallow peak at 3.50 K (see Figure S9). The FC magnetic susceptibility was also measured and is not shown since no hysteresis was observed for any of the compounds except Ba 2 Table 2, of the inverse susceptibility χ −1 were carried out for each compound at low temperatures to avoid the contribution of low-lying excited states. 14 Due to the observation of magnetic ordering in Ba 2 TbSbO 6 at T = 3.5 K, fitting to the Curie− Weiss law was carried out at higher temperatures for the Tb 3+containing materials. Since the magnetic susceptibility was measured in the field region where M scales linearly with H, the Heisenberg approximation of free-spins is valid and μ eff should be close to the theoretical prediction. 50 The fit moments, Table 2, are in broad agreement with the theoretical moments, consistent with previous reports. 16,28,29 The fit μ eff for all Gd compounds is slightly greater than the 7.94 μ B /f.u. prediction, as has been observed in the similar series Li 3 Ln 3 Te 2 O 12 . 14 All compounds exhibit negative Curie−Weiss temperatures, Table  2, indicative of antiferromagnetic superexchange. For all Ln, the lower limit for the frustration index f = |Θ CW |/T 0 exceeds 1, where T 0 is the magnetic ordering temperature, and when no magnetic ordering is observed T 0 is assumed to be the lowest temperature measured, i.e., T 0 = 2 K, or T 0 = 0.5 K in the case of Gd-containing samples. Materials with f > 10 are considered "strongly" frustrated 51 and so lower temperature measurements are therefore required to gain a more accurate indication of the level of frustration. Heat capacity measurements down to 0.3 K showed a lack of ordering in Ba 2 GdSbO 6 and Sr 2 GdSbO 6 , while the disordered Ca 2 GdSbO 6 orders at 0.52 K. 26 Mean-field estimates for the nn exchange J ex and dipolar interaction D nn , Table 2, indicate that J ex exceeds D nn in all the materials except Ln = Gd.  6 , agree with the predicted magnetization for free Heisenberg spins, although they exhibit a slightly lower magnetization at low fields (μ 0 H = 0−2 T) due to nn antiferromagnetic fluctuations. 26 The Ln compounds with unquenched orbital angular momentum exhibit single-ion anisotropy, as they do not saturate at either the maximum Ising (0.5g J J) or Heisenberg predictions (g J J).
Changes to the chemical pressure via tuning of the A site cation appear to have a small effect on χ, Figure 2, with the exception of Ln = {Tb,Dy}. All other Ln compounds have similar magnetic susceptibilities for temperatures of 2 K and above. Both Ca 2 TbSbO 6 and Ca 2 DySbO 6 exhibit site disorder and demonstrate increased magnetic susceptibility at low temperatures relative to the fcc A = {Ba, Sr} versions, indicating that disorder may promote ferromagnetic interactions rather than chemical pressure.
The isothermal magnetization varies with the A site cation for each Ln with single ion anisotropy, likely due to change in the oxygen coordination and crystal electric field effect. The local site symmetry for the rare earths changes with the alkaline earth cation and could play a role in the magnetism of the Kramers versus non-Kramers ions. Note that for Ln = Tb and Ln = Dy, where significant differences in the magnetic susceptibility χ are observed, there are also significant differences in the isothermal magnetization for A = {Ba, Sr} versus A = Ca.
Deviations from Curie−Weiss Behavior. To enable a comparison across compounds, deviations from the Curie−Weiss law were investigated using a dimensionless plot of χ −1 , Figure 3a−c). As in refs 52 and 53, we write the Curie−Weiss law in the dimensionless form as follows: where Θ is the Curie temperature and C is the Curie constant. In these dimensionless units, paramagnetic behavior corresponds to the linear relationship of  The inverse magnetic susceptibility χ −1 was fit using linear regression to the Curie−Weiss law over the specified temperature range. Estimates for the nearest-neighbor exchange J ex and the dipolar interaction D nn are computed as described in the SI using the method from reference 49. The Ln = Gd compound data are taken from our previous report, where heat capacity indicated ordering of Ca 2 GdSbO 6 at 0.52 K and a lack of ordering to 0.4 K for Ba 2 GdSbO 6 and Sr 2 GdSbO 6 . 26 The site disorder for each Ca compound is listed according to the formula 6 , with x = 1.0 corresponding to an ordered fcc structure of Ln 3+ on the B site and x = 0 corresponding to a disordered structure of Ln 3+ shared equally with Ca 2+ on the A site.

Inorganic Chemistry
pubs.acs.org/IC Article netic deviations, while the Kramers ions tend toward ferromagnetic deviations. This has implications for the magnetocaloric performance of these materials. For example, Figure 3d depicts the temperature derivative of the magnetization (∂M/∂T) H = (∂S/∂H) T from which the magnetic entropy change ΔS m is derived. Dy, a Kramers ion, exhibits a maximum in (∂M/∂T) H at the lowest temperatures measured and a small (0.5−1 T) field, in agreement with the ferromagnetic shortrange fluctuations in χ −1 . Instead, for non-Kramers ions (e.g., Tb, Ho), (∂M/∂T) H is maximized at finite temperatures and fields, Figure  3d.
Two possible explanations for the positive deviations in χ −1 of non-Kramers ions include (1) antiferromagnetic short-range fluctuations between spins and/or (2) crystal electric field (CEF) effects. In the first case, polarization of spins at any temperature would require a larger external field to counteract the energetically preferable antialignment between nn spins. M(H) measurements, Figure 2, support this explanation, as M(H) for Ln = {Tb, Ho} underestimates the prediction for Heisenberg and Ising spins at low fields (μ 0 H = 1−3 T).
A second possible cause is the CEF effect. In ref 28, positive deviations of χ −1 of Ba 2 HoSbO 6 from Curie−Weiss behavior at low temperature are attributed to a gradual depopulation of excited states and strong quantum fluctuations. 28 In this case, one might expect a maximum in (∂M/∂T) H at finite temperatures and fields, as (1) a finite temperature is required to access these excited, magnetic states and (2) an applied magnetic field can alter the energy difference between these states. This behavior is observed for all Ho-and Tbcontaining compounds in this work, e.g., those in Figure 3d.
Effect of Chemical Pressure: A = {Ba, Sr}. The effect of chemical pressure on the deviations from Curie−Weiss behavior in the ordered fcc A 2 LnSbO 6 compounds, Figure 3a−c) (and Figure S10), depends on the Ln ion. While the dipolar interaction, crystal electric field parameters, and superexchange interactions need to be characterized to make definitive claims about the changes with chemical pressure, some trends between the different Ln ions can be observed.
First, for the Kramers ions Ln = {Nd, Dy}, the cubic A = Ba 2+ version exhibits decreased ferromagnetic deviations compared to those with A = Sr 2+ . For Ln = Er, a different behavior is observed in which the ferromagnetic deviations from the Curie−Weiss law increase with the increasing radius of the A cation. One possible explanation for the change for A = Ba 2+ relative to the A = {Sr 2+ , Ca 2+ } counterparts is the increased orbital overlap of 4f electrons due to the cubic lattice, resulting in enhanced superexchange. Another could be the alteration of the ground state and low-lying excited states via the CEF effect. All three types of fcc compounds Ln = {Nd, Dy,  Table 2. Second, for the non-Kramers Ln = Ho compounds, the cubic A = Ba 2+ compound also exhibits the largest deviations, followed by Ca and then Sr (Figure 3c). This could be due to the interplay of orbital overlap and the nn distance in determining the magnitude of the superexchange interaction as well. For Ln = Tb, there is no observable difference in the magnitude and temperature onset of the positive deviations in the inverse magnetic susceptibility for A = {Ba, Sr}. The dipolar to superexchange ratios in these systems are more distinct for Ln = {Ho, Tb}, where D nn /J ex ∼ 0.6 and ∼0.1, respectively, which could suggest that different interactions might be more relevant in Magnetocaloric Effect. The magnetocaloric effect of each material was studied under applied fields of 0.2−7.0 T and temperatures of 2−20 K. The isothermal magnetic entropy change ΔS m was measured from the isothermal magnetization, Figure 4. Key values are summarized in Table 3.
Slices of ΔS m for A 2 LnSbO 6 versus temperature at 7 and 2 T are shown in Figure 5a. The Ln = Gd compounds are the highest performing, reaching up to −16 J/K/mol Ln , at 7 T and 2 K compared to −13.0 J/K/mol Ln for Gd 3 Ga 5 O 12 . Ba 2 ErSbO 6 is also a promising magnetocaloric material, with entropy changes of −10 and −6 J/K/ mol Ln at 2 T, on par with the 2 T value for Gd 3 Ga 5 O 12 . 54 This can likely be explained by the free spin nature of Ba 2 ErSbO 6 reported by Calder et al. 29 Unlike the Ga-based garnets Ln 3 Ga 5 O 12 in which Ln = {Tb, Dy} outperform Gd at low (μ 0 H ≤ 2 T) fields, 14 Gd remains the ideal Ln ion at 2 K across all fields, Figure S11. However, Ba 2 HoSbO 6 outperforms Ba 2 GdSbO 6 at f inite temperatures: 8−16 K at 7 T and 4−10 K at 2 T. The peak in −ΔS m with temperature for Ba 2 HoSbO 6 in Figure 5a is likely due to the population of its low-lying magnetic, excited states, the first of which is 10 K. 28 The fcc Tb compounds show a very small magnetic entropy change starting at 10 to 20 K, continuing up to 30 K. This could be a result of polarizable defects in a short-range correlated or long-range ordered state or the thermal population of excited states. Figure S11 depicts ΔS m as a function of the applied field. All Ln except Nd and Gd reach a plateau at fields less than 7 T, indicating that some compounds, namely Ba 2 LnSbO 6 (Ln = {Dy, Ho, Er}), could be used as magnetocaloric materials in smaller fields. The site-disordered Ca compounds (Ln = {Gd−Dy}) plateau in ΔS m at smaller fields (∼3−4 T), consistent with ferromagnetic short-range fluctuations suggested by Figure 3.
The related fcc [LaA] A CoNbO 6 series was found to have the lowest ordering temperature for the largest A site cation, Ba, compared to Sr and Ca due to enhanced frustration afforded by a uniform lattice. 20 Thus, it is possible that the Ba series presented here could also enabling cooling down to lower temperatures than its Sr and Ca counterparts, which we found to the be the case for Ln = Gd 3+ . 26

■ CONCLUSION
This work investigates the effect of tuning the magnetic Ln ion and chemical pressure (A site cation) on the structural, magnetic, and magnetocaloric properties of fcc lanthanide    With the exception of the Tb-containing phases, none of the materials exhibit long-range order down to 1.8 K, signaling the possibility of magnetic refrigeration down to this temperature. Bulk magnetic measurements suggest that the magnetocaloric effect in frustrated fcc magnets is optimized in the presence of minimal short-range correlations, as evidenced by the nearly free-spin A 2 GdSbO 6 materials; 26 for Ln ions with quenched orbital angular momentum (i.e., Gd); and in materials with uniform magnetic sublattices (A = Ba 2+ ), possibly due to decreased single-ion anisotropy.
The measurements indicate a possible link between the magnetic entropy change and the apparent short-range fluctuations in the system. This work suggests that the magnetic ground state of the system, determined by the Ln ion and chemical pressure, can be utilized to tune the fieldtemperature phase space of the magnetocaloric effect through changes to the superexchange, dipolar interactions, and the crystal electric field. The role of disorder in the magnetocaloric effect in this temperature range is still outstanding. For Ln = Tb 3+ , the presence of site disorder in Ca 2 TbSbO 6 enables a magnetic entropy change 4.5× greater than Sr 2 TbSbO 6 and Ba 2 TbSbO 6 . Low-temperature μSR experiments, heat capacity in field, and magnetic neutron scattering will be key in elucidating the role of disorder in the magnetic ground state and magnetocaloric properties of these rare-earth fcc systems. ■ ASSOCIATED CONTENT
Refined structural parameters, analysis of magnetic susceptibility, magnetocaloric effect calculations, and further magnetic characterization (PDF) Data associated with this publication can be found at: https://doi.org/10.17863/CAM.96860.