Giant Anisotropic Magnetocaloric Effect in Double-perovskite Gd2CoMnO6 Single Crystals

The magnetocaloric effect (MCE) is described by the change in temperature of a material by magnetic field variation and is a crucial subject in magnetism; it is motivated by the desire to enhance energy-efficient magnetic refrigeration for clean technology. Despite the recent discovery of the giant cryogenic MCE in double perovskites, the role of magnetic anisotropy has not yet been clearly discussed, because of the averaging effect of polycrystalline samples. Here, we investigated the anisotropic MCE in the single-crystal double perovskite Gd2CoMnO6. In addition to the ferromagnetic order of the Co2+ and Mn4+ moments, the large Gd3+ moments align below T Gd = 21 K, exhibiting an isotropic nature. Because of the intricate temperature development of magnetically hysteretic behaviour and metamagnetism, the change in magnetic entropy along the c-axis appears to be relatively small. On the contrary, the smaller but almost reversible magnetization perpendicular to the c-axis leads to a large MCE with a maximum entropy change of 25.4 J/kg·K. The anisotropic MCE generates a giant rotational MCE, estimated as 16.6 J/kg·K. Our results demonstrate the importance of magnetic anisotropy for understanding the MCE and reveal essential clues for exploring suitable magnetic refrigerant compounds aiming at magnetic functional applications.


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(ΔS M = 31.0 J/kg·K for ΔH = 0-8 T). However, most of the studies were performed on polycrystalline forms, preventing detailed characterization of the intrinsic properties of the giant MCE associated with magnetic and crystalline anisotropy.
To investigate the influence of the anisotropic characteristics on the giant MCE in one of the transition metal oxides, we have synthesized single crystals of the double perovskite Gd 2 CoMnO 6 (GCMO) using the conventional flux method 14 . Double perovskite R 2 CoMnO 6 (R = La, …, Lu) compounds, where Co 2+ and Mn 4+ ions are alternately located in corner-shared octahedral environments, exhibit assorted physical properties such as metamagnetism [15][16][17] , exchange bias 18,19 , the re-entrant spin-glass state 20,21 , and multiferroicity 16,[22][23][24] because of the intricate magnetic interactions and ionic valence/antisite disorders between mixed-valence magnetic ions. The ferromagnetic order originates from the dominant Co 2+ and Mn 4+ superexchange interactions, and its transition temperature varies linearly from 204 K for La 2 CoMnO 6 25 to 48 K for Lu 2 CoMnO 6 26 as the size of the rare earth ions decreases. GCMO crystallizes in a monoclinic P2 1 /n double-perovskite structure with a unit cell of a = 5.3158 Å, b = 5.6050 Å, c = 7.5759 Å, and β = 89.9541°. The crystal structures viewed from the a-and c-axes are depicted in Fig. 1(a) and (b), respectively. The oxygen octahedral cages are considerably distorted due to the comparatively small radius of the Gd 3+ ion. In a previous study, the polycrystalline form of GCMO revealed a large maximum entropy change of ΔS M ≈ 24 J/kg·K 27 , attributed to the large magnetic moments of Gd 3+ ions.
From our examination of the anisotropic MCE in GCMO single crystals, we only found a ΔS M value of half that in the polycrystalline specimen along the magnetic easy c-axis despite the large magnetization (M) at an applied magnetic field (H). The significant reduction in MCE was caused by the strong temperature (T) dependence of the magnetic hysteresis and metamagnetic transition. Instead, the isothermal M perpendicular to the c-axis exhibited almost reversible hysteretic behaviour, which contributed to the giant MCE associated with the magnetic entropy change ΔS M = 25.4 J/kg·K and adiabatic temperature change ΔT ad = 7.3 K in ΔH = 0-9 T. As a result, the highly-anisotropic ΔS M produced a giant rotational MCE, estimated as 16.6 J/kg·K at 4 K. These results clearly suggest that a meticulous understanding of strongly anisotropic characteristics is crucial for finding improved functional properties in double-perovskite compounds.

Results and Discussion
The anisotropic magnetic properties of GCMO single crystals were examined parallel (H//c) and perpendicular to the c-axis (H⊥c). The T dependence of the magnetic susceptibility, χ = M/H, was measured upon warming at μ 0 H = 0.2 T after zero-H-cooling (ZFC χ) and upon cooling at the same field (FC χ), as shown in Fig. 2(a) and (b), respectively. As T decreases, χ increases smoothly until exhibiting a sharp rise at T C = 112 K, ascribed to the ferromagnetic order of the Co 2+ (S = 3/2) and Mn 4+ (S = 3/2) moments. The ferromagnetic behaviour was characterized by the positive Curie T determined by the Curie-Weiss law. T C was determined by the T derivative of χ and by the sharp anomaly in the T dependence curve of the heat capacity divided by the temperature (C/T) at zero magnetic field (Fig. 2(c)). Reducing T C further, FC χ reaches an approximate plateau. In contrast, ZFC χ decreases at the beginning of the warming from 2 K and the slope of χ changes at around T Gd = 21 K, below which C/T exhibits an abrupt increase, indicating the ordering of the Gd 3+ moments. Above T Gd , the χ increases gradually due to the thermally activated domain wall motions. Just below T C , the ZFC χ shows a distinct peak, which signifies an additional domain wall de-pinning process. At μ 0 H = 2 T, ZFC and FC χ's exhibit conventional ferromagnetic behaviour without any sharp anomaly near T C . The T at which the ZFC χ and FC χ curves start to split is observed, indicating the onset of magnetic irreversibility. The thermally hysteretic behaviour of the χ around T C indicates the first-order nature of the transition. The χ for the two different orientations at μ 0 H = 0.2 T exhibiting a strong magnetic anisotropy near T C indicates that the Co 2+ and Mn 4+ spins are mainly aligned along the c-axis.
To estimate the entropy change based solely on the spin order of Gd 3+ ions, ΔS Gd , the C/T for Eu 2 CoMnO 6 , which includes nonmagnetic Eu 3+ ions with a similar ionic radius to Gd 3+ ions, was measured, as shown in the inset of Fig. 2(c). The ΔS Gd below T Gd was obtained by integrating C/T by T (2-21 K) for GCMO after subtracting the data from Eu 2 CoMnO 6 . The calculated ΔS Gd was 17.3 J/mole·K, which is 50% of the expected value of the fully saturated Gd 3+ moments, i.e., 2R ln(2J+1) = 34.6 J/mole·K, where R is the gas constant and J is the total angular momentum (J = 7/2 for the Gd 3+ ion). Figure 3(a) and (b) display the isothermal M for the two different orientations, measured up to μ 0 H = 9 T at 2 K. The initial M curve at H//c exhibits a gradual increase as H increases before a sudden jump at 6.2 T. The M at the maximum H of 9 T is found to be 15.7 μ B /f.u., which is 72% of the completely saturated moments by considering the effective magnetic moment of a Gd 3+ ion as μ Gd = 7.98 μ B . The consecutive sweeping of H between to the c-axis, respectively, measured upon warming from 2 to 300 K after zero-field-cooling and upon cooling at the same field. The vertical dashed line indicates the ferromagnetic transition temperature, T C = 112 K. (c) Temperature dependence of specific heat divided by temperature, C/T, measured at zero magnetic field. The inset shows a comparison of C/T up to 100 K between GCMO and Eu 2 CoMnO 6 measured at zero magnetic field. The vertical dashed line denotes the ordering temperature of Gd 3+ moments as T Gd = 21 K. +9 and −9 T leads to the sharp double-step metamagnetic transitions at H = ±3.9 and ±6.2 T. Consequently, the full curve exhibits narrow hysteretic behaviour with the remanent M as M r = 2.1 μ B /f.u. and the coercive field as H c = 0.9 T. In contrast, the M at H⊥c varies smoothly without any magnetic hysteresis. Regardless of the hard magnetic axis for the ferromagnetic Co 2+ and Mn 4+ sublattice, the large magnetic moment of 11.6 μ B /f.u. at 9 T implies the somewhat isotropic nature of the Gd 3+ spins associated with the half-filled 4 f electronic configuration. In other words, the difference of the M values at 9 T between the two orientations is caused by the Co 2+ and Mn 4+ spins mainly aligned along the c-axis.
The plausible cause for the features of the metamagnetic transitions 18,28 found in the fully hysteretic M curve at H//c ( Fig. 3(a)) can be determined from the distinctive magnetic anisotropy between Gd 3+ and Co 2+ /Mn 4+ moments. After ZFC, the Co 2+ and Mn 4+ moments are mostly in a parallel or antiparallel arrangement along the c-axis, while the Gd 3+ moments are oriented in random directions reflecting the isotropic character. Upon increasing H, the continuous increase of M up to 10.4 μ B /f.u. is mainly caused by the alignment of Gd 3+ moments along with the flipping of only the partial Co 2+ and Mn 4+ spins due to the large magnetic anisotropic energy. At 6.2 T, the abrupt jump of M occurs because the Zeeman energy of the Co 2+ /Mn 4+ sublattice overcomes the anisotropic energy. The gradual decrease in H from +9 T indicates the reduction of M until it encounters the two consecutive metamagnetic transitions, originating from the flipping of the Gd 3+ spins and then the Co 2+ and Mn 4+ spins, respectively. This assumption is compatible with the magnetically anisotropic energy of the Co 2+ and Mn 4+ spins being larger than that of the Gd 3+ spins. Although the postulation of rather isotropic nature of Gd 3+ moments gives moderate interpretation for isothermal M at 2 K, the narrow hysteretic behaviour with a small M r may indicate small degree of interaction between Gd 3+ and ferromagnetic Co 2+ /Mn 4+ sublattices. Upon decreasing H from +9 T, the negative exchange coupling between Gd 3+ and Co 2+ /Mn 4+ spins accompanied by a smaller magnetocrystalline anisotropy energy and larger moment of Gd 3+ ions leads to the progressive decrease in the net Gd 3+ moments, followed by the considerable reduction of M r .  magnetic anisotropy due to thermal energy. As T increases further, the area of the magnetic hysteresis loop rapidly shrinks and M r and H c also decrease. At 100 K, a slight hysteretic behaviour remains but the metamagnetic transitions almost vanish.
Based on the distinctive magnetic properties for the two different orientations, an anisotropic MCE in the GCMO was obtained by measuring the initial M curves with dense T steps ranging from 2 to 180 K in Fig. 5. In contrast to the typical reduction of M values with the increase in T, the initial M curves at H//c develops in a complicated manner. The sharp steps of the metamagnetic transitions at 2 K move progressively to lower H and become broader as T increases. For this reason, the M value in a given H regime is lower than that at higher T. In the inset of Fig. 5(a), the isothermal M values measured at 5, 10, and 15 K are magnified. The green shaded areas represent specific examples of the reversed order of magnitude for the M values. As T is further increased, the occurrence of the reversed order shifts gradually to the lower H regime. At H⊥c, a small but broad transition feature also occurs at some temperature regime while moving to lower H as T is further increased, however, the overall magnitude of M is reduced in most of the regime of H with increasing T, as shown in the inset of Fig. 5(b).
At a given T, the isothermal magnetic entropy change, ΔS M , can be obtained from the initial M curves using the Maxwell relation: By taking advantage of the strong magnetic anisotropy due to the distinctive characteristics of the double perovskite GCMO compound, the rotating MCE was measured by the angular dependence of ΔS M , denoted as ΔS θ , where θ is the angle deviating from the c-axis, i.e., θ = 0° for H//c and θ = 90° for H ⊥c (Inset of Fig. 7). Figure 7 shows ΔS θ obtained at 4 and 8 K for ΔH = 0-9 T. As there is a different T dependence of ΔS M between H//c and H ⊥c, the angle-dependent modulation of ΔS θ varies strongly with T. At 8 K, ΔS θ negligibly changes with the rotation of θ to 30° and increases linearly above 30°. The maximum ΔS θ was evaluated as only 7.8 J/kg·K. At 4 K, on the contrary, the continued variation of ΔS θ by θ rotation generates a giant rotational MCE as the maximum change of 16.6 J/kg·K, which would be beneficial for rotary magnetic refrigerator technology. The maximum difference of ΔS θ in the GCMO is comparable to the other rotating magnetic refrigerants such as HoMn 2 O 5 29 (12.4 J/ kg·K for ΔH = 0-7 T) and DyNiSi 30 (17.6 J/kg·K for ΔH = 0-5 T).
A more feasible aspect of MCE can be attained as the adiabatic T change, ΔT ad , from the following equation: ad H 0 0 f where C(T, H) is the heat capacity at a given T and H. In many cases, C appears to be independent of the applied H, thus, it can be considered as a constant for the integral. However, in GCMO, the T dependence of C/T clearly varies depending on the magnitude of the applied H, as shown in Fig. 8(a) and (b) for H//c and H ⊥c, respectively, measured at H = 0, 3, 5, 7, and 9 T. At H//c, the C/T at very low temperatures decreases with H along with the emergence of a broad peak shifting to higher T. As T increases further, C/T decreases more slowly as H gradually increases. Therefore, the order of magnitude of C/T with respect to H is reversed at about 4 K. The C/T for H ⊥c exhibits similar T and H dependences as H//c. The C/T exhibits a greater reduction as H increases  at the very low T regime with a further shift of the peak to higher T. ΔS Gd is also estimated from C/T taken at 9 T for H//c. ΔS Gd = 23.7 J/mole·K, which is about 69% of the value, assuming full saturation of Gd 3+ moments, consistent with the measured magnetization at 9 T ( Fig. 3(a)). Figure 8(c) and (d) display the T dependence of ΔT ad , estimated for H//c and H ⊥c, respectively, with ΔH = 0-3, 0-5, 0-7, and 0-9 T. At H//c, the T dependence of ΔT ad behaves similarly to that of ΔS M . For ΔH = 0-9 T, starting from ΔT ad = 1.3 K at 2 K, ΔT ad increases with T and reaches 8.3 K at the peak position as T = 17.0 K. However, the estimated T dependence of ΔT ad for H ⊥c was strongly influenced by the reciprocal of C/T during the calculation of the integral. Interestingly, the ΔT ad for ΔH = 0-9 T maintains its magnitude between 6.5 and 7.3 K up to T = 17.0 K, suggesting that the MCE steadily covers the wide range of the low T regime for H ⊥c.
In summary, we explored the anisotropy of the magnetic and magnetocaloric properties of single-crystal double perovskite GCMO. Contrary to the anticipated large MCE along the magnetic easy c-axis, we attained a maximum entropy change of only half the magnitude of that found in the polycrystalline specimen. This substantial reduction is attributed to the intricate temperature evolution of metamagnetic transitions. Alternatively, an almost reversible hysteretic behaviour of isothermal magnetization perpendicular to the c-axis results in a large entropy change of ΔS M = 25.4 J/kg·K, and thus the giant rotational MCE is taken as ΔS θ = 16.6 J/kg·K at 4 K. The strongly anisotropic magnetic properties of the double-perovskite compound offer essential clues for the fundamental and applied research on magnetic materials, aiming to enhance the functional properties.

Methods
Rod-shaped single crystals of GCMO were grown using the conventional flux method with Bi 2 O 3 flux in air. The stoichiometric ratio of Gd 2 O 3 , Co 3 O 4 , and MnO 2 powders was mixed and ground in a mortar, followed by pelletizing and calcining at 1000 °C for 12 h. The calcined pellet was reground and sintered at 1100 °C for 24 h. The same sintering procedure after regrinding was performed at 1200 °C for 48 h. A mixture of pre-sintered polycrystalline powder and Bi 2 O 3 flux at a 1:12 ratio was heated to 1300 °C in a Pt crucible. It was melted at the soaking temperature for 5 h, slowly cooled to 985 °C at a rate of 2 °C/h, and cooled to room temperature at a rate of 250 °C/h. The temperature and magnetic field dependences of the DC magnetization, M, were examined by a vibrating sample magnetometer at T = 2-300 K and H = −9-9 T using a Physical Properties Measurement System (PPMS, Quantum Design, Inc.). The temperature dependence of specific heat, C, at various magnetic fields was measured with the standard relaxation method using the PPMS.