Magnetic phase transition and continuous spin switching in a high-entropy orthoferrite single crystal

Abstract

Rare-earth orthoferrite REFeO₃ (where RE is a rare-earth ion) is gaining interest. We created a high-entropy orthoferrite (Tm_0.2Nd_0.2Dy_0.2Y_0.2Yb_0.2)FeO₃ (HEOR) by doping five RE ions in equimolar ratios and grew the single crystal by optical floating zone method. It strongly tends to form a single-phase structure stabilized by high configurational entropy. In the low-temperature region (11.6‒ 14.4 K), the spin reorientation transition (SRT) of Γ₂ (F_x, C_y, G_z)‒Γ₂₄‒Γ₄ (G_x, A_y, F_z) occurs. The weak ferromagnetic (FM) moment, which comes from the Fe sublattices distortion, rotates from the a- to c-axis. The two-step dynamic processes (Γ₂‒Γ₂₄‒Γ₄) are identified by AC susceptibility measurements. SRT in HEOR can be tuned in the range of 50‒60000 Oe, which is an order of magnitude larger than that of orthoferrites in the peer system, making it a candidate for high-field spin sensing. Typical spin-switching (SSW) and continuous spin-switching (CSSW) effects occur under low magnetic fields due to the strong interactions between RE‒Fe sublattices. The CSSW effect is tunable between 20‒50 Oe, and hence, HEOR potentially can be applied to spin modulation devices. Furthermore, because of the strong anisotropy of magnetic entropy change (-\mathrm{\Delta }{S}_{\text{m}}) and refrigeration capacity (RC) based on its high configurational entropy, HEOR is expected to provide a novel approach for refrigeration by altering the orientations of the crystallographic axes (anisotropic configurational entropy).

Graphical abstract

Keywords

high-entropy oxide / rare-earth orthoferrite / spin reorientation transition / spin switching / magnetocaloric effect

1 Introduction

There are plenty of magnetic properties caused by specific crystal and magnetic structures [1, 2] in rare-earth orthoferrite REFeO₃ (where RE is a rare-earth element). REFeO₃ usually belongs to the orthorhombic system and has a distorted perovskite structure with the Pbnm space group [3]. The tolerance factor τ implies the degree of distortion:

(1)\tau = {\displaystyle \frac{R_{RE}+R_{\mathrm{O}}}{\sqrt{R_{\mathrm{F}\mathrm{e}}+R_{\mathrm{O}}}}} ,

where R_RE, R_Fe, and R_O represent the ionic radii of RE, Fe, and O sites [4]. Since the majority of RE and Fe ions are magnetic, there are three interactions between RE and Fe sublattices: RE‒RE, RE‒Fe, and Fe‒Fe interactions [5, 6]. At the Néel temperature T_N1 (650‒750 K), Fe‒Fe interactions cause the Fe sublattices’ transition from a canted antiferromagnetic (AFM) to a paramagnetic (PM) state. The canted AFM state refers to the non-strictly antiparallel alignment of Fe ion moment caused by the Dzyaloshinsky−Moriya (D−M) interaction [5, 7]. Thus, there is a weak ferromagnetic (FM) moment along the easy-axis in orthoferrites. The REFeO₃ unit cell contains 4 Fe ions, each with a magnetic moment of m₁, m₂, m₃, and m₄, respectively. Therefore, the weak FM moment (F) and A-, C- and G-type AFM moment can be expressed as

(2)\begin{array}{rl}& F=m_1+m_2+m_3+m_4,A=m_1-m_2-m_3+m_4,\\ & C=m_1+m_2-m_3-m_4,G=m_1-m_2+m_3-m_4.\end{array}

Using Bertaut’s notation, the configuration and the net moment associated with it are identified as Γ₁ (A_x, G_y, C_z), Γ₂ (F_x, C_y, G_z), Γ₄ (G_x, A_y, F_z) [8, 9]. The rotation of the Fe sublattices net moment from one axis of symmetry to another is known as spin reorientation transition (SRT) [10, 11]. Typically, SRTs are classified into two types upon cooling: Γ₄‒Γ₂ [12–16] and Γ₄‒Γ₁ [17,18]. The magnetic ordering temperature of RE sublattices T_N2 is generally lower, at 2‒10 K. Yet, some of the RE sublattices will be magnetized by the molecular field of ordered Fe sublattices above T_N2, resulting in a net moment. Because of the RE−Fe interactions, magnetic sublattices may undergo a spin flip called the spin-switching (SSW) effect. The type-I SSW effect occurs when RE and Fe sublattices spin flip simultaneously [19–21], while the type-II SSW occurs if only the RE sublattice spin flip [15, 18].

REFeO₃ has lately attracted interest as a novel series of materials of magnetocaloric effect (MCE) [22–24]. The temperature decreases when a magnet is magnetized by an external field through the adiabatic process [25]. MCE-based magnetic refrigeration can replace conventional gas compression or expansion method. And, magnetocrystalline anisotropy has been reported to be directly applicable to refrigeration in REFeO₃, REMnO₃, and REMn₂O₅ [22, 26, 27]. High-entropy alloy (HEA) has drawn increasing attention since the first proposal by Yeh et al. in 2004 [28]. And the high-entropy oxide A_xB_yO_z (HEO) developed from HEA provides ideas and guidance for the development of new material systems [29–31]. The definition is a single-phase oxide solid solution containing five or more elements in an equal or close to equal atomic ratio at A or B site, and the term “entropy” refers to the mixing entropy. The configurational entropy of HEO can be computed using the formula (3) and if the contribution of particles at B and O sites to the configurational entropy is ignored, it can be simplified to the formula (4) [32]:

(3)\begin{array}{rl}{S}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{g}}=& -R[x{\left(\sum _{a=1}^M{x}_a\mathrm{l}\mathrm{n}{x}_a\right)}_{a\text{-}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e}}+y{\left(\sum _{b=1}^M{y}_b\mathrm{l}\mathrm{n}{y}_b\right)}_{b\text{-}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e}}\\ & +z{\left(\sum _{c=1}^M{z}_c\mathrm{l}\mathrm{n}{z}_c\right)}_{c\text{-}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e}}],\end{array}

(4)S_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{g}}=-R\left[x{\left({\displaystyle \sum _{a=1}^M{x}_a\mathrm{l}\mathrm{n}{x}_a}\right)}_{a\text{-}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e}}\right],

where x_a, x_b, x_c is the mole fraction of particles at A, B, and C sites, and R is the gas constant [the value is 8.314 J/(mol·K)]. The configurational entropy of a multi-component system is higher when the amount of moles of each cation is identical. When the number of components N = 5 and the moles of each component are equal, S_config = 1.61 R [29]. The large configurational entropy of HEO lowers the free energy to increase system stability.

We combined the concept of orthoferrite REFeO₃ and HEO to create a high-entropy orthoferrite (Tm_0.2Nd_0.2Dy_0.2Y_0.2Yb_0.2)FeO₃ (HEOR). Intriguing magnetic characteristics are obtained by the high-entropy design. The tunable SRT occurs, proving that the interactions of Fe‒Fe sublattices can be impacted by both temperature and magnetic field. The typical and tunable continuous SSW effects indicate that the RE‒Fe interactions can also be affected by physical fields. By measuring AC susceptibility, the dynamic process of the SRT is determined. Fe sublattices undergo two-step transitions from Γ₂ to Γ₂₄ and then to Γ₄. Also, HEOR has a considerable magnetic entropy anisotropy and an excellent magnetic refrigeration capacity based on the high configurational entropy. So, it can be used for spintronic and magnetic refrigeration applications.

2 Experimental details

HEOR single crystal with high quality was grown by the optical floating zone method (see Appendix A). A powder X-ray diffraction (XRD) pattern was collected on a diffractometer with monochromatic copper K_α radiation (Bruker D2 PHASER) to examine the phase purity. Crystallographic orientations were achieved using a back reflection Laue X-ray diffractometer with a tungsten target (Try-SE. Co., Ltd.). The crystallographic orientations were confirmed by XRD after cutting it into a cube. The high-resolution energy-dispersive-spectroscopy (EDS) mapping of RE elements was performed by field emission scanning electron microscopy (SEM) (Hitachi FlexSEM1000). Magnetization was measured utilizing a Physical Property Measurement System (PPMS-14T, Quantum Design Inc.) with a Vibrating Sample Magnetometer (VSM) option. The temperature dependences of the magnetization were obtained in the zero-field-cooling (ZFC), field-cooled-cooling (FCC), as well as field-cooled-warming (FCW) modes.

For X-ray photoelectron spectroscopy (XPS) experiments the HEOR sample was mounted on Mo sample holders and then were annealed under ultra-high vacuum (UHV) conditions at 600 °C for 30 min and sputtered by using Ar⁺ for 15 mins (under 1.5 × 10⁻⁵ mbar, 1.5 keV, and 10 mA conditions). Temperature of the sample was measured using calibrated pyrometer. Laboratory-based XPS experiments were performed in UHV station installed at Shanghai University and consisting of preparation and analysis chambers with a base pressure better than 1 × 10⁻¹⁰ mbar (SPECS Surface Nano Analysis GmbH). XPS spectra were measured using a monochromatized Al Kα (hν = 1486.6 eV) X-ray source and SPECS PHOIBOS 150 hemispherical analyzer combined with a 2D-CMOS detector.

3 Results and discussion

3.1 Structural characterization

The Laue back reflection XRD was performed to determine the crystallographic axes. The distinct Laue diffraction patterns demonstrate the high quality of HEOR as illustrated in Fig.1(a)‒(c). XRD was conducted on a slice of crystal face to confirm the crystallographic orientation found in the Laue photograph. The XRD patterns with θ‒2θ scanning of the cutting plane are displayed in Fig.1(d)‒(f). The peaks can be donated by (h00), (0k0), or (00l) (h, k = 2, 4, and l = 2, 4, 6). Thus, the cut plane was precisely perpendicular to the a-, b-, and c-axes, respectively, according to both XRD and Laue photography. The powder XRD spectrum [see Fig.1(g)] with no impurity or orientation faults indicates the high quality and high homogeneity degree of the HEOR single crystal. The lattice parameters a = 5.3030 Å, b = 5.5917 Å, and c = 7.6310 Å are obtained from Rietveld refinement. The lattice parameters and Fe−O bonding lengths are also obtained and shown in Tab.1. The crystal structure was created using Vesta software, as shown in Fig.1(h), and it features a distorted perovskite structure with a space group of Pbnm.

Survey XPS spectrum of the HEOR sample is presented in Fig.2, the contaminated carbon and adsorbed oxygen were removed after the annealing and Ar⁺ sputtering treatment, indicating the presence of Tm, Nd, Dy, Y, Yb, Fe, and O elements. The peak located at 530.3 eV is assigned to the O 1s, 709 and 721.5 eV are corresponding to Fe 2p, 124.7 and 178 eV correspond to Tm 4d, 984.5 and 1006.5 eV to Nd 3d, 1299.0 and 1336.5 eV to Dy 3d, 158.9 and 190.8 eV to Y 4d, and 186.6 eV to Yb 4d. We quantitatively analyzed the elements of the full spectrum with atomic percentages of 60.350% (O), 20.111% (Fe), 3.931% (Tm), 3.937% (Nd), 3.963% (Dy), 3.908% (Y), and 3.900% (Yb). The atomic ratio of the RE site elements Tm:Nd:Dy:Y:Yb is 1:1.00:1.01:0.99:0.99, which fits the definition of HEO. The result of EDS mappings (Fig. A2) is consistent with the XPS spectrum and proves the isoproportionality of the HEOR RE-site elements. The atomic ratio of the RE, Fe, and O sites is 1:1.03:3.08, indicating that HEOR composition is in accordance with the REFeO₃ definition of 1:1:3.

3.2 Magnetic characterization

Under a magnetic field of 50 Oe, the M−T curves were measured (Fig.3). The strong magnetic anisotropy originating from Fe and RE sublattices spin−orbit coupling is one of the key characteristics of HEOR, which leads to strikingly distinct temperature dependences of M_a, M_b, and M_c. In ZFC mode, the initial magnetization along the a-axis is 1.86 emu/g and that along the b- and c-axes are approximately zero at 2 K, indicating that the Fe sublattices are in the spin configuration Γ₂ (F_x, C_y, G_z). The magnetic characteristics are dominated by both RE and Fe sublattices in the low-temperature region. With the temperature increasing, the interactions weaken, and the total magnetization increases. As the temperature rises from T_SR1 = 11.6 K to T_SR2 = 14.4 K (T_SR1 and T_SR2 are the starting and ending temperatures of SRT), the magnetization along the a-axis declines to zero, while that along the c-axis climbs to 2.77 emu/g synchronously. The magnetization along the b-axis remained negligible throughout the test temperature range. Therefore, the net moment rotates from the a- to c-axis, and correspondingly, the spin configuration of HEOR changes from Γ₂ (F_x, C_y, G_z) state to Γ₄ (G_x, A_y, F_z). This is consistent with the parent phase YbFeO₃ [15], TmFeO₃ [33], and NdFeO₃ [21], but inconsistent with going to DyFeO₃ [18], due to the different electron arrangements of the various RE ions, which are the effect of the interactions between RE-4f and Fe-3d electrons. Besides, the magnitude of magnetization is generally unchanged before and after the SRT in the REFeO₃ family. However, the magnetization of 1.86 emu/g at T_SR1 is much smaller than that of 2.77 emu/g at T_SR2 in HEOR, due to the rearrangement of RE sublattices moment (from antiparallel to parallel coupling with Fe ions). The flip occurs in the SRT, resulting in the change of the net moment. A similar phenomenon was reported in TmFeO₃ [33], in which the SRT depends strongly on the 4f electrons magnetic anisotropy and an AFM state of Tm moment is observed below T_SR1.

The shifting trend of magnetization with temperature in the FCC mode between 2 K and 11 K is opposite to the M‒T curves in the ZFC and FCW modes along the a-axis. As the temperature declines, the magnetization progressively rises until it reaches a peak at 2.7 K, after which it gradually falls. The opposite trend in the heating and cooling process along the same crystal axis has been found in DyFeO₃ [18]. Similarly, in HEOR, influenced by the Fe sublattice molecular field, some RE sublattices align their moments parallel to Fe during the cooling process until RE sublattices undergo an AFM transition at T_N2 = 2.7 K, and then the magnetization lowers. Some RE sublattices’ moments are antiparallel to that of Fe sublattices in ZFC and FCW modes, resulting in a decrease in magnetization. As temperature increases, the interactions between RE sublattices weaken, and that between Fe sublattices strengthen, resulting in the increasing of magnetization.

As shown in Fig.4(a), we subsequently investigated the M−T curves in ZFC mode under varied applied magnetic fields along the c-axis. The temperature dependence of magnetic field (H−T) phase diagram obtained from M−T curves clearly emphasizes the magnetic behavior, as shown in Fig.5. With an increasing of magnetic field, T_SR1 and T_SR2 are lowering and the temperature region broadens, demonstrating that SRT can be induced not only by temperature but also by a magnetic field. At 50 Oe, the net moment in c-axis is negligible when T < T_SR1, indicating that the Fe sublattice is completely in the Γ₂ state. The initial magnetization strength increases with the applied magnetic field, indicating that the SRT is gradually suppressed with the magnetic field, and a part of the net moment of the Fe sublattice is in the c-axis at T < T_SR1, leading to an incomplete antiferromagnetic state in the c-axis, and that the spin configuration is not a complete Γ₂ state either. Whereas, for magnetic fields up to 40000 Oe and above, the Γ₂ state of the Fe sublattice has disappeared and only the Γ₂₄ to Γ₄ transition exists. Compared to other orthoferrites in the RFeO₃ system, the SRT modulation range of HEOR is an order of magnitude larger, which suggests that it is promising for applications in high-field magnetic sensing.

When it turns to low magnetic fields in FCC mode, there are interesting SSW effects as shown in Fig.4(b). SSW effect does not occur at 20 Oe, because the system is in a metastable state. When the magnetic field reaches 25 Oe, the typical type-II SSW effect occurs at 86.4 K. Due to the interactions between RE-4f and Fe-3d electrons, RE sublattices spin flip from parallel to antiparallel with Fe sublattices and magnetization drops from 2.0 to 1.4 emu/g. A similar phenomenon is reported in DyFeO₃ [18]. The typical SSW effect turns to the continuous spin-switching (CSSW) effect from 30 Oe. When the D−M interaction between RE and Fe sublattices is greater than the influence of the applied field, the net moment of RE ions will reverse and result in the SSW effect. It still causes a change in magnetization to reach a lower energy stable state, but a continuous jump rather than a sudden change of the typical SSW effect. Increasing the applied magnetic field from 30 to 45 Oe, the temperature that the CSSW effect occurs (T_CSSW) decreases as shown in the inset of Fig.5, so the CSSW effect can be modulated by applied magnetic fields. As to 50 Oe, the SSW effect occurs in the SRT process as mentioned above, so there is no jump on the M‒T curve.

3.3 AC magnetic measurements

With measurements of AC susceptibility at various frequencies, the dynamic process of SRT in HEOR was systematically investigated. The oscillating component of magnetic field H(t)=H_{\mathrm{A}\mathrm{C}}\mathrm{c}\mathrm{o}\mathrm{s}\omega t is applied, hence, the magnetization has the oscillating component M(t)=M_{\mathrm{A}\mathrm{C}}\mathrm{c}\mathrm{o}\mathrm{s}(\omega t+\phi ). And the susceptibility is defined as

(5){\text{χ}}_{\mathrm{A}\mathrm{C}}=M_{\mathrm{A}\mathrm{C}}/H_{\mathrm{A}\mathrm{C}}=\text{χ}\text{'}-\mathrm{i}\text{χ}\text{''},

where χ' denotes the real component correlated with the fluctuation in sample magnetization, and χ'' refers to the imaginary component and represents the absorption of the applied alternating magnetic field energy. We applied an AC magnetic field of 1 Oe along the c-axis without a DC magnetic field. χ'−T and χ''−T curves are shown in Fig.6(a) and (d). χ' and χ'' show no frequency dispersion below T_SR1 and above T_SR2, indicating that the spin relaxation time (τ) is too short to be observed. At various frequencies, a peak appears at around T_SR1 of 11.7 K [see Fig.6(b)] because the configuration of Fe sublattice changes from Γ₂ to Γ₂₄, and a step appears at around T_SR2 of 14.2 K [see Fig.6(c)], corresponding to the transition from Γ₂₄ to Γ₄. The phenomenon indicates two-step dynamic processes of Fe sublattices spin rotating from the a- to c-axis. A similar phenomenon has been reported in ErFeO₃ [34], TmFeO₃ [35], and NdFeO₃ [36], but the change in those orthoferrites is irregular and unstable. The larger configurational entropy of HEOR makes the Gibbs free energy lower. The design of HEOR can stabilize the structure and make the dynamic process clearer. As the increase of frequency, the position of the peak and step of χ' remain unchanged. The independence shows the long-range order of HEOR. However, the peak value decreases with increasing frequency as shown in Fig.6(b), because of the decrease in order degree. In Fig.6(d) and (e), the position of the peak of χ'' also remains unchanged but the value is not monotonically decreasing. As the test frequency increases, it first increases and then decreases. The peak at 333 Hz indicates the greatest magnetic energy absorption.

3.4 Magnetocaloric effect

Calculate \mathrm{\Delta }{S}_{\text{m}} of the a-, b-, and c-axes according to Maxwell’s equations:

(6)\mathrm{\Delta }{S}_{\mathrm{m}}={\displaystyle {\int }_0^H{\displaystyle \frac{\mathrm{\partial }M}{\mathrm{\partial }T}}\mathrm{d}H.}

Since the magnetization measurement is performed between discrete fields and temperatures, the \mathrm{\Delta }{S}_{\text{m}} is calculated numerically by means of the expression:

(7)\mathrm{\Delta }{S}_{\mathrm{m}}={{\displaystyle \sum }}_i {\displaystyle \frac{M_{i+1}-M_i}{T_{i+1}-T_i}}\mathrm{\Delta }{H}_i,

where M_i and M_i+1 are the magnetic moments at T_i and T_i+1, respectively, and ΔH_i is the little variation in the magnetic field. The temperature dependences of the magnetic entropy changes are depicted in Fig.7(a)‒(c). At 7 K and 70 kOe, the maximum of -\mathrm{\Delta }{S}_{\text{m}} in a-axis is 8.11 J/(kg·K), while that in b- and c-axes are 6.99 J/(kg·K) and 2.32 J/(kg·K), respectively. The difference between a- and c-axes gets a maximum of 7.11 J/(kg·K) at 7 K and 50 kOe. The magnetic entropy values for the a- and b-axes are much larger than that for the c-axis, indicating that HEOR is easily magnetized in the ab plane. The refrigeration capacity (RC) is calculated to determine its anisotropy, as shown in Fig.7(d). Using such a magnetic anisotropy for refrigeration instead of traditional methods eliminates the mechanical loss of repeating the cold end and the heat dissipation end. Using the magnetic refrigeration formula (8) to calculate the magnetic refrigeration capacity (RC) of the three crystal axes,

(8)RC =-{\displaystyle {\int }_{T_1}^{T_2}\mathrm{\Delta }S(T)\mathrm{d}T,}

where T₁ and T₂ are the lower and higher temperatures at half the maximum of the entropy change [37]. As shown in Fig.7(d), RC reaches the maximum: 70.43 J/kg on the a-axis, 66.35 J/kg on the b-axis, and 16.27 J/kg on the c-axis at 70 kOe. Thus, the strong magnetic anisotropy makes HEOR an excellent refrigeration material.

4 Conclusion

In conclusion, we have grown the HEOR single crystal with high quality by the optical floating zone method and have studied its magnetic properties based on the high configurational entropy. Due to the rotation of the Fe ions moment, the SRT from Γ₂ to Γ₄ occurs, and it can be easily modulated by temperature and a broad applied magnetic field. Combined with the tunable SSW and CSSW, HEOR could be a potential material for magnetic sensing and/or spin switching applications. The AC susceptibility measurements identify the two-step SRT dynamic processes of Γ₂‒Γ₂₄‒Γ₄ and the long-range order. The magnetocaloric results show high anisotropy. At 50 kOe and 7 K, -\mathrm{\Delta }{S}_{\text{m}} reaches 8.12 J/(kg·K) along a-axis but only 0.99 J/(kg·K) along c-axis. The large difference of -\mathrm{\Delta }{S}_{\text{m}} in different crystallographic axes makes HEOR to be a good candidate for new magnetic refrigeration material at low temperatures.

References

[1] S. E. Hahn, A. A. Podlesnyak, G. Ehlers, G. E. Granroth, R. S. Fishman, A. I. Kolesnikov, E. Pomjakushina, K. Conder. Inelastic neutron scattering studies of YFeO₃. Phys. Rev. B, 2014, 89(1): 014420

[2] W. C. Fan, H. Y. Chen, G. Zhao, X. X. Ma, R. Chakaravarthy, B. J. Kang, W. L. Lu, W. Ren, J. C. Zhang, S. X. Cao. Thermal control magnetic switching dominated by spin reorientation transition in Mn-doped PrFeO₃ single crystals. Front. Phys., 2022, 17(3): 33504

[3] R. L. White. Review of recent work on the magnetic and spectroscopic properties of the rare‐earth orthoferrites. J. Appl. Phys., 1969, 40(3): 1061

[4] V. M. Goldschmidt. Die Gesetze der Krystallochemie. Naturwissenschaften, 1926, 14(21): 477

[5] L. Shekhtman, O. Entin-Wohlman, A. Aharony. Moriya’s anisotropic superexchange interaction, frustration, and Dzyaloshinsky’s weak ferromagnetism. Phys. Rev. Lett., 1992, 69(5): 836

[6] D. Treves. Magnetic studies of some orthoferrites. Phys. Rev., 1962, 125(6): 1843

[7] I.Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4(4), 241 (1958)

[8] T. Yamaguchi, K. Tsushima. Magnetic symmetry of rare-earth orthochromites and orthoferrites. Phys. Rev. B, 1973, 8(11): 5187

[9] E.F. Bertaut, Spin configurations of ionic structures: Theory and practice, in: Spin Arrangements and Crystal Structure, Domains, and Micromagnetics, edited by G. T. Rado and H. Suhl, Elsevier, 1963, page 149

[10] D. Treves. Studies on orthoferrites at the Weizmann institute of science. J. Appl. Phys., 1965, 36(3): 1033

[11] T. Yamaguchi. Theory of spin reorientation in rare-earth orthochromites and orthoferrites. J. Phys. Chem. Solids, 1974, 35(4): 479

[12] W. Y. Zhao, S. X. Cao, R. X. Huang, Y. M. Cao, K. Xu, B. J. Kang, J. C. Zhang, W. Ren. Spin reorientation transition in dysprosium-samarium orthoferrite single crystals. Phys. Rev. B, 2015, 91(10): 104425

[13] Ya. B. Bazaliy, L. T. Tsymbal, G. N. Kakazei, V. I. Kamenev, P. E. Wigen. Measurements of spin reorientation in YbFeO₃ and comparison with modified mean-field theory. Phys. Rev. B, 2005, 72(17): 174403

[14] X. Y. Zhao, K. L. Zhang, X. M. Liu, B. Wang, K. Xu, S. X. Cao, A. H. Wu, L. B. Su, G. H. Ma. Spin reorientation transition in Sm_0.5Tb_0.5FeO₃ orthoferrite single crystal. AIP Adv., 2016, 6(1): 015201

[15] X. X. Ma, N. Yuan, X. Luo, Y. K. Chen, B. J. Kang, W. Ren, J. C. Zhang, S. X. Cao. Field tunable spin switching in perovskite YbFeO₃ single crystal. Mater. Today Commun., 2021, 27: 102438

[16] J. S. Zhang, W. Y. Zhao, Z. J. Feng, J. Y. Ge, J. C. Zhang, S. X. Cao. Spin reorientation and rare earth antiferromagnetic transition in single crystal Sm_0.15Dy_0.85FeO₃. J. Alloys Compd., 2019, 804: 396

[17] L. Hou, L. Shi, J. Y. Zhao, S. Y. Pan, Y. Xin, X. Y. Yuan. Spin-reorientation transition driven by double exchange in CeFeO₃ ceramics. J. Phys. Chem. C, 2020, 124(28): 15399

[18] S. X. Cao, L. Chen, W. Y. Zhao, K. Xu, G. H. Wang, Y. L. Yang, B. J. Kang, H. J. Zhao, P. Chen, A. Stroppa, R. H. Zheng, J. C. Zhang, W. Ren, J. Íñiguez, L. Bellaiche. Tuning the weak ferromagnetic states in dysprosium orthoferrite. Sci. Rep., 2016, 6(1): 37529

[19] S. X. Cao, H. Z. Zhao, B. J. Kang, J. C. Zhang, W. Ren. Temperature induced spin switching in SmFeO₃ single crystal. Sci. Rep., 2014, 4(1): 5960

[20] X. X. Zhang, Z. C. Xia, Y. J. Ke, X. Q. Zhang, Z. H. Cheng, Z. W. Ouyang, J. F. Wang, S. Huang, F. Yang, Y. J. Song, G. L. Xiao, H. Deng, D. Q. Jiang. Magnetic behavior and complete high-field magnetic phase diagram of the orthoferrite ErFeO₃. Phys. Rev. B, 2019, 100(5): 054418

[21] S. J. Yuan, W. Ren, F. Hong, Y. B. Wang, J. C. Zhang, L. Bellaiche, S. X. Cao, G. Cao. Spin switching and magnetization reversal in single-crystal NdFeO₃. Phys. Rev. B, 2013, 87(18): 184405

[22] M. Das, S. Roy, P. Mandal. Giant reversible magnetocaloric effect in a multiferroic GdFeO₃ single crystal. Phys. Rev. B, 2017, 96(17): 174405

[23] R. X. Huang, S. X. Cao, W. Ren, S. Zhan, B. J. Kang, J. C. Zhang. Large rotating field entropy change in ErFeO₃ single crystal with angular distribution contribution. Appl. Phys. Lett., 2013, 103(16): 162412

[24] S. Mahana, U. Manju, D. Topwal. Giant magnetocaloric effect in GdAlO₃ and a comparative study with GdMnO₃. J. Phys. D Appl. Phys., 2017, 50(3): 035002

[25] V.K. PecharskyJrGschneidner, Magnetocaloric effect and magnetic refrigeration, J. Magn. Magn. Mater. 200(1‒3), 44 (1999)

[26] M. J. Shao, S. X. Cao, S. J. Yuan, J. C. Shang, B. J. Kang, B. Lu, J. C. Zhang. Large magnetocaloric effect induced by intrinsic structural transition in Dy_1−xHo_xMnO₃. Appl. Phys. Lett., 2012, 100(22): 222404

[27] Y. J. Ke, X. Q. Zhang, H. Ge, Y. Ma, Z. H. Cheng. Low field induced giant anisotropic magnetocaloric effect in DyFeO₃ single crystal. Chin. Phys. B, 2015, 24(3): 037501

[28] J. W. Yeh, S. K. Chen, S. J. Lin, J. Y. Gan, T. S. Chin, T. T. Shun, C. H. Tsau, S. Y. Chang. Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. Adv. Eng. Mater., 2004, 6(5): 299

[29] C. M. Rost, E. Sachet, T. Borman, A. Moballegh, E. C. Dickey, D. Hou, J. L. Jones, S. Curtarolo, J. P. Maria. Entropy-stabilized oxides. Nat. Commun., 2015, 6(1): 8485

[30] S.C. JiangT. HuJ.GildN.X. ZhouJ.Nie M.D. QinT. HarringtonK.VecchioJ.Luo, A new class of high-entropy perovskite oxides, Scr. Mater. 142, 116 (2018)

[31] S. Y. Zhou, Y. P. Pu, Q. W. Zhang, R. K. Shi, X. Guo, W. Wang, J. M. Ji, T. C. Wei, T. Ouyang. Microstructure and dielectric properties of high entropy Ba(Zr_0.2Ti_0.2Sn_0.2Hf_0.2Me_0.2)O₃ perovskite oxides. Ceram. Int., 2020, 46(6): 7430

[32] A. Sarkar, B. Breitung, H. Hahn. High entropy oxides: The role of entropy, enthalpy and synergy. Scr. Mater., 2020, 187: 43

[33] U. Staub, L. Rettig, E. M. Bothschafter, Y. W. Windsor, M. Ramakrishnan, S. R. V. Avula, J. Dreiser, C. Piamonteze, V. Scagnoli, S. Mukherjee, C. Niedermayer, M. Medarde, E. Pomjakushina. Interplay of Fe and Tm moments through the spin-reorientation transition in TmFeO₃. Phys. Rev. B, 2017, 96(17): 174408

[34] H. Shen, Z. X. Cheng, F. Hong, J. Y. Xu, S. J. Yuan, S. X. Cao, X. L. Wang. Magnetic field induced discontinuous spin reorientation in ErFeO₃ single crystal. Appl. Phys. Lett., 2013, 103(19): 192404

[35] A.BombikA. W. Pacyna, AC susceptibility of TmFeO₃ single-crystal, J. Magn. Magn. Mater. 220(1), 18 (2000)

[36] G. B. Song, J. J. Jiang, B. J. Kang, J. C. Zhang, Z. X. Cheng, G. H. Ma, S. X. Cao. Spin reorientation transition process in single crystal NdFeO₃. Solid State Commun., 2015, 211: 47

[37] K. A. GschneidnerJr, V. K. Pecharsky, A. O. Tsokol. Recent developments in magnetocaloric materials. Rep. Prog. Phys., 2005, 68(6): 1479

[38] A. Arrott. Criterion for ferromagnetism from observations of magnetic isotherms. Phys. Rev., 1957, 108(6): 1394

[39] J. Inoue, M. Shimizu. First- and second-order magnetic phase transitions in (R-Y)Co₂ and R(Co-Al)₂ (R = heavy rare-earth element) compounds. J. Phys. F Met. Phys., 1988, 18(11): 2487

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