Anisotropic magnetic entropy change in RFeO3 single crystals(R = Tb, Tm, or Y)

Compared with traditional gas-compression/expansion refrigeration, magnetic refrigeration based on magnetocaloric effect (MCE) exhibits the advantages of high energy efficiency and environment friendliness. Here, we created large MCE in RFeO3 (R = Tb or Tm) single crystals by the magnetization vector rotation of single crystal with strong magnetocrystalline anisotropy (MCA), rather than merely via the order-disorder magnetic phase transition or magnetic structural transition. Owing to the difference in charge distribution of 4f-electrons between Tb3+  and Tm3+ ions, the rotating field entropy with different signs, −ΔSMR = 17.42 J/kg K, and –ΔSMR = −9.01 J/kg K are achieved at 9 K and 17 K for TbFeO3 and TmFeO3 single crystals from b axis to c axis, at 50 kOe, respectively. The finding of the large anisotropic MCE not only advances our understanding of the anisotropy of MCE, but also extends the application for single crystals to magnetic refrigeration.

Magnetocaloric effect (MCE), which describes the temperature change of magnetic materials in an adiabatic process caused by magnetic entropy change Δ S M under external magnetic field, has been extensively investigated. In comparison with traditional gas-compression/expansion refrigeration, magnetic refrigeration based on MCE exhibits the advantages of high energy efficiency and environment friendliness. The giant or very large magnetic entropy change was obtained in various kinds of magnetic materials, including Gd-based alloys Gd 5 (Si x Ge 1-x) 1,2 , Mn-based Ni-Mn-Ga(Sn) alloys 3,4 and MnFeP 0.45 As 0.55 5 , Fe-based LaFe 13-x (Si, Al) x 6,7 , as well as rare-earth perovskite-type manganites (La 1-x M x )MnO 3 (M = Ca, Sr, and Ba etc.) 8,9 . Although numerous studies on MCE have been concentrated on exploring new materials with giant MCE near room temperature for domestic applications, giant MCE in the low-temperature region from about 30 K down to sub-Kelvin temperatures is also essential for utilization in certain fields, such as liquid hydrogen economy and space application 10 .
The magnetic, barocaloric and electrocaloric effects can be tuned or created by element substitution 11 , pressure [12][13][14][15] , strain 16,17 , electric field 18,19 , or elastic force 20 . The giant magnetic entropy change in the vicinity of magnetic ordering temperature is usually accompanied by a field-induced or temperature-induced magnetic phase transition with the changes in either crystal symmetry or volume 21 . In addition to magnetic entropy change, mechanical properties and chemical stability are key issues for the practical use of magnetic refrigerator 22 . The material will definitely become very brittle and even break into smaller grains if its crystal symmetry or volume is changed very frequently, and consequently the corrosion resistance and the lifetime of a magnetic refrigerator will be deteriorated. Therefore, it is interesting to explore whether the giant MCE can be created by the magnetization vector rotation of single crystal with strong magnetocrystalline anisotropy (MCA), rather than merely via the order-disorder magnetic phase transition or magnetic structural transition.
Although the anisotropic MCE, which was discovered in Ni single crystal more than 70 years ago 23 , is lower than that from the paramagnetic-ferromagnetic phase transition, it should be large for materials with high values of derivatives of the MCA with respect to temperature [24][25][26][27][28][29][30][31][32][33][34][35] . Here, we explore the anisotropic magnetic entropy change of RFeO 3 single crystals with R = Tb, Tm or Y. The reasons for choosing RFeO 3 (R = Tb, Tm, or Y) single crystals are three-fold. Firstly, RFeO 3 show a complex magnetic transformation and spin-reorientation transitions 36 . The magnetoelectric properties and superfast optomagnetic effect of RFeO 3 single crystal have been extensively investigated 37,38 . Unfortunately, the effect of the complex magnetic transformation on MCE is not understood yet. Secondly, the magnetic moments of Tb 3+ ion and Tm 3+ ion are large, and we can achieve a larger magnetic entropy change in where R is the gas constant and J is the total angular momentum of the magnetic ion. Thirdly, the 4f shell of Tb 3+ , Tm 3+ and Y 3+ has an oblate, a prolate, and a spherical shape, respectively, a different anisotropy of MCE would be expected between the TbFeO 3 and TmFeO 3 single crystals on the basis of single-ion-anisotropy model 39 . The rotating field entropy with different signs, −Δ S M R = 17.42 J/kg K, and −Δ S M R = − 9.01 J/kg K are achieved at 9 K and 17 K for TbFeO 3 and TmFeO 3 single crystals from b axis to c axis, respectively. The finding not only advances our understanding of the MCE anisotropy in magnetic single crystals, but also opens a new arena for magnetic refrigerator by rotating its magnetization vector.
X-ray diffraction (XRD) patterns and back-reflection Laue XRD patterns demonstrate that RFeO 3 (R = Tb, Tm or Y) single crystals have an orthorhombically distorted pervoskite structure with Pbnm symmetry (not shown). Figure 1(a,b) display the zero-field-cooled (ZFC) and field-cooled (FC) thermal magnetization curves along a, c axes from 2 K to 300 K under a magnetic field of 100 Oe for TbFeO 3 and TmFeO 3 single crystals, respectively. The kink point at 3 K indicated by the arrows in inset of Fig. 1(a) corresponds to the ordering temperature of Tb 3+ moments (T N Tb ). From the inset thermal magnetization curves of a and c axes, two spin-reorientation transitions are observed in the temperature range from 8.5 K to 6 K and 3.5 K to 2.5 K, corresponding to the spin-reorientation of Fe 3+ moments from Γ 4 (G x ,A y ,F z ) configuration to Γ 2 (F x ,C y ,G z ) configuration, and then back to the high temperature configuration Γ 4 (G x ,A y ,F z ) 36,37,40 . From the thermal magnetization curves of a and c axes of TmFeO 3 single crystal shown in Fig. 1(b), a spin-reorientation transitions is observed in the temperature range from 85 K to 95 K, corresponding to the spin-reorientation of Fe 3+ moments rotate from Γ 4 (G x ,A y ,F z ) configuration to Γ 2 (F x ,C y ,G z ) configuration 36 . Figure 2(a-c) illustrate the isothermal magnetization curves along a, b and c axes of TbFeO 3 single crystal in the temperature range of 2-40 K with an interval of 2 K, respectively. The magnetization curves for these three directions are different either in shape or in magnetization values. Data for increasing and decreasing the magnetic field at 2 K to 10 K along all the three directions are given, for better viewing we enlarged the data along b axis in the inset , which demonstrates a little hysteresis loss in the cycling process. A spin-flip phenomenon can be observe along a, b and c axis of the TbFeO 3 single crystal at 2 K due to the antiferromagnetic interaction of Tb-Tb ions 40,41 . Form the data we can see that the easy magnetization direction (EMD) lies in ab plane for TbFeO 3 single crystal. The significant difference in the isothermal magnetization curves along a, b and c axis of TbFeO 3 single crystal implies that an anisotropic MCE can be expected.
At temperature T, the magnetic entropy change due to applied field H can be calculated from the isothermal curves by the Maxwell relation where the slope of two adjacent data points is approximatively used for the numerical calculation of the gradient of (∂M/∂T) H . By selecting Δ T = 1 K and Δ H = 2 kOe, the calculated −Δ S M vs temperature is shown in Fig. 2     The anisotropy of magnetic entropy change results from the MCA. In general, the overall MCA of RFeO 3 single crystal is the sum of R 3+ sublattice anisotropy and Fe 3+ sublattice one, as similar with RMnO 3 series 29 . In order to separate the individual contribution from R 3+ ion sublattice, we measured the magnetization curves and magnetic entropy change of YFeO 3 single crystal for comparison. Since Y ion has non-magnetic moments, and consequently makes no contribution to the overall MCA. Therefore, it affords a separate investigation of the Fe 3+ sublattice anisotropy. Isothermal magnetization curves along a, b and c axis of YFeO 3 single crystal are shown in Fig. 4(a-c), respectively. The magnetization curves indicate that the magnetic anisotropy among a, b and c axis is not significant. Furthermore, the magnetic entropy change of YFeO 3 are nearly zero (Fig. 4(d-f)), suggesting that the anisotropy of magnetic entropy change in TbFeO 3 and TmFeO 3 single crystals is arisen mainly from the contribution of Tb 3+ and Tm 3+ ions sublattice anisotropy.
In the first approximation, the MCA constant K 1,R can be described as 42 .
where α J is the second-order Stevens coefficient, and A 2 0 is the second-order crystalline electrical field (CEF) coefficient. < > r f 4 2 is the squared 4f shell radius. J R is the Hund's rules angular moment of R ion. Since the sign of A 2 0 for orthorhombically distorted pervoskite structure RFeO 3 (R = Tb, Tm or Y) single crystals is the same and negative 43 , the easy magnetization directions of these single crystals are governed by the sign of the second-order Stevens factor α J of rare earth ions. The signs of α J for Tb 3+ and Tm 3+ are negative and positive, respectively. Therefore, the MCA constants K 1,Tb < 0, and K 1,Tm > 0, suggesting that the easy magnetization direction of TbFeO 3 and TmFeO 3 single crystals aligns in ab plane and c axis, respectively. Similar results were also observed in DyFeO 3 and ErFeO 3 single crystals 33,34 .
The connection between anisotropic magnetic entropy change and magnetic anisotropy is evident from the field-dependence of −Δ S M for TbFeO 3 single crystal at 9 K and TmFeO 3 single crystal at 17 K along different axis ( Fig. 5(a,c)). For magnetic refrigeration application, not only a large entropy change value, but also a large refrigeration capacity (RC) is required. RC is defined as The rotating magnetic entropy change −∆S M R can be obtained by rotating the crystal from b to c axis and measuring the corresponding isothermal magnetization curves. Figure 6(a,b) indicate the representative isothermal magnetization curves at different angles for temperatures of 8 K and 10 K for TbFeO 3 single crystal and of 16 K and 18 K for TmFeO 3 single crystal, respectively. Taking b axis as the starting angle, we can get the rotating magnetic entropy change −Δ S M R as a function of angle by using Eq. (1). As is shown in Fig. 7(a,b), the largest values of − Δ S M R = 17.42 J/kg K can be achieved at temperature of 9 K for TbFeO 3 and −Δ S M R = − 9.01 J/kg K can be achieved at temperature of 17 K for TmFeO 3 both under a magnetic field of 50 kOe from b to c axis. Since RFeO 3 (R = Tb, Tm) single crystals exhibit almost magnetic isotropy in ab plane and a strong magnetocrystalline anisotropy between ab plane and c axis, Fig. 7(c-d) display the "expected" magnetic entropy change −Δ S M R . As proposed by Kuz'min and Tishin 24 , the large and reversible anisotropic magnetic entropy change with broad temperature span suggests that a promising candidate for new type magnetic refrigeration can be achieved by simply rotating the RFeO 3 (R = Tb, or Tm) single crystals or magnet.
In conclusion, we investigated the MCE of RFeO 3 single crystals among a, b and c axis. The large MCE with broad temperature span and little hysteresis loss is ideal for the application of magnetic refrigeration operated in a wide temperature window. The detailed analysis of magnetization data shows that both TbFeO 3 single crystal and TmFeO 3 single crystal exhibit a strong magnetocrystalline anisotropy between ab plane and c axis and almost magnetic isotropy in ab plane. Owing to the difference in charge distribution of 4f-elctrons between Tb 3+ and Tm 3+ ions, the rotating field entropy with different signs, −Δ S M R = 17.42 J/kg K, and −Δ S M R = − 9.01 J/ kg K are achieved at 9 K and 17 K for TbFeO 3 and TmFeO 3 single crystals from b axis to c axis, respectively. This discovery not only gives us a deeper insight into the understanding of the MCE anisotropy in spin canting anti-ferromagnetic single crystal, but also opens a new arena for rotary magnetic refrigerator by rotating its magnetization vector.  X-ray diffraction (XRD) patterns showed the prepared samples were single-phase with Pbnm crystallographic symmetry. The ceramics were compressed into rods under the hydrostatic pressure and sintered at 1400 °C for 48 hours. TbFeO 3 , TmFeO 3 and YFeO 3 single crystals were grown with four ellipsoidal mirrors (Crystal Systems Inc,  FZ-T-10000-H-VI-VP) by the floating zone method. X-ray diffraction (XRD) patterns were collected by Rigaku D/MAX 2400 x-ray diffractometer with Cu-Kα radiation (λ = 1.5406Å). Back-reflection Laue x-ray diffraction measurements were carried out to determine the crystallographic direction. Magnetization measurements were performed on commercial superconducting quantum interference device (SQUID) magnetometer (Quantum design MPMS-XL).