Structural, magnetic and magnetocaloric properties in distorted RE 2NiTiO6 double perovskite compounds

The magnetocaloric effect based Magnetic refrigeration (MR) was considered a novel energy-efficient and environmentally benign cooling method. However, the lack of suitable magnetic solids has slowed the development of its practical applications. We herein fabricated the RE 2NiTiO6 (RE = Gd, Tb and Ho) double perovskite (DP) compounds and systematically determined their structural, magnetic and magnetocaloric properties by experimental determination and density functional theory calculations, in which the Gd2NiTiO6 was realized to exhibit promising cryogenic magnetocaloric performances. The results indicated that all the RE 2NiTiO6 DP compounds crystallized in a distorted monoclinic structure with P21/n space group and underwent a second order type magnetic phase transition around 4.3, 4.5 and 3.9 K, for Gd2NiTiO6, Tb2NiTiO6 and Ho2NiTiO6, respectively. The magnetocaloric performances were checked by the parameters of maximum magnetic entropy change and relative cooling power, which are 31.28 J·kg−1·K−1 and 242.11 J·kg−1 for Gd2NiTiO6, 13.08 J·kg−1·K−1 and 213.41 J·kg−1 for Tb2NiTiO6, 11.98 J·kg−1·K−1 and 221.73 J·kg−1 for Ho2NiTiO6 under the magnetic field change of 0–50 kOe, respectively. Evidently, the Gd2NiTiO6 compound exhibit promising magnetocaloric performances and therefore is of potential for practical cryogenic MR applications.


Introduction
The development of novel magnetic materials with promising functional characters is of great significance for the advancement of modern technology and society. Among them, the magnetocaloric effect (MCE) based magnetic refrigeration (MR) technology promises to replace the conventional vapor cycle refrigeration, but also has a wide range for potential applications from room temperature to ultra-low temperature [1][2][3][4][5][6]. The MCE is a magnetic field induced thermodynamic phenomenon, which can be manifested as the heat generated or absorbed by the materials when the external magnetic field is changed. As a result, a large number of theoretical and experimental researches have been carried out on a variety of MR materials. Up to now, a series of MR materials with potential application near ambient temperature have been identified, such as Gd-Si-Ge [6], La-Fe-Si/Al [7], Mn-Fe-P-As/Ge/Si [8,9], and Ni-Mn-X (X = Ga, In and Sn) [10,11], etc. In comparison, rare earth (RE)-based compounds and oxides are regarded as the promising cryogenic MR materials for MR technology on account of their unique advantages and application prospects in the liquefaction of extremely low-temperature resources including helium (He), hydrogen (H 2 ) and nitrogen (N 2 ) [12][13][14][15][16].
In recent years, some of the RE-based oxides were fabricated and systematically checked, which are found to exhibit many intriguing physical properties in terms of magnetodielectric effect, magnetoresistive effect, luminescence characteristic and large/giant MCE effects, etc. For examples, Zhao et al have implemented the phase transition from antiferromagnetic-paraelectric to ferromagnetic-ferroelectric order in the (EuTiO 3 ) 0.5 :(MgO) 0.5 composite through the enhancement of spin-phonon coupling by negative pressure [17]. Arh et al have found that strong spin-orbit coupling (SOC) plays a key role in stabilizing spin liquid derived from magnetic anisotropy in the Ising triangular-lattice antiferromagnet NdTa 7 O 19 oxide [18]. Blasco et al reported that each Fe 2+ ion in the NaREFeWO 6 (RE = Pr and Sm) oxides has strong antiferromagnetic coupling with the three nearest RE 3+ ions and follows a unique magnetic order of 'up-up-down-down' sequence running along the [1 0 0] direction [19]. Moreover, Zeng et al have investigated the MCE performances in the weberite-type oxides Gd 3 MO 7 (M = Nb, Sb and Ta), and found that they are promising alternatives for MR techniques [20]. Fkhar et al have found the employment composite or spray drying as the effective strategy to improve magnetic properties in the La 0.45 Nd 0.25 Sr 0.3 MnO 3 /CuO compound [21,22]. Koskelo et al have reported a series of fcc oxides A 2 GdSbO 6 (A = Ca, Sr and Ba) with small superexchange interactions, the maximum magnetic entropy change (−∆S max M ) are 20% higher than that of the standard MR material Gd 3 Ga 5 O 12 using in extremely low-temperature [23]. Very recently, Xu et al have used the combination of experiment and density functional theory (DFT) calculation to reveal electronic, magnetic and MCE properties of the isostructural RE 2 BaZnO 5 compounds, in which Dy 2 BaZnO 5 and Ho 2 BaZnO 5 compounds exhibit excellent magnetocaloric performances at liquid He temperature [24].
As an important branch of RE-based oxides, the RE 2 TMTM'O 6 (where TM and TM' are transition metal elements) double perovskite (DP) compounds derived from the ABO 3 perovskite oxides have become the research focus in recent years. Because their intrinsic properties can be regulated by the variability of ions at RE, TM and TM' sites, they are endowed with outstanding optical, electrical, catalytic, magnetic and MCE properties [25][26][27][28]. In particular, the RE 2 TMTM'O 6 compounds have attracted extensive attention in exploring the exotic magnetic properties caused by strong SOC, structural variation diversity and anisotropic exchange interaction [29][30][31]. The competition of ferromagnetic and antiferromagnetic couplings among RE 3+ , Ni 2+ and Ir 4+ ions in the RE 2 NiIrO 6 (RE = La, Pr and Nd) compounds can not only change the magnetic moment arrangement of Ni 2+ and Ir 4+ ions, but also increase the corresponding magnetically ordered temperatures with the decrease of the size of RE 3+ [32]. The spontaneous magnetization of the RE 2 LiFeO 6 (RE = Sm and Eu) compounds with abnormally high valence Fe 5+ ions is closely related to the Dzyaloshinskii Moriya interaction, and the magnetization increases with increasing local geometric spin frustration between the nearest Fe 5+ ions in the [1 1 1] direction [33]. In terms of MCE performances, the RE 2 TMTM'O 6 compounds commonly have lower hysteresis and higher chemical stability than rare earth (RE)-transition (TM) intermetallic compounds and alloys, as well as higher resistivity that facilitates reduced eddy current losses. Up to now, the excellent MCE performances in the field of extremely low-temperature have also been researched in the RE 2 CuMnO 6 [34], RE 2 ZnMnO 6 [35] and RE 2 FeAlO 6 compounds [36]. It is evident from the above results that the exploration and investigation of the RE 2 TMTM'O 6 compounds with promising MCE performances is of great interest in the field of extremely low-temperatures MR, meanwhile, understanding its magnetic exchange interaction can also provide valuable theoretical information for the discipline of condensed matter physics.
Based on this background, we found that the RE 2 NiTiO 6 compounds containing light RE ions have unique properties in the areas of optics, electricity and magnetism through the results of the relevant literatures [37][38][39]. However, there are few reports on the RE 2 NiTiO 6 compounds containing heavy RE ions to date, especially in term of the magnetic and MCE properties. Therefore, we have studied the crystal structures, magnetic properties, electronic structures as well as MCE of the RE 2 NiTiO 6 (RE = Gd, Tb and Ho) DP compounds by combining experiments with DFT calculations. As a consequence, we found that the anisotropic distortion in the monoclinic crystal structure of the RE 2 NiTiO 6 compounds increase with decreasing RE 3+ ion radius, resulting in the reduction of crystal symmetry. Furthermore, considerable reversible MCE performances have been observed in Gd 2 NiTiO 6 compound, which provides a crucial clue for the exploration of MR materials suitable for extremely low-temperature.

Experimental and theoretical details
The RE 2 NiTiO 6 (RE = Gd, Tb and Ho) polycrystalline compounds were prepared by citric acid-assisted sol-gel route. The precursor materials Gd(NO 3 ) 3 (⩾99.99%), Tb(NO 3 ) 3 (⩾99.99%), Dy(NO 3 ) 3 (⩾99.99%), Ni(NO 3 ) 2 (⩾99.99%) and Ti(SO 4 ) 2 (⩾99.99%) are purchased from the Shanghai Macklin Biochemical Co., Ltd. Firstly, stoichiometric amounts high purity raw materials of Gd(NO 3 ) 3 , Tb(NO 3 ) 3 Dy(NO 3 ) 3 , Ni(NO 3 ) 2 and Ti(SO 4 ) 2 were stirred in distilled water until they were completely dissolved. Subsequently, anhydrous citric acid was added to the precursor mixture solution. As a complex adhesive, anhydrous citric acid can help the good dispersion of various elements in the precursor gel. The obtained precursor mixture solutions were kept under constant magnetic stirring at 353 K for 12 h until viscous gels were formed. The gels were then fired at 1073 K for 2 h in an air atmosphere to remove organic residues and produce fluffy black powders. Finally, the black powders obtained after grinding were cold-pressed into pellets with the pressure of 30 MPa, and then annealed at 1473 K for 24 h. The phase characterization of the polycrystalline RE 2 NiTiO 6 (RE = Gd, Tb and Ho) compounds were identified by the Rigaku x-ray diffraction technique (SmartLab-9 KW diffractometer). The surface morphology and chemical composition were investigated by using the field emission scanning electron microscope (FESEM, JEOL-JSM5800) and the attached energy dispersive X-ray spectroscopy (EDS). DC-susceptibility measurements of the RE 2 NiTiO 6 (RE = Gd, Tb and Ho) compounds were conducted by the magnetic properties measurement system (MPMS, QD).
The structural optimizations, electronic and magnetic properties calculations were determined based on the projector augmented-wave (PAW) method within the DFT calculation by using the Vienna ab initio simulation package code [40,41]. The spin-polarized generalized gradient approximation (GGA) was used to describe the exchange-correlation effects, and combined with both the GGA + U (Hubbard potential) and SOC to optimize the on-site Coulomb repulsion of localized RE-f electrons and determine the magnetic anisotropy, respectively [42,43]. The value of U eff with 3.4 eV has been set for Ni 2+ ion according to the relation U eff = U−J, where U and J are Coulomb and Hund's exchange parameters, respectively. The PAW method was used to resolve the electron-core interaction and the valence electron contributions for Gd, Tb, Ho, Ni, Ti and O were generated as [5s 2 5p 6 4f 7 5d 1 6s 2 ], [5s 2 5p 6 4f 9 5d 0 6s 2 ], [5s 2 5p 6 4f 10 5d 0 6s 2 ], [3p 6 3d 8 4s 2 ], [3p 6 3d 2 4s 2 ] and [2s 2 2p 4 ], respectively [44,45]. The kinetic energy cutoff was set at 600 eV to expansion the electronic wave functions. To optimize the structure, the conjugate gradient algorithm was used to completely relax the lattice constant and atomic position when the Hellman-Feynman forces converge to less than 0.01 eV·Å −1 . The Brillouin zone was sampled using k-point mesh of 9 × 9 × 7 under the Monkhorst-Pack scheme, which can improve the accuracy of the density of states (DOS) and SOC calculations.

Results and discussion
Figures 1(a)-(c) illustrate the obtained XRD patterns at room temperature and the Rietveld refinement results by aid of the FULLPROF software of the RE 2 NiTiO 6 (RE = Gd, Tb and Ho) compounds. The present RE 2 NiTiO 6 compounds are crystalized in the monoclinic structure with B-site ordered DP structure (P2 1 /n space group, No. 14). In the Tb 2 NiTiO 6 and Ho 2 NiTiO 6 compounds, small amounts of Tb 4 O 7 and Ho 2 Ti 2 O 7 impurity phases were detected around 29 • and 30.5 • (the symbols '·'and '♢'), and the corresponding weight ratios were determined to be 1.83 and 3.25 wt%, respectively [46,47]. The Rietveld indices were calculated, and the values of the refinement factors R p , R wp , R exp and χ 2 are all lower than 10% (as listed in table 1), which verifies the reliability of refinements. A schematic presentation of the crystal structure of the Gd 2 NiTiO 6 compound along the b axis is illustrated in figures 2(a)-(d) with the environments of metal atom in RE 2 NiTiO 6 compounds. The formation of the Gd 2 NiTiO 6 compound superstructure makes the alternating distribution of the Ni located on the 2c and Ti on the 2d Wyckoff positions, which are surrounded by six O (4e) atoms to establish NiO 6 and TiO 6 octahedrons, respectively. Each TiO 6 octahedron and the adjacent NiO 6 octahedron share an O atom in the form of alternating z-shape chains along the a-axis. In parallel, Gd atoms are located on the 4e Wyckoff position, which not only occupy the cavities formed by co-point NiO 6 and TiO 6 octahedrons, but also superpose alternately with Ni/Ti atomic layers along the c-axis. In order to further distinguish the changes in crystal structure caused by different RE 3+ ions, the refined lattice constants       9.87 and 10.21 µ B / f.u. for the Gd 2 NiTiO 6 , Tb 2 NiTiO 6 and Ho 2 NiTiO 6 compounds, respectively. In the case of Gd 2 NiTiO 6 compound, the value of M sat approximates to the sum of two isolated Gd 3+ ions and one Ni 2+ ion. In contrast, the values of M sat deviate from the individual magnetic ions for the Tb 2 NiTiO 6 and Ho 2 NiTiO 6 compounds, which may be due to the non-negligible magnetic anisotropy [48,49]. The temperature dependent magnetic entropy change (∆S M ) curve provides crucial information about the present RE 2 NiTiO 6 series compounds, which can not only verify whether they are suitable for the application of MR technology, but also further judge their MPTs type. The ∆S M is given by the following formula based on thermodynamic theory [50]: From the well measured M(µ 0 H) curve, the ∆S M can be approximately evaluated by the following expression: Here, M i and M i+1 can be obtained by the magnetization at the corresponding T i and T i+1 when a certain µ 0 H is fixed. According to equation (2) It can be found from the normalization ∆S ′ (θ) curves that the right part can converge to one single curve when the present RE 2 NiTiO 6 compounds take T M as the symmetry point, which indicates that they have the characteristics of SO-MPTs around T M . Since the temperatures of the present RE 2 NiTiO 6 compounds below T M are close to the absolute zero, the left part of the normalization ∆S ′ (θ) curves do not in accordance with the scaling relations, so that it is difficult to confirm the type of MPT. Accordingly, a novel criterion for the relationship between MCE and the exponent n proposed by Law et al [53,54] was used for verification research, which can be expressed as following formula:

Conclusions
To conclude, we have successfully fabricated the polycrystalline RE 2 NiTiO 6 (RE = Gd, Tb and Ho) DP compounds and their crystallographic structures, electronic structures, magnetic properties and MCE were investigated in combination with experiment and theory. All the RE 2 NiTiO 6 compounds are confirmed to crystallize in monoclinic structure with P2 1 /n space group by XRD refinements.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).