Free-Spin Dominated Magnetocaloric Effect in Dense Gd3+ Double Perovskites.

Frustrated lanthanide oxides with dense magnetic lattices are of fundamental interest for their potential in cryogenic refrigeration due to a large ground state entropy and suppressed ordering temperatures but can often be limited by short-range correlations. Here, we present examples of frustrated fcc oxides, Ba2GdSbO6 and Sr2GdSbO6, and the new site-disordered analogue Ca2GdSbO6 ([CaGd] A [CaSb] B O6), in which the magnetocaloric effect is influenced by minimal superexchange (J 1 ∼ 10 mK). We report on the crystal structures using powder X-ray diffraction and the bulk magnetic properties through low-field susceptibility and isothermal magnetization measurements. The Gd compounds exhibit a magnetic entropy change of up to -15.8 J/K/molGd in a field of 7 T at 2 K, a 20% excess compared to the value of -13.0 J/K/molGd for a standard in magnetic refrigeration, Gd3Ga5O12. Heat capacity measurements indicate a lack of magnetic ordering down to 0.4 K for Ba2GdSbO6 and Sr2GdSbO6, suggesting cooling down through the liquid 4-He regime. A mean-field model is used to elucidate the role of primarily free-spin behavior in the magnetocaloric performance of these compounds in comparison to other top-performing Gd-based oxides. The chemical flexibility of the double perovskites raises the possibility of further enhancement of the magnetocaloric effect in the Gd3+ fcc lattices.

Introduction

Cryogenic cooling is imperative to modern technologies, including quantum computing and magnetic resonance imaging. While liquid He can be used to reach temperatures as low as 20 mK (using 3-He and 4-He) or 2 K (4-He only), it is a depleting resource, and sustainable alternatives capitalizing on magnetic, structural, and/or electric ordering of materials are of key interest.[1] In adiabatic magnetic refrigerators (ADRs), an applied magnetic field induces a change in entropy of the spins of a material, ΔS. When followed by adiabatic demagnetization, the system exhibits a proportional decrease in temperature ΔT as dictated by the magnetocaloric (MC) effect. MC materials are operable at temperatures above their ordering transition T0 and are often characterized by the maximum isothermal magnetic entropy change ΔS that can be achieved for a given change in field ΔH.[2] Current top-performing MC materials are based on Gd3+ containing compounds, as the minimal single-ion anisotropy (L = 0) of the magnetic ions allows for full extraction of the theoretical entropy change in high magnetic fields.[3−5] Recent advances in materials like Gd(HCOO)3, GdF3, and GdPO4, with dense magnetic sublattices, have highlighted the importance of weak magnetic correlations in enabling a large MC effect.[3,4,6] However, these materials can be limited by a lack of tunability via chemical substitution and/or large volumes per magnetic ion.[5,6] This limits the opportunities for tuning the magnitude and temperature of the maximum ΔS.

On the other hand, frustrated magnetic oxides, in which the geometry of the lattice prevents all exchange interactions from being satisfied simultaneously, present a diverse class of MC candidates given their chemical stability and exotic magnetic properties such as a large ground state degeneracy and suppressed ordering temperature.[7] Gd3Ga5O12, a frustrated garnet, is the standard among this class of materials, with an entropy change of −13.0 J/K/molGd in a field of 7 T at 2 K.[5] In addition to the garnet lattice which is comprised of two interpenetrating networks of bifurcating loops of ten corner-sharing Ln3+ triangles, a wealth of frustrated geometries exist, including the pyrochlore and kagome lattices and the fcc lattice, which as a set of edge-sharing tetrahedra is frustrated under antiferromagnetic exchange. However, one limitation of oxide materials is that their MC performance can be strongly influenced by short-range correlations.[8] For example, Gd3Ga5O12 has a relatively large superexchange between Gd3+ ions, |J1| ∼ 100 mK,[9] compared to |J1| ∼ 70 mK for GdF3.[3]

Lanthanide oxide double perovskites with the general formula A2LnSbO6 (A = alkaline earth (Ba, Sr), Ln = lanthanide) represent a family of frustrated magnets in which Ln ions lie on an fcc magnetic sublattice, enforced by the rock-salt arrangement with the other B site cation, Sb5+. Chemical pressure via A site cation substitution can alter the distortion of a single Ln-ion tetrahedron due to small changes in the nearest neighbor nn distance dictated by rotations of the BO6 octahedra.[10]

Here we present fcc oxides with minimal superexchange interactions, up to 10 times smaller than those of other frustrated oxides. We report on the solid-state synthesis, structural characterization, bulk magnetic properties, and magnetocaloric effect in these materials, Ba2GdSbO6 and Sr2GdSbO6, and the new site-disordered Ca analogue, Ca2GdSbO6 ([CaGd][CaSb]O6). We show that tuning of the A site ion influences the exchange through changes in the nearest neighbor distance and O–Gd–O bond angles, with small effect on the overall magnetocaloric performance, suggesting that free-spin behavior is dominant for 1.8 K and above. Furthermore, the low Curie–Weiss temperatures (∼0.8 K), frustrated lattice geometry, and lack of ordering of the Ba and Sr compounds suggest that cooling may persist through the cooperative paramagnetic regime to temperatures well below 0.4 K.

Experimental Methods

Solid State Synthesis

Powder samples, of ∼1 g, of Ba2GdSbO6, Sr2GdSbO6, and Ca2GdSbO6 were prepared as described in the literature.[10] Stoichiometric mixtures of predried gadolinium(III) oxide (99.999%, Alfa Aesar REacton), antimony(V) oxide (99.9998%, Alfa Aesar Puratronic), and the appropriate alkaline earth carbonate, barium carbonate (99.997%, Alfa Aesar Puratronic), strontium carbonate (99.99%, Alfa Aesar), or calcium carbonate (99.99%, Alfa Aesar Puratronic) were initially ground using a mortar and pestle and heated in air at 1400 °C for 24 h. Heating was repeated until the amount of impurity phases as determined by X-ray diffraction no longer reduced upon heating (one additional 24 h cycle). Ba2GdSbO6, Sr2GdSbO6, and Ca2GdSbO6 each contain impurity phases of Gd3SbO7 of 0.45(4), 0.67(4), and 0.48(1) wt %, respectively, with antiferromagnetic ordering at 2.6 K.[11]

Structural Characterization

Room temperature powder X-ray diffraction (XRD) measurements were carried out using a Bruker D8 Advance diffractometer (Cu Kα radiation, λ = 1.54 Å). Data was collected with d(2θ) = 0.01° from 2θ = 15–150°, with an overall collection time of 2–3 h. During each scan, the sample stage was rotated to avoid preferred orientation effects. Additional high resolution X-ray powder diffraction measurements were conducted at the I11 beamline at the Diamond Light Source using a position sensitive detector for Ca2GdSbO6 at room temperature and at 100 K. Data was collected with λ = 0.826866 Å from 2θ = 8–100° using a position sensitive detector, with an overall collection time of 1 min. The powder sample was mounted in a 0.28 mm diameter capillary inside a brass sample holder.

Rietveld refinements[12] of the powder XRD data were completed using the Diffrac.Suite TOPAS5 program.[13] Peak shapes were modeled using a pseudo-Voigt function,[14] and the background was fit using a 13-term Chebyshev polynomial. Except for Ca2GdSbO6, where synchrotron XRD data was available, all Debye–Waller factors were kept constant at the literature reported values from powder neutron diffraction.[10,15] 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.[16]

Magnetic Characterization

Magnetic susceptibility χ(T) = dM/dH (∼ M/H in the low field limit) and isothermal magnetization M(H) measurements were conducted using a Quantum Design Magnetic Properties Measurement System (MPMS) with a superconducting interference device (SQUID) magnetometer. Susceptibility measurements were made in zero-field-cooled conditions (μ0H = 1000 Oe, where M(H) is linear and the χ = M/H approximation is valid) over a temperature range of 1.8–300 K and in field-cooled conditions from T = 1.8–30 K. M(H) measurements were made over a field range of 0 ≤ μ0H ≤ 7 T, in steps of 0.2 T from 2 to 20 K, in 2 K steps from 2 to 10 K, and in 5 K steps from 10 to 20 K. The magnetic entropy change for a field Hmax relative to zero field was extracted from M(H) by computing the temperature derivative of the magnetization usingand then integrating in discrete steps of 0.1 T across fields using the trapezoidal method:

Low Temperature Heat Capacity

Magnetic heat capacity measurements were carried out using a Quantum Design PPMS using the 3-He probe (0.4 ≤ T ≤ 30 K) in zero field. Equal masses of the sample and Ag powders were mixed with a mortar and pestle and pressed into a 0.5 mm pellet to enhance the thermal conductivity. Pellets were mounted onto the sample platform using N-grease to ensure thermal contact. Addenda measurements of the sample platform and grease were calibrated at each temperature before measurement. The sample heat capacity, C, was obtained from the measured heat capacity, C, by subtracting the Ag contribution using the literature values.[17] The magnetic heat capacity C was obtained from a subtraction of the lattice contribution C from the sample heat capacity C:The lattice contribution C was determined using least-squares fits of the zero-field C at high temperatures (8–50 K) to the Debye model:where T is the Debye temperature, R is the molar gas constant, and n is the number of atoms per formula unit. The total magnetic entropy, relative to the lowest temperature T measured, was computed usingnumerically for the temperatures measured.

Structural Characterization

Powder X-ray diffraction indicates formation of an almost phase pure sample for A2GdSbO6 (A = {Ba, Sr, Ca}). Rietveld refinements, Figure and Table , show that all three compounds exhibit small 0.7 wt % impurities of Gd3SbO7.[11] The structures of Ba2GdSbO6 and Sr2GdSbO6 are consistent with those of prior reports.[10] Both materials exhibit full rock-salt ordering of Gd3+ and Sb5+ on the B sites, attributable to the large charge and ionic radii differences between cations; Ba2GdSbO6 forms a cubic structure, resulting in a uniform tetrahedron of Gd3+ ions, while Sr2GdSbO6 forms a monoclinic P21/n structure, resulting in a distorted tetrahedron of Gd3+ ions, Figure .[10]

Figure 1

Crystal structures of the double perovskites (a) Ba2GdSbO6, (b) Sr2GdSbO6, and (c) [CaGd][CaSb]O6. In [CaGd][CaSb]O6, the Gd3+ ions lie in a disordered arrangement with Ca2+ on the A sites. The rock-salt ordering of Gd3+ and Sb5+ on the B sites produce a fcc magnetic sublattice, which is (d) uniform for Ba2GdSbO6 and (e) distorted for Sr2GdSbO6, with the listed side lengths. (f) The fcc sublattice is a frustrated geometry because it composes a network of edge-sharing tetrahedra. (g) High-resolution powder X-ray diffraction Rietveld refinement of [CaGd][CaSb]O6. Observed intensities and calculated intensities obtained from a Rietveld refinement are shown as red circles and a black line, respectively; the difference (data – fit) is shown by a green line. Reflection positions are indicated by blue and orange tick marks, for phases [CaGd][CaSb]O6 and the small phase impurity Gd3SbO7 (0.48(1)% by weight), respectively.

Table 1

Lattice Parameters and Crystal Structures of Ba2GdSbO6, Sr2GdSbO6, and Ca2GdSbO6 ([CaGd][CaSb]O6) as Determined from Rietveld Refinements of Powder X-ray Diffraction at Room Temperature for Ba2GdSbO6 and Sr2GdSbO6 and at 100 K for [CaGd][CaSb]O6a

atom	Wyckoff position	x	y	z
Ba2GdSbO6, Fm3̅m
Ba	8c	0.25	0.25	0.25	0.67
Gd	4a	0	0	0	0.48
Sb	4b	0.5	0.5	0.5	0.41
O	24e	0.257(2)	0	0	0.76
a (Å)	8.47517(2)
Gd3SbO7 (wt %)	0.45(4)
χ2	1.41
Rwp	11.6
Sr2GdSbO6, P21/n
Sr	4e	0.0105(5)	0.0346(2)	0.2489(7)	0.79
Gd	2d	0.5	0	0	0.24
Sb	2c	0	0.5	0	0.39
O(1)	4e	0.253(3)	0.317(3)	0.021(3)	0.79
O(2)	4e	0.190(4)	0.761(3)	0.042(3)	0.79
O(3)	4e	–0.086(2)	0.486(2)	0.239(3)	0.79
a (Å)	5.84113(5)
b (Å)	5.89402(5)
c (Å)	8.29127(7)
β (deg)	90.2373(7)
Gd3SbO7 (wt %)	0.67(4)
χ2	1.20
Rwp	8.7
[CaGd]A[CaSb]BO6, P21/n
Ca1/Gd	4e	–0.0174(1)	0.05939(7)	0.25403(8)	0.90(1)
Ca2	2d	0.5	0	0	0.68(8)
Sb	2c	0	0.5	0	0.54(1)
O(1)	4e	0.1660(8)	0.2149(7)	–0.0728(6)	1.25(5)
O(2)	4e	0.2089(8)	0.1769(7)	0.5511(6)	1.25(5)
O(3)	4e	1.1205(7)	0.4390(7)	0.2254(5)	1.25(5)
a (Å)	5.58025(2)
b (Å)	5.84820(2)
c (Å)	8.07706(2)
β (deg)	90.3253(2)
OccCa1	0.5
OccGd	0.5
Gd3SbO7 (wt %)	0.48(1)
χ2	5.80
Rwp	3.7

The Debye–Waller factors for Ba2GdSbO6 and Sr2GdSbO6 were kept constant to values reported in the literature for the related compounds Ba2DySbO6 and Sr2GdSbO6, respectively.[10,15].

Structural refinements, Table , indicate that Ca2GdSbO6 adopts the monoclinic space group P21/n. However, additional reflections ((011) and (101)) at 2θ ≈ 18° (d = 4.6 – 4.8 Å) indicate that Gd3+ occupies the A sites as in the case of its of nonmagnetic analogue [CaLa][CaSb]O6.[18] Refinement of the occupancy of Gd3+ and Ca2+ across the A and B sites indicated that Gd3+ only occupies the A sites, and so this cation distribution was fixed in subsequent refinements. Thus, a clearer description of the compound is [CaGd][CaSb]O6. (Here, the bracketed notation [XY][LZ]O6 refers to a double perovskite in which species X and Y lie on the A sites and species L and Z lie on the B sites.) Consistent with a prior study of Mn-doped [Ca1–SrGd][CaSb1–]O6:Mn (x = 0.4, y = 0.003)[19] and the structure of [CaLa][CaSb]O6,[18] we find a disordered arrangement on the A sites with half of the sites occupied by the Gd3+ ions and the other half by Ca2+ and rock-salt ordering of Ca2+ and Sb5 on the B sites.

There is no evidence of A-site ordering in the compound with no further superstructure peaks observed in the synchrotron XRD. This is likely due to the minimal charge and ionic radii differences of the Ca2+ and Gd3+ ions which rules out rock-salt and columnar ordering on the A sites.[20]

To analyze whether the site disorder in [CaGd][CaSb]O6 is due to close-packing efficiency considerations, we computed the Goldschmidt tolerance factor (GTF), t. t predicts whether the ionic radii of the A-site cation and B-site cation are well-scaled for a cubic structure in which A-site cations lie at the cavities of B–O octahedra.[21] It can be extended to double perovskites with the formula AA′BB′O6 by computing average A-site and B-site ionic radii so thatwhere .[22] The GTF for [CaCa][GdSb]O6 in which Gd3+ and Sb5+ are located on the B sites is 0.82 compared to 0.80 for [CaGd][CaSb]O6 in which Gd3+ lies on the A sites. Since t ≈ 1 in stable perovskite structures, these results suggest that the Gd3+ ions should lie preferentially on the B-site.

It is also possible that charge differences of the cations stabilize the observed disordered structure.[20] However, an additional calculation using a charge-based tolerance factor also predicted [CaCa][GdSb]O6 as the more stable structure.[23] Thus, the A site occupancy of Gd3+ is unlikely to be due to the greater close cubic packing efficiency or charge differences between cations. It could be that the additional entropy associated with a random distribution of Ca2+ and Gd3+ on the A site favors the observed cation distribution, although we note that a random distribution of Ca2+/Gd3+ across both sites is more entropically favorable. Changes to the synthesis procedure, e.g., slow cooling, may result in differences in the Ca2+/Gd3+ distribution but are beyond the scope of this study.

Magnetic Characterization and Results

The zero-field-cooled (ZFC) magnetic susceptibility χ(T), Figure , indicates paramagnetic behavior of each material down to 1.8 K, in agreement with prior investigations.[10] Curie–Weiss fits to the inverse susceptibility χ–1(T) were conducted from temperatures T = 8 to 50 K. For all compositions, the negative Curie–Weiss temperatures Θ, Table , indicate antiferromagnetic interactions between spins that increase in strength from the monoclinic (A = Sr) to cubic lattice (A = Ba). The Curie–Weiss law can be written in a dimensionless form given by (for Θ < 0), where Θ is the Curie temperature and C is the Curie constant.[24] This dimensionless form can elucidate the presence of short-range correlations from the inverse magnetic susceptibility and enable a comparison across compounds.[24,25] In these dimensionless units, free-spin behavior is indicated by the linear relationship of with with a y-intercept of 1. Positive (negative) deviations from linearity can indicate antiferromagnetic (ferromagnetic) short-range correlations between spins. Figure highlights the minimal short-range correlations of each A2GdSbO6 compound, all of which exhibit extremely small deviations of less than 5% from free-spin behavior at 1.8 K. As a comparison, the MgCr2O4 spinels, which order at , exhibit 20–60% deviations at temperatures of .[25] The positive deviations of [CaGd][CaSb]O6 are likely to correspond to antiferromagnetic short-range correlations rather than disorder-induced quantum fluctuations. Field-cooled measurements below 20 K indicate no hysteresis (see Figures S1 and S2).

Figure 2

(a) Low-field magnetic susceptibility χ ≈ M/H versus temperature T of A2GdSbO6 (A = {Ba, Sr, Ca}) (inset: χ–1 versus T). (b) Dimensionless inverse magnetic susceptibility scaled by the appropriate factors of the Curie constant C and Curie–Weiss temperature Θ for each material. The error bars are smaller than the points in the graph. All compounds remain paramagnetic down to 1.8 K. The inset depicts the percent deviation of χ–1 from the Curie–Weiss law, C/(T – Θ). Error bars are determined assuming a 0.1 mg mass error.

Table 2

Fit Nearest Neighbor Exchange J1 for the fcc Ba2GdSbO6 and Sr2GdSbO6 and Overall Exchange Field, az, for Site Disordered Ca2GdSbO6 Based on Curie–Weiss Analysis of the Inverse Magnetic Susceptibility χ–1 (Equation S1) and a Mean-Field Model Fit (Equations and 8) to the Isothermal Magnetization Curves from 2 to 20 Ka

	from χ–1 fit		from M(H) fit
	Θ (K)	(K)	J1 (K)	R2
Ba2GdSbO6	–0.78(1)	0.0124(2)	0.0113(5)	1.0000
Sr2GdSbO6	–0.51(1)	0.0081(2)	0.0070(2)	1.0000

Quoted uncertainties represent a 95% confidence interval from the least squares fits.

A mean-field estimate for the nearest neighbor (nn) superexchange J1, Table , indicates weak coupling between spins in the fcc compounds, ∼10 mK, compared to 100 mK in Gd3Ga5O12.[9] Although the number of nearest neighbors is not constant for the disordered [CaGd][CaSb] analogue, a mean-field estimate for the six nearest A sites (R = 4.063(3) Å from distances 2 × 3.918(3), 2 × 4.171(3), 4.162(3), and 4.038(3) Å) was computed, giving an order of magnitude estimate for J1.

The zero field measured magnetic heat capacities C of A2GdSbO6 (A = {Ba, Sr, Ca}) from 0.4 to 30 K are depicted in Figure . The Debye temperatures T were determined from fits to the Debye model (eq ) from 6 to 30 K, Table . No magnetic ordering is observed in the fcc compounds down to 0.4 K. The magnetic entropy of Ba2GdSbO6 and Sr2GdSbO6 at 10 K, relative to that at 0.4 K, is 1.6 J/K/molGd, corresponding to only 10% of that available for S = 7/2 Heisenberg spins. In contrast, the site-disordered Ca2GdSbO6 exhibits a sharp λ-type anomaly at 0.52 K, indicative of a long-range ordering transition. The total entropy contained from 0.4 to 30 K is 12 J/K/molGd, or 0.7R ln(2S + 1). This ordering transition may be due to the larger dipolar interaction D in Ca2GdSbO6, Table , which is times that of Ba2GdSbO6 and Sr2GdSbO6, and/or a different Gd3+ ion arrangement.

Figure 3

Zero field magnetic heat capacity normalized by temperature C/T of A2GdSbO6 (A = {Ba, Sr, Ca}) and corresponding magnetic entropy released from 0.4 to 10 K. The Debye temperatures for each material (Table ) were found from fits of the total heat capacity to the Debye model (eq ) from 6 to 30 K. The small anomaly in each measurement at 2.6 K is likely due to the ordering of the ∼0.5–1 wt % Gd3SbO7 impurity.[11]

Table 3

Curie–Weiss Temperature Θ, Ordering Temperature T0, Debye Temperature T, and Corresponding Estimates for the Mean-Field nn Exchange J1 and Dipolar Interaction D for A2GdSbO6 (A = {Ba, Sr, Ca}) and Reported Top-Performing Gd-Based Magnetocaloric Materials Compared to Three Commonly Used Paramagnetic Salts: Ferric Ammonium Alum (FAS), Copper Ammonium Sulfate (CAS), and Copper Potassium Sulfate (CPS).a,b

	ΘCW (K)	J1 (K)	D (K)	D/J1	T0 (K)	TD (K)
Ba2GdSbO6	–0.78(1)	0.0124(2)	0.0116	0.94	<0.4	365
Sr2GdSbO6	–0.51(1)	0.0081(2)	0.0123	1.5	<0.4	475
Ca2GdSbO6 (z ≈ 6)	–0.92(1)	0.029	0.037	1.3	0.52	360
Sr2GdNbO6[31]	3.2	–0.051	0.012	–0.24	∼2	-
Gd(HCOO)3[3]	–0.3	0.0286	0.0393	1.4	0.8	168
GdPO4[4]	–0.9	0.029	0.0362	1.3	0.8	220
GdF3[5]	+0.7	–0.067	0.0503	–0.75	1.25	284(3)
Gd3Ga5O12[9,33,34]	–2.6(1)	0.107	0.0457	0.43	≈0.14	≈500
Gd2ZnTiO6[27]	–4.0	0.024	0.044	1.84	2.43	156.4
Gd2Be2GeO7[29]	–4.09(5)	0.156(2)	0.043	0.28	<2	-
FAA[35−37]	0.042	–0.007	0.010	–1.4	0.026	80
CAS[38,39]	0.010(5)	–0.007(3)	0.0070	–1.1	-	-
CPS[38,39]	0.016(5)	–0.010(3)	0.0070	–0.7	-	-

The mean field nn exchange was calculated using Equation S1 and the dipolar interaction using D = D/S(S + 1) (with D from Equation S2 as in refs (9 and 32). The nn exchange estimated from the Θ reported for Gd(HCOO)3 and GdF3 was taken to be along the Gd–Gd chains, so that z = 2, and in the Gd–Gd planes for Gd2Be2GeO7, so that z = 5. Gd2ZnTiO6 was treated as having 6 nn with an average distance of 3.83 Å. Ca2GdSbO6 was treated as having z = 6 with an average distance of 4.063(3) Å, as described in the text. CAS and CPS were treated as having 6 nn with an average distance of 7.1 Å as in ref (38) and FAA as having 2 nn at 6.24 Å.

The reports of magnetism in Gd3Ga5O12 are highly sample dependent.[40,41]

Isothermal magnetization M(H) measurements, shown in Figures and 5, were conducted to measure the magnetocaloric effect, ΔS(H, T). At 2 K, all compounds are saturated by μ0H = 7 T at the maximum value for free Heisenberg spins, gJ = 7 μ/Gd3+. The measured magnetic entropy change ΔS for applied fields of 0.2–7 T at temperatures of 2–8 K is shown in Figure . The A2GdSbO6 compounds are a high performing set of dense lanthanide oxides, reaching above 90% of the maximum entropy change (per mol Gd) predicted for uncoupled Heisenberg spins, R ln(2S + 1), in a 7 T field at 2 K. Somewhat surprisingly, the presence of site disorder and magnetic ordering at 0.52 K in [CaGd][CaSb]O6 has only a small effect on the overall magnetocaloric performance in this temperature regime, suggesting that minimal superexchange may play a role in enhancing the magnetocaloric effect in the liquid He regime.

Figure 4

Isothermal magnetization of of A2GdSbO6, A = {Ca,Sr,Ba} at T = 2, 6, and 10 K compared to the Brillouin function for free S = 7/2 spins. Error bars are smaller than the data points.

Figure 5

Isothermal magnetization M versus field μ0H for A2LnSbO6 (A = {Ba, Sr, Ca}). Measured data are shown as points, while theoretical predictions based on a fit of the nn exchange, J1, for each material are shown as solid lines. The prediction of free Heisenberg spins at 2 K is shown as a dashed line. Ca2GdSbO6 was fit to an overall exchange field, a, with the number of nn, z, set to one, due to the presence of site disorder. All error bars are smaller than the data points.

Figure 6

(a) Magnetic entropy change ΔS for uncoupled S = 7/2 spins determined from the Brillouin function M(H, T) with ΔT = 2 K and ΔH = 0.1 T steps, compared to the measured ΔS for the three A2LnSbO6 compounds, A = {Ba, Sr, Ca}. (b) Differences between the theoretical entropy change for free-spins, ΔS, and that measured for A2LnSbO6, ΔS. All compounds exhibit deviations of 0.04R ln(2S + 1) to 0.08R ln(2S + 1) at low (1–2 T) fields, possibly indicating the contribution of AFM superexchange. (c) Differences between the theoretical magnetic entropy change predicted for the nn exchange field model using the fit J1, ΔS, and the measured data, ΔS, for A2LnSbO6. Using this nn exchange field model, the deviations are reduced to less than 0.01R ln(2S + 1) for Ba2GdSbO6 and Sr2GdSbO6 and to 0.04R ln(2S + 1) for Ca2GdSbO6.

Investigating the Role of Superexchange on the High Magnetocaloric Effect

To elucidate the origin of the large magnetocaloric effect in these materials, we investigate two models: first, an uncoupled model of S = 7/2 Heisenberg spins, and second, a mean-field model that accounts for antiferromagnetic superexchange between Gd3+ ions.

Uncoupled Spin Analysis

Predictions for the theoretical magnetic entropy change ΔS of uncoupled Gd3+ (S = 7/2) spins were computed from the isothermal magnetization curves determined from the Brillouin function and maximum saturation gJ (eq S4). M(H, T) curves were evaluated at 2–10 K, with 2 K steps, and from 0 to 7 T, with 0.1 T steps, in accordance with the measured temperatures and fields. Figure a,b demonstrates that the predictions, ΔS, for paramagnetic S = 7/2 spins are remarkably close to the measured entropy changes, ΔS, for the three A2GdSbO6 compounds. Ba2GdSbO6 and Ca2GdSbO6 exhibit a maximum deviation of 0.09R ln(2S + 1), corresponding to 10% of the maximum entropy change of 0.9R ln(2S + 1) predicted for free-spins. These deviations occur at low fields (1–3 T) and smaller temperatures (∼2–4 K), in accordance with small antiferromagnetic exchange indicated in the Curie–Weiss analysis. The deviations of ΔS from ΔS for Sr2GdSbO6 are lower, only 0.04R ln(2S + 1), and are concentrated at 2 K. None of the measured compounds exceeds the magnetic entropy change predicted for free S = 7/2 spins; this result is in agreement with the ∼1 K Curie–Weiss temperatures of the materials which imply that, for the measured 2–10 K temperatures, the materials are paramagnetic.

Incorporating an Exchange Field

A recent paper on the kagome compound Gd3Mg2Sb3O14 showed that an nn exchange field can be used to explain deviations from free-spin behavior below the saturation field.[26] Here, we apply this model to characterize the nn exchange J1 in A2GdSbO6 (A = {Ba, Sr, Ca}) and its role in the isothermal field gradient of the entropy, (∂S/∂H) = (∂M/∂T), the determining factor in the magnetocaloric effect.

The model treats antiferromagnetic coupling between S = 7/2 spins using a mean-field approach so that the net field experienced by a single spin, S, is composed of the external field H and the exchange field H due to z nearest neighbors, which scales with the bulk magnetization of the system.[26] This mean-field approach is justified for A2GdSbO6 because the Curie–Weiss analysis indicates that the compounds are paramagnetic in the given temperature range (2–22 K) and thus that the role of quantum fluctuations need not be considered.

Since L = 0 for Gd3+, the exchange constant J1 can be assumed to be isotropic, so that the exchange field is given bywhere M is the bulk magnetization in units of the Bohr magneton and a is the “field parameter” in units of magnetic field.[26] The bulk magnetization of the system at a given temperature T and external field H is given by the roots of the transcendental equation:where B is the Brillouin function (eq S4).[26]

Using this model, estimates of the nearest neighbor exchange J1 in Ba2GdSbO6 and Sr2GdSbO6 and overall exchange field a in Ca2GdSbO6 were found using least-squares fits of the observed isothermal magnetization curves M(H) at 2–20 K, Figure . The free-spin magnetization was used as an initial parameter for the mean-field exchange model magnetization (eq ). For the fcc A = {Ba, Sr}, the number of nn, z, was set to 12, while the site disordered Ca version was fit to an overall exchange field, a, with z = 1. All compounds were fit with a scaled fraction of M = gS; here, M = 1.04gSμ, the observed saturated value of the magnetization.

Table shows the fit nn exchange interaction J1 and overall exchange field a for each of the materials, compared to estimates from low field susceptibility measurements. Overall, there is broad agreement across the two methods. The Curie–Weiss superexchange estimates are slightly larger than from the M(H) curves, which could be due to a small contribution from thermally excited states at the higher temperatures fit or due to the fact that only one field was considered in the Curie–Weiss fits.

The role of superexchange in the magnetocaloric effect is examined in Figure c, which depicts the difference between the mean-field model predicted entropy change, ΔS, and the measured entropy change ΔS for 2–20 K and 0–7 T. The mean-field model reduces the difference between the predicted and measured magnetic entropies to 1, 2, and 4% of R ln(2S + 1) for Ba2GdSbO6, Sr2GdSbO6, and Ca2GdSbO6, approximately 1, 2, and 5% of the max entropy observed. Furthermore, Figure S3 hows that the mean-field model accurately captures the saturation field and overall magnitude of (∂M/∂T) at low temperatures, to within the error of the data, compared to the free-spin prediction for both fcc compounds. The mean-field prediction for (∂M/∂T) of Ca2GdSbO6 at 2 K is not in as good of agreement with the measured data likely due to the presence of site disorder, onset of long-range order (T0 ∼ 0.52 K), or a larger dipolar contribution . Further experimental validation of these exchange constants could be accomplished by low temperature neutron magnetic diffuse scattering experiments to probe short- and long-range correlations between spins. At temperatures of 2 K and above, the mean-field model with antiferromagnetic superexchange thus serves as a good prediction of the observed magnetocaloric effect in A2GdSbO6.

Comparison to Top Performing Gd3+ Magnetocaloric Materials

The magnetic entropy change ΔS attained by the A2GdSbO6 compounds at 2 K and a field of 7 T is compared to those of other top-performing Gd-based magnetocaloric materials in Figure . When comparing the entropy change per mole of Gd, the fcc A2GdSbO6 compounds outperform the top dense oxide magnetocaloric, GdPO4, exhibiting an entropy change of 0.92 ± 0.1R ln(2S + 1), only 0.02R ln(2S + 1) below Gd(HCOO)3.[3,4] It should be noted that this order of performance would inevitably change when comparing ΔS per unit volume or per unit mass; however, evaluating ΔS per mole of Gd highlights the role of superexchange in the magnetocaloric effect. For example, the other top performers Gd(HCOO)3 and GdPO4 have been reported to behave like paramagnets down to 2 K with minimal antiferromagnetic correlations and GdF3 similarly with minimal ferromagnetic correlations (Table ). Along with the mean-field and free-spin analysis in the preceding sections, these results suggest that minimal coupling between spins plays an important role in maximizing the magnetocaloric effect.

Figure 7

Magnetic entropy change ΔS of A2LnSbO6 (A = {Ba, Sr, Ca}) in J/K/molGd compared to top performing magnetocaloric materials from Hmax = 7 T to zero field at 2 K, scaled by R ln(2S + 1).[3−5,27−31] Dense lanthanide oxides are shown in orange, formate-based magnetocalorics in turquoise, ligand-based compounds in brown, and fcc lanthanide oxides in blue, green, and red. Note that the Gd2TiZnO6 value represented is at 2.1 K, as it occurs below the ordering transition. Error bars for ΔS of A2GdSbO6 were estimated using propagation of errors for a mass uncertainty of ±0.1 mg.

Table lists the nn exchange constant J1 and dipolar interaction D in each of the materials estimated from the reported Curie–Weiss temperature Θ and crystal structure.

The top performing materials, Gd(HCOO)3, and GdF3 all have a D/J1 ratio on the order of 1–1.5, indicating that a small dipolar interaction may also improve magnetocaloric performance. Notably, J1 for the fcc A2GdSbO6 is around 15 mK or less, approximately 0.1–0.5 of the estimated nn exchange in the other materials shown and comparable to common paramagnetic salts, including FAA, CAS, and CPS.[35,39] Aside from Gd3Ga5O12, Sr2GdSbO6 and Ba2GdSbO6 have the largest Debye temperatures, indicating the smallest lattice heat capacities, an ideal property in magnetocaloric applications.[3−5]

The A2GdSbO6 (A={Ba,Sr,Ca}) materials investigated in this work provide evidence that minimal superexchange is important in enhancing the magnetocaloric effect in lanthanide oxides. Furthermore, the frustrated fcc geometry of A = {Ba, Sr} and antiferromagnetic superexchange enable enhanced cooling to at least 400 mK in contrast to some nonfrustrated candidates such as GdF3 and Gd(HCOO)3, which are limited to their ordering temperatures of 1.25 and 0.8 K, respectively. Although Gd(HCOO)3 may exhibit a better magnetocaloric effect per unit volume or mass, the fcc double perovskite structure is more chemically tunable and thus allows for the temperature and magnitude of ΔS to be tuned. For example, one useful future study would be to investigate partial substitution of Sb5+ on the B sites or A site substitution. For Gd3Ga5O12, replacement of a single Ga3+ ion with Cr3+ improved the entropy change by over 10%.[30]

The role of the M5+ B site ion in the superexchange is highlighted by the recent report of the magnetocaloric effect in Sr2GdNbO6. Sr2GdNbO6 shows differing fundamental magnetic properties (i.e., ferromagnetic interactions), resembling d0 versus d10 distinctions observed in transition metal oxides.[42,43] This material exhibits a maximum magnetocaloric effect near its ordering temperature (3 K) for μ0H = 7 T, −15.5 J/K/mol,[31] comparable to the performance of Sr2GdSbO6 at 2 K reported in this work.

Our results indicate that changes in the magnetic lattice, such as site disorder in A = Ca, do not substantially alter the magnetocaloric effect for the A2GdSbO6 series at T ≥ 2 K. However, disorder does play a role in the magnetic ordering of the compounds, with A = Ca exhibiting a transition at 0.52 K and A = {Ba, Sr} remaining disordered down to 0.4 K. Future low-temperature heat capacity in applied field, μ-SR, and/or low-temperature neutron diffraction using isotopically enriched samples will be important in understanding how disorder affects the low temperature magnetic behavior. Disorder has recently been shown to play a role in the magnetocaloric effect observed in AGdS2, A = {Li, Na}, with a significant enhancement of the magnetocaloric effect observed in ordered NaGdS2 compared to cation disordered LiGdS2. This is rationalized by differences in the exchange interaction and the onset of ordering at higher temperatures in LiGdS2. At high temperatures, T > 2 K, a similar effect is not observed in the A2GdSbO6 double perovskites but may result in significant differences in the magnetocaloric effect closer to the ordering temperature in Ca2GdSbO6.[44]

The fcc materials presented here, Ba2GdSbO6 and Sr2GdSbO6, are likely able to cool below the industry standard, Gd3Ga5O12 (which has a lower cooling limit of K, due to spin–spin correlations[45]), into the temperature regime of paramagnetic salts ( mK or less[46]) based on their minimal superexchange. This presents a possible significant advancement as the frustrating lattice should have a better per unit volume magnetic entropy change than a Gd3+-based paramagnetic salt.

Conclusion

We synthesized three frustrated lanthanide oxides A2GdSbO6 (A = {Ba, Sr, Ca}) and characterized their structural and magnetic properties through X-ray powder diffraction and bulk magnetic measurements. The frustrated fcc lattice and small (J1 ∼ 10 mK) antiferromagnetic superexchange of Ba2GdSbO6 and Sr2GdSbO6 prevents magnetic ordering down to 0.4 K. In contrast, Ca2GdSbO6 is found to be site-disordered, with all Gd3+ ions lying on the A sites and an antiferromagnetic ordering transition at 0.52 K.

Intriguingly, all three materials make promising magnetocaloric candidates in the liquid He regime (2–20 K), achieving up to 92(1)% of the ideal magnetic entropy change R ln(2S + 1) in an applied field of up to 7 T. The comparable, high magnetocaloric performance (ΔS = 0.88(2)R ln(2S + 1)) of the site-disordered compound Ca2GdSbO6 suggests that the magnetocaloric effect is governed by primarily free-spin behavior at these temperatures. We demonstrate that the measured magnetocaloric effect of the frustrated Ba2GdSbO6 and Sr2GdSbO6 can be predicted to within experimental uncertainty using a mean-field model with a fit nn superexchange constant, J1. These results suggest that future top-performing Gd-based magnetocaloric materials should search for a balance between minimal superexchange between magnetic ions and frustration to suppress the magnetic ordering temperature. The tunability of the double perovskites via chemical substitution makes the fcc lanthanide oxides a promising set of materials for magnetic refrigeration.