Enhanced magnetocaloric effect from Cr substitution in Ising lanthanide gallium garnets $Ln_3\text{CrGa}_4\text{O}_{12}$ ($Ln$ = Tb, Dy, Ho)

A detailed study on the crystal structure and bulk magnetic properties of Cr substituted Ising type lanthanide gallium garnets $Ln_3\text{CrGa}_4\text{O}_{12}$ ($Ln$ = Tb, Dy, Ho) has been carried out using room temperature powder X-Ray and neutron diffraction, magnetic susceptibility, isothermal magnetisation and heat capacity measurements. The magnetocaloric effect (MCE) in $Ln_3\text{CrGa}_4\text{O}_{12}$ is compared to that of $Ln_3\text{Ga}_5\text{O}_{12}$. In lower magnetic fields attainable by a permanent magnet ($\leq$ 2 T), Cr substitution greatly enhances the MCE by 20% for $Ln$ = Dy and 120% for $Ln$ = Ho compared to the unsubstituted $Ln_3\text{Ga}_5\text{O}_{12}$. This is likely due to changes in the magnetic ground state as Cr substitution also significantly reduces the frustration in the magnetic lattice for the Ising type $Ln_3\text{Ga}_5\text{O}_{12}$.


Introduction
Many areas of fundamental and applied scientific research including spintronics and quantum computing as well as devices such as magnetic resonance imaging (MRI) scanners and low temperature sensors (such as those in space detectors) require cooling to low temperatures. This is usually achieved using liquid cryogens such as liquid nitrogen T > 80 K, liquid helium ( 4 He) for T > 2 K or a mixture of 3 He and 4 He for cooling down to 20 mK. However, the increasing scarcity of helium (the 3 He isotope is even less abundant) and rising costs means that alternatives to cryogens must be explored. One such alternative is solid state magnetic cooling using adiabatic demagnetisation refrigerators (ADRs) which are based on the principle of the magnetocaloric effect (MCE) in magnetic materials. Here the cooling limit is determined by the magnetic ordering temperature, T0, of the material. [1][2][3][4] ADRs using dilute paramagnetic salts are used to cool down to temperatures of few mK. [5][6][7] However, the poor chemical stability of these materials make them less viable for widespread practical applications. A different approach is to use ceramic materials which have geometrically frustrated magnetic lattices where the geometry of the magnetic lattice prevents all the nearest-neighbour magnetic interactions from being satisfied simultaneously. [8] This suppresses or in some cases, completely inhibits magnetic long range ordering. Geometrically frustrated magnets (GFMs) typically show ordering features at T0 ~ θCW /10 where θCW is the Curie-Weiss temperature, thereby suppressing the ordering temperature. [9] In complex lanthanide oxides, the highly localised 4f orbitals have weak magnetic interactions, i.e. θCW is small and so when the magnetic lattice is frustrated, ordering is suppressed to even lower T.
The theoretical magnetic entropy that can be extracted is much higher than in transition metal compounds. GFMs with Ln 3+ ions are therefore ideal candidates for sub 20 K magnetocaloric materials (MCMs). Another advantage is that the lanthanides are chemically very similar but their magnetic properties vary widely. This allows tuning of the properties for optimisation of the MCE. [10][11][12] The lanthanide gallium garnets, Ln3Ga5O12, are a family of materials, where the magnetic Ln 3+ spins form two interpenetrating networks of ten membered-rings of corner-sharing triangles leading to a high degree of geometrical frustration. [13] Of these, gadolinium gallium garnet (GGG), which shows no long range ordering down to 25 mK, has been established as a MCM for magnetic refrigeration in the liquid helium temperature regime. The absence of long range ordering, high density of magnetic ions, chemical stability and lack of single ion anisotropy (L=0 for Gd 3+ ) allowing for the full magnetic entropy (Rln[2J+1] = 17.29 J K -1 molGd -1 ) to be extracted in high magnetic fields makes it an ideal MCM for T<20 K. [14][15][16] In recent years, a number of Gd containing MCMs with better performance at 2 K have been reported [17][18][19][20] but GGG continues to be used and serves as the benchmark for MCMs in this temperature regime.
However, for all the Gd based magnetocalorics, the change in magnetic entropy is maximised in fields of 5 T or higher. Such high magnetic fields can only be produced using a superconducting magnet which again requires cooling using cryogens. For more practical applications, we need to focus on developing materials with high MCE in fields ≤ 2 T, attainable by a permanent magnet. This has been discussed in a recent study on Tb(HCO2)3 where the MCE is significantly higher than Gd(HCO2)3 at higher temperatures and lower fields as the Tb 3+ have Ising-like spins contrasted with the Heisenberg nature of the Gd 3+ spins. [21] For Ln3Ga5O12 the MCE in fields ≤ 2 T is expected to be maximised for the Ln 3+ having Ising-like spins, such as Dy3Ga5O12 (DGG), Ho3Ga5O12 (HoGG) and Tb3Ga5O12 (TbGG). [22][23][24] DGG is a more efficient MCM than GGG at fields ≤ 2 T. [25] There have been no detailed studies on the MCE in Tb3Ga5O12 and Ho3Ga5O12 but the Ising nature of the spins could lead to large changes in the magnetic entropy at low fields.
Much remains to be explored about the optimisation of the MCE in the Ln3Ga5O12 family.
One approach is to maximise the MCE by chemical substitution. Studies in GGG substituting the magnetic Gd 3+ site with Tb 3+ or Dy 3+ [25][26][27] and the nonmagnetic Ga 3+ site with Al 3+ or Fe 3+ partially or completely [28][29][30][31] have shown to have a measurable impact on the MCE. There is a lot of potential for further research on studying the effect of chemical substitution on the MCE in the different Ln3Ga5O12.
In this paper, we report on the synthesis, characterisation, bulk magnetic properties and MCE in terbium, dysprosium and holmium gallium garnets substituted with chromium, Ln3CrGa4O12 (Ln = Tb, Dy, Ho) and compare them with Ln3Ga5O12. The change in magnetic entropy in TbGG in a field of 2 T is of comparable magnitude to DGG, albeit slightly smaller, while that of HoGG is almost half that of DGG. Cr substitution has a dramatic impact on the magnetic properties with increased transition temperatures and enhanced MCE in all Cr containing samples. Most significantly, the change in magnetic entropy in Ho3CrGa4O12 is more than twice that of Ho3Ga5O12 in all measured temperatures and magnetic fields.

Structural Characterisation
PXRD indicated the formation of phase pure Ln3CrGa4O12 (Ln = Tb, Dy, Ho). Attempts to synthesise Ln3CrxGa5-xO12 (Ln = Tb, Dy, Ho) with x > 1, resulted in the formation of LnCrO3 (Ln = Tb, Dy, Cr) perovskite impurities. We conclude that only partial substitution of Ga on the octahedral site with Cr (maximum 1:1 ratio) is possible using this synthetic route.
The cubic 3 ̅ structure of Ln3Ga5O12 (Ln = Tb, Dy, Ho) is preserved on Cr substitution ( Figure 1a). In the cubic Ln3Ga5O12 garnet structure there are three distinct cation sitesdodecahedral occupied by Ln 3+ , octahedral occupied by Ga 3+ and tetrahedral also occupied by Ga 3+ . The connectivity of magnetic Ln 3+ ions is shown in Figure 1b.
Combined PXRD + PND structural refinements were carried out for Ln3CrGa4O12 (Ln = Tb, Ho). For Dy3CrGa4O12 and Ln3Ga5O12 (Ln = Tb, Dy, Ho), the structural refinements were carried out using only PXRD. The combined room temperature PXRD + PND Rietveld refinement for Ho3CrGa4O12 is shown in Figure 2. The crystallographic parameters obtained from the fits for Ln3CrGa4O12 (Ln = Tb, Dy, Ho) are given in Table 1 and for Ln3Ga5O12 (Ln = Tb, Dy, Ho) in Table S1. Very little change in lattice parameter is observed on Cr 3+ substitution. This is expected given the similar size of Cr 3+ and Ga 3+ ions. The difference in the neutron scattering factor for Cr (bCr = 3.635 fm) and Ga (bGa= 7.288 fm) [32] allows for the position of Cr 3+ to be determined. For Ln = Tb and Ho, Cr 3+ is found to exclusively occupy the octahedral site, as would be expected from crystal electric field (CEF) considerations.
Therefore, it was also assumed that Cr exclusively occupies the octahedral site in DyCrGa4O12. The refined composition for Ln = Tb, Ho was determined to be the same as the nominal composition within error. The composition for Ln = Dy was fixed at the nominal composition as PXRD is not sensitive enough to refine the Cr/Ga occupancy. We will use the nominal composition in all further discussions.
On Cr substitution, the changes in the Ln-O, Ln-Ln, Cr/Ga1-O and Ga2-O bond lengths are small and almost all within error for Ln = Tb, Dy, Ho (Table S2). Therefore, no significant change in Ln 3+ single-ion anisotropy is expected on Cr substitution. The resultant change in the dipolar interaction (D ∝ 1/rLn-Ln 3 ) between adjacent Ln 3+ ions on Cr substitution is also small, less than 0.1% for all samples.

Magnetic Measurements
The Zero Field Cooled (ZFC) magnetic susceptibility, , of Ln3CrGa4O12 (Ln = Tb, Dy, Ho) measured in a field of 100 Oe from 2-300 K is shown in Figure 3 and in Figure S1 for Ln3Ga5O12 (Ln = Tb, Dy, Ho). No long-range magnetic ordering is observed down to 2 K for any sample. Above T > 100 K, the inverse susceptibility   is linear and fits to the Curie-Weiss law for the Cr substituted garnets are summarised in Table 2 Table 2. Figure  Mmax for all samples is much lower than the theoretical saturation value for a Heisenberg system, Msat = 3gJJ + gSS. However, for the Ising-like Tb 3+ , Dy 3+ and Ho 3+ spins in Ln3Ga5O12, [22][23][24] the saturation value for the magnetic Ln 3+ is expected to be close to 3gJJ/2.
Our Mmax values are in agreement with this and so we propose that the Ising nature of the Ln 3+ (Ln = Tb, Dy, Ho) is retained on Cr substitution in these garnets. Thus the MCE for the Cr substituted garnets is also expected to be optimized in fields up to 2 T. The contribution of Cr 3+ spins to the net magnetisation is very small compared to Ln 3+ and so we cannot definitively comment on their nature. However, Cr 3+ (d 3 ) spins are likely to have Heisenberg nature [33] and the Mmax values are consistent with this.

Heat Capacity Measurements
The magnetic heat capacity, Cmag, as a function of temperature and field for Ln3CrGa4O12 (Ln = Tb, Dy, Ho) is shown in Figure 5. Inset shows Cmag/T in zero field measured down to 0.5 K.
The lattice contribution was subtracted using a Debye model [34] with θD = 360 K for Tb3CrGa4O12, θD = 340 K for Dy3CrGa4O12 and θD = 330 K for Ho3CrGa4O12. The nuclear Schottky anomaly for Ho3CrGa4O12 was subtracted using a model for the hyperfine interactions for HoCrO3. [35] In zero field, Tb3CrGa4O12, Dy3CrGa4O12 and Ho3CrGa4O12 show magnetic ordering features at 1.72 K, 1.75 K and 1.55 K respectively. In higher fields the ordering transition shifts to higher temperatures and is broadened. At 9 T, the transition manifests as a very broad feature at ~5, 10 and 12 K for Ln3CrGa4O12 (Ln= Tb, Dy, Ho) respectively.
TbGG, DGG and HoGG are reported to order at 0.25 K, 0.373 K and 0.19 K respectively. [24,36] Cr substitution significantly enhances the transition temperature for these Ising type lanthanide gallium garnets. T0 is increased from 0.25 K to 1.72 K for Ln = Tb, from 0.373 K to 1.75 K for Ln = Dy and from 0.19 K to 1.55 K for Ln = Ho. The frustration index, f, of the magnetic lattice, defined by f = θCW /T0 is reduced on Cr substitution (Table 2). In the most extreme case, for Dy3CrGa4O12, the frustration index is only slightly higher than would be expected for an antiferromagnet and is significantly reduced from f ~ 23 for Dy3Ga5O12.
The origin of the changes in the magnetic frustration is not clear. It has been reported that increased single-ion anisotropy in the Ln3Al5O12 garnets increases T0. [37] However, the lack of any significant changes in the Ln-O environment would suggest that this is not the case here.
Further experiments using PND are required to determine a) the nature of magnetic ordering in Ln3CrGa4O12 (Ln= Tb, Dy, Ho) b) whether there are any differences in the magnetic ground state for the different Ln compared to the unsubstituted gallium garnets.

Magnetocaloric Effect
The magnetocaloric effect (MCE) can be characterised by the change in magnetic entropy, ΔSm, per mole which can be calculated from the M(H) curves using Maxwell's thermodynamic relation: [38] ∆ = ∫ ( )

Contour plots for ΔSm per mole as a function of temperature T and magnetic field μ0H for
Ln3CrGa4O12 (Ln = Tb, Dy, Ho) are given in Figure 6. The MCE is compared to unsubstituted Ln3Ga5O12 (Ln = Tb, Dy, Ho) in a field of 2 T in Figure 7. Insets show the variation of ΔSm per mole in field at 2 K. Figure 7 shows that DGG has a higher Sm than TbGG and HoGG.
Sm for TbGG at 2 K, 2 T (8.66 J K -1 mol -1 ) is lower than DGG (11.32 J K -1 mol -1 ); however for HoGG, the change in Sm is about half that for DGG. These differences could be due to differences in the nature of the magnetic ordering in these garnets.
On Cr substitution, Dy3CrGa4O12 has the largest change in magnetic entropy over the entire temperature and field range among the three Cr substituted garnets. The contour plots ( Figure   6) also show the onset of field-induced transitions at fields > 2 T for all three Cr substituted samples. The most pronounced field induced transition is observed in DyCrGa4O12 at ~ 5 K and 5 T, further experiments are required to investigate the nature of the observed transitions.
The differences in the effect of Cr substitution on the MCE for the different Ising-type Ln 3+ is striking. For Ln = Tb, the difference in the MCE on Cr substitution is minimal at low fields, however an increase in ΔSm is observed at fields above 2.5 T. Whereas for Ln = Dy, there is a 20% increase in ΔSm in a field of 2 T. The most dramatic increase in ΔSm is seen for Ln = Ho where ΔSm shows ~120% increase for Ho3CrGa4O12 compared to Ho3Ga5O12 in a field of 2 T.

Thus, substitution with Cr significantly enhances the MCE in DGG and HoGG (especially Ln
= Ho) in magnetic fields ≤ 2 T and temperatures below 10 K. The origin of the impact of Cr substitution on ΔSm is likely due to changes in the magnetic ordering and nature of the magnetic ground state, indicated by the dramatic change in the magnetic frustration and enhancement of the ordering temperature for Ln3CrGa4O12. For a MCM, the maximum change in the magnetic entropy is obtained around the ordering temperature, T0. The minimum temperature for our ΔSm (T) calculations, 2 K, is very close to T0 for Ln3CrGa4O12 (Table 2)  LnVO4 (Ln = Dy, Ho). [39][40][41] However for these systems, ΔSm is maximized at higher temperatures, T > 20 K, restricting their use for cooling in the liquid helium temperature regime. Ln3CrGa4O12 (Ln = Dy, Ho), however, can be used as effective MCMs for T ≥ 2 K in fields up to 2 T. Further Ln3CrGa4O12 and Ln3Ga5O12 (Ln = Dy, Ho) could be used to develop potential graded magnetocalorics so that the cooling limit is further reduced to T ≥ 0.4 K (T0 for the Ln3Ga5O12).

Conclusion
We have prepared powder samples of Ln3CrGa4O12 (Ln = Tb, Dy, Ho) and carried out a detailed investigation of the crystal structure and bulk magnetic properties. The MCE has been calculated and compared to unsubstituted Ln3Ga5O12 (Ln = Tb, Dy, Ho). It is seen that in lower magnetic fields, μ0H ≤ 2 T, Cr substitution greatly enhances the MCE in Ising type lanthanide gallium garnets -by 20% for Ln = Dy and 120% for Ln = Ho in a field of 2 T.
These materials are viable MCMs in the liquid helium temperature regime (T ≥ 2 K). The enhancement in MCE is postulated to be due to the changes in magnetic ordering as Cr substitution also significantly reduces the magnetic frustration and enhances the transition temperature in Ln3Ga5O12 (Ln = Tb, Dy, Ho).

Experimental Section
Sample preparation: Powder samples of Ln3CrGa4O12 (Ln = Tb, Dy, Ho) were prepared using a solid-state synthesis by mixing stoichiometric amounts of Tb4O7 (99.999% purity, Alfa Aesar) or Dy2O3 (99.999% purity, Alfa Aesar) or Ho2O3 (99.999% purity, Alfa Aesar), Ga2O3 (99.99% purity, Alfa Aesar) and Cr2O3 (99.99% purity, Alfa Aesar). Ga2O3 was pre-dried at 500 o C prior to weighing out to ensure accurate chemical composition. The powders were intimately mixed and pressed into pellets which were heated between 1200 -1400 o C for 48-72 hours with intermittent regrindings. Samples of Ln3Ga5O12 (Ln = Tb, Dy, Ho) were prepared in a similar fashion except heat treatments were only carried out at 1200 o C as described elsewhere. [31] Structural Characterisation: Powder X-Ray diffraction (PXRD) was used to confirm the formation of phase pure products. Initially short scans were collected over (Ln = Tb, Ho). The structural Rietveld refinement was carried out using the Fullprof suite of programmes. [42] Linear interpolation was used to fit the background and the peak shape was modelled using a pseudo-Voigt function. Heat Capacity Measurements: Heat capacity measurements for Ln3CrGa4O12 (Ln = Tb, Dy, Ho) were performed using a Quantum Design PPMS in the temperature range 1.8 -30 K in fields 0 -9 T. Equal amounts of sample and silver powder (99.99% Alfa Aesar) were mixed and pressed into pellets which were then used for measurement. To obtain the sample heat capacity, the contribution from silver was subtracted using values from the literature. [43] Additional measurements were made using the He3 option down to 0.5 K in zero field.          Supporting Information Figure S1. ZFC molar susceptibility χ(T) for Ln3Ga5O12 (Ln = Tb, Dy, Ho) measured from 2-300 K in a field of 100 Oe; inset: inverse molar susceptibility χ -1 (T) Figure S2. Isothermal M(H) curves measured from 0 -9 T at select temperatures for Ln3Ga5O12 (Ln = Tb, Dy, Ho)