research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

IUCrJ
Volume 4| Part 5| September 2017| Pages 598-603
ISSN: 2052-2525

Spin-reorientation magnetic transitions in Mn-doped SmFeO3

aDepartment of Physics, International Center of Quantum and Molecular Structures and Materials Genome Institute, Shanghai University, Shanghai 200444, People's Republic of China, bHangzhou Key Laboratory of Quantum Matter, Department of Physics, Hangzhou Normal University, Hangzhou 310036, People's Republic of China, cCNR-SPIN, L'Aquila, Italy, and dShanghai Key Laboratory of High-Temperature Superconductors, Shanghai University, Shanghai 200444, People's Republic of China
*Correspondence e-mail: renwei@shu.edu.cn

Edited by Y. Murakami, KEK, Japan (Received 4 April 2017; accepted 29 May 2017; online 4 July 2017)

Spin reorientation is a magnetic phase transition in which rotation of the magnetization vector with respect to the crystallographic axes occurs upon a change in the temperature or magnetic field. For example, SmFeO3 shows a magnetization rotation from the c axis above 480 K to the a axis below 450 K, known as the Γ4Γ2 transition. This work reports the successful synthesis of the new single-crystal perovskite SmFe0.75Mn0.25O3 and finds interesting spin reorientations above and below room temperature. In addition to the spin reorientation of the Γ4Γ2 magnetic phase transition observed at around TSR2 = 382 K, a new spin reorientation, Γ2Γ1, was seen at around TSR1 = 212 K due to Mn doping, which could not be observed in the parent rare earth perovskite compound. This unexpected spin configuration has complete antiferromagnetic order without any canting-induced weak ferromagnetic moment, resulting in zero magnetization in the low-temperature regime. MT and MH measurements have been made to study the temperature and magnetic-field dependence of the observed spin reorientation transitions.

1. Introduction

The emerging demand for next-generation spintronic devices calls for more functional materials with outstanding properties. In this context, the RFeO3 (R = rare earth ion) oxide family with the Pbnm structure are promising candidates, in which not only the magnetic interactions between the 3d spins of the transition metals (Fe–Fe) but also those with the 4f moments of the rare earth ions (R–Fe) have important roles in their magnetic behaviour and magnetoelectric coupling (Zvezdin & Mukhin, 2009[Zvezdin, A. K. & Mukhin, A. A. (2009). JETP Lett. 88, 505-510.]). Up to now, RFeO3 compounds have been investigated for future applications such as inertia-driven spin switching (Kimel et al., 2009[Kimel, A. V., Ivanov, B. A., Pisarev, R. V., Usachev, P. A., Kirilyuk, A. & Rasing, T. (2009). Nat. Phys. 5, 727-731.]), laser-induced spin reorientation (SR) (de Jong et al., 2011[Jong, J. A. de, Kimel, A. V., Pisarev, R. V., Kirilyuk, A. & Rasing, T. (2011). Phys. Rev. B, 84, 104421.]), ultrafast manipulation of spins through thermally induced SR transition (de Jong et al., 2012[Jong, J. A. de, Razdolski, I., Kalashnikova, A. M., Pisarev, R. V., Balbashov, A. M., Kirilyuk, A., Rasing, T. & Kimel, A. V. (2012). Phys. Rev. Lett. 108, 157601.]), temperature and magnetic field control of SR (Cao et al., 2014[Cao, S., Zhao, H., Kang, B., Zhang, J. & Ren, W. (2014). Sci. Rep. 4, 5960.]; Hong et al., 2011[Hong, F., Cheng, Z., Zhao, H., Kimura, H. & Wang, X. (2011). Appl. Phys. Lett. 99, 092502.]; Cao et al., 2016[Cao, Y., Xiang, M., Zhao, W., Wang, G., Feng, Z., Kang, B., Stroppa, A., Zhang, J., Ren, W. & Cao, S. (2016). J. Appl. Phys. 119, 063904.]; Zhao et al., 2015[Zhao, W., Cao, S., Huang, R., Cao, Y., Xu, K., Kang, B., Zhang, J. & Ren, W. (2015). Phys. Rev. B, 91, 104425.]; Wu et al., 2014[Wu, H., Cao, S., Liu, M., Cao, Y., Kang, B., Zhang, J. & Ren, W. (2014). Phys. Rev. B, 90, 144415.]; Wang et al., 2016[Wang, G., Zhao, W., Cao, Y., Kang, B., Zhang, J., Ren, W. & Cao, S. (2016). J. Alloys Compd. 674, 300-304.]; Yuan et al., 2013[Yuan, S. J., Ren, W., Hong, F., Wang, Y. B., Zhang, J. C., Bellaiche, L., Cao, S. X. & Cao, G. (2013). Phys. Rev. B, 87, 180405.]) and large rotating-field entropy change (Cao et al., 2016[Cao, Y., Xiang, M., Zhao, W., Wang, G., Feng, Z., Kang, B., Stroppa, A., Zhang, J., Ren, W. & Cao, S. (2016). J. Appl. Phys. 119, 063904.]; Huang et al., 2013[Huang, R., Cao, S., Ren, W., Zhan, S., Kang, B. & Zhang, J. (2013). Appl. Phys. Lett. 103, 162412.]). The RMnO3 family also draws a lot of attention due to spontaneous electric polarizations induced by noncollinear spiral magnetic order (Kenzelmann et al., 2005[Kenzelmann, M., Harris, A. B., Jonas, S., Broholm, C., Schefer, J., Kim, S. B., Zhang, C. L., Cheong, S. W., Vajk, O. P. & Lynn, J. W. (2005). Phys. Rev. Lett. 95, 087206.]), a collinear E-type antiferromagnetic structure (Okuyama et al., 2011[Okuyama, D., Ishiwata, S., Takahashi, Y., Yamauchi, K., Picozzi, S., Sugimoto, K., Sakai, H., Takata, M., Shimano, R., Taguchi, Y., Arima, T. & Tokura, Y. (2011). Phys. Rev. B, 84, 054440.]) and strong antiferromagnetic pinning effects (Jin et al., 2015[Jin, Y., Cui, X. P., Cheng, J. A., Cao, S. X., Ren, W. & Zhang, J. C. (2015). Appl. Phys. Lett. 107, 072907.]). In RFeO3 and RMnO3 compounds, below their Néel temperatures (TN), the Fe3+ or Mn3+ sublattice will be ordered in a slightly canted antiferromagnetic configuration due to an antisymmetric exchange Dzyaloshinsky–Moriya interaction, while also showing weak ferromagnetism (Dzyaloshinsky, 1958[Dzyaloshinsky, I. (1958). J. Phys. Chem. Solids, 4, 241-255.]; Moriya, 1960[Moriya, T. (1960). Phys. Rev. 120, 91-98.]). Magnetoelectric (ME) coupling, which breaks spatial inversion and time-reversal symmetries (Mostovoy, 2006[Mostovoy, M. (2006). Phys. Rev. Lett. 96, 067601.]), has been the focus of extensive research to explore the mutual control of electric and magnetic degrees of freedom (Cao et al., 2016[Cao, Y., Xiang, M., Zhao, W., Wang, G., Feng, Z., Kang, B., Stroppa, A., Zhang, J., Ren, W. & Cao, S. (2016). J. Appl. Phys. 119, 063904.]; Fina et al., 2010[Fina, I., Fàbrega, L., Martí, X., Sánchez, F. & Fontcuberta, J. (2010). Appl. Phys. Lett. 97, 232905.]). Various magnetic phase transitions also occur in the presence of ME processes (Hemberger et al., 2007[Hemberger, J., Schrettle, F., Pimenov, A., Lunkenheimer, P., Ivanov, V. Y., Mukhin, A. A., Balbashov, A. M. & Loidl, A. (2007). Phys. Rev. B, 75, 035118.]; Kimura et al., 2005[Kimura, T., Lawes, G., Goto, T., Tokura, Y. & Ramirez, A. P. (2005). Phys. Rev. B, 71, 224425.]) and dielectric properties may also change around the magnetic phase transition, thus providing an approach to trigger magnetodielectric coupling. It is worth noting that DyFeO3 has been found experimentally to have a field-induced gigantic ME effect (Nakajima et al., 2015[Nakajima, T., Tokunaga, Y., Taguchi, Y., Tokura, Y. & Arima, T. H. (2015). Phys. Rev. Lett. 115, 197205.]). Consequently, the modification of magnetic and electric polarization by controlling the phase transition is the main theoretical and experimental objective to realise new multiferroic materials that have application at room temperature.

One of the special magnetic phase transitions in RFeO3 which might be closely related to magnetically driven ferro­electricity is spin reorientation (SR). According to symmetry considerations and the antiferromagnetic nature of the coupling between the ions, there are three magnetic configurations allowed for the Fe3+ sublattice, namely Γ1, Γ2 and Γ4, with different major antiferromagnetic directions (White, 1969[White, R. L. (1969). J. Appl. Phys. 40, 1061-1069.]). Complex R3+R3+, R3+–Fe3+ and Fe3+–Fe3+ interactions can lead to competitive anisotropic magnetic features in RFeO3, possessing slightly different free energies when the magnetic moments align along the three main axes over varying temperature ranges. For RFeO3, the Γ4 spin configuration appears in the higher temperature region, while the other two spin configurations can be found when the temperature is reduced (White, 1969[White, R. L. (1969). J. Appl. Phys. 40, 1061-1069.]). At extremely low temperatures a different spin configuration may appear, due to the more complicated ordering of sets of rare earth ions, such as observed in TbFeO3 (Cao et al., 2016[Cao, Y., Xiang, M., Zhao, W., Wang, G., Feng, Z., Kang, B., Stroppa, A., Zhang, J., Ren, W. & Cao, S. (2016). J. Appl. Phys. 119, 063904.]) and DyFeO3 (White, 1969[White, R. L. (1969). J. Appl. Phys. 40, 1061-1069.]).

SmFeO3 has attracted much attention due to its intriguing behaviours, like fast magnetic switching (Jeong et al., 2012[Jeong, Y. K., Lee, J.-H., Ahn, S.-J. & Jang, H. M. (2012). Solid State Commun. 152, 1112-1115.]), temperature-induced spin switching (Cao et al., 2014[Cao, S., Zhao, H., Kang, B., Zhang, J. & Ren, W. (2014). Sci. Rep. 4, 5960.]), the highest SR temperature (TSR) among the RFeO3 system and its curious ferroelectric properties (Lee et al., 2011[Lee, J. H., Jeong, Y. K., Park, J. H., Oak, M. A., Jang, H. M., Son, J. Y. & Scott, J. F. (2011). Phys. Rev. Lett. 107, 117201.]; Kuo et al., 2014[Kuo, C. Y. et al. (2014). Phys. Rev. Lett. 113, 217203.]). SmMnO3 is one of the A-type antiferromagnetic (AFM) RMnO3 compounds, showing negative magnetization (Cheng et al., 2011[Cheng, J. G., Zhou, J. S., Goodenough, J. B., Su, Y. T., Sui, Y. & Ren, Y. (2011). Phys. Rev. B, 84, 104431.]) and magnetocapacitive effects (Jung et al., 2010[Jung, J.-S., Iyama, A., Nakamura, H., Mizumaki, M., Kawamura, N., Wakabayashi, Y. & Kimura, T. (2010). Phys. Rev. B, 82, 212403.]) as reported recently. In addition, the RFexMn1−xO3 (R = Dy, Tb and Y) family has been studied a lot due to their varying physical properties and interesting phase transitions (Nair et al., 2016[Nair, H. S., Chatterji, T., Kumar, C. M. N., Hansen, T., Nhalil, H., Elizabeth, S. & Strydom, A. M. (2016). J. Appl. Phys. 119, 053901.]; Mandal et al., 2013[Mandal, P., Serrao, C. R., Suard, E., Caignaert, V., Raveau, B., Sundaresan, A. & Rao, C. N. R. (2013). J. Solid State Chem. 197, 408-413.], 2011[Mandal, P., Bhadram, V. S., Sundarayya, Y., Narayana, C., Sundaresan, A. & Rao, C. N. R. (2011). Phys. Rev. Lett. 107, 137202.]; Hong et al., 2011[Hong, F., Cheng, Z., Zhao, H., Kimura, H. & Wang, X. (2011). Appl. Phys. Lett. 99, 092502.]). Typically, the usual way to control the temperature and configuration of the SR transition is to dope other lanthanides into RFeO3, such as Sm1−xDyxFeO3 (Zhao et al., 2015[Zhao, W., Cao, S., Huang, R., Cao, Y., Xu, K., Kang, B., Zhang, J. & Ren, W. (2015). Phys. Rev. B, 91, 104425.]) and Dy0.5Pr0.5FeO3 (Wu et al., 2014[Wu, H., Cao, S., Liu, M., Cao, Y., Kang, B., Zhang, J. & Ren, W. (2014). Phys. Rev. B, 90, 144415.]). Here, we report a new way to change the SR transition by modifying the 3d–4f interaction between R3+–Fe3+ with Mn3+ doping in single-crystal SmFeO3. By doing so, we found that the SmFexMn1−xO3 family can possess novel properties that are absent from the parent SmFeO3 and SmMnO3 rare earth perovskites. Here, we focus our investigation on the twofold SR magnetic transitions of SmFe0.75Mn0.25O3 and the continuously tunable phase transition as observed from the temperature dependence of the magnetization (MT) under external applied fields and hysteresis loops (MH).

2. Experimental

The SmFe0.75Mn0.25O3 (SFMO) single crystal was grown by the optical floating-zone method (Crystal System Inc., model FZ-T-10000H-VI-P-SH). The compounds of the feed and seed rods were prepared by a solid-state reaction in which the stoichiometric starting materials were Sm2O3 (99.99%), Fe2O3 (99.9%) and MnO2 (99.9%) in a properly mixed proportion of 4:3:2. The temperature of the molten zone was controlled by adjusting the power of four lamps. The molten zone moved upwards at a rate of 3 mm h−1.

The crystallinity and crystallographic orientations were determined by X-ray Laue photography. The microstructure of the crystal was checked by X-ray diffraction using a Rigaku 18 kW D/MAX-2550 diffractometer (Cu Kα radiation) with a scanning step of 0.02° and 2θ from 10° to 120°. The dc magnetization measurements were performed using a Physics Property Measurement System (Quantum Design, PPMS-9). Zero-field-cooling (ZFC) and field-cooling (FC) processes were used to acquire the temperature dependence of the magnetization.

3. Results

Fig. 1[link](a) shows the Rietveld refinement of powder X-ray diffraction (XRD) data from the single crystal of SmFe0.75Mn0.25O3 performed using the AutoFP (Cui et al., 2015[Cui, X., Feng, Z., Jin, Y., Cao, Y., Deng, D., Chu, H., Cao, S., Dong, C. & Zhang, J. (2015). J. Appl. Cryst. 48, 1581-1586.]) and FULLPROF (Rodríguez-Carvajal, 2001[Rodríguez-Carvajal, J. (2001). IUCr Commission Powder Diffr. Newsl. 26, 12-19.]) programs. The diffraction patterns can be assigned to the single-phase orthorhombic perovskite structure with space group Pbnm and no impurity phases were detected. The lattice parameters thus obtained are a = 5.39392 Å, b = 5.63707 Å and c = 7.67156 Å (Rwp = 0.133). Fig. 1[link](b) shows the clear Laue diffraction spots, indicating the high quality of our SmFe0.75Mn0.25O3 single crystal. Both XRD and Laue photography confirmed the excellent quality of the sample, and the cutting planes are precisely perpendicular to the a, b and c axes, respectively.

[Figure 1]
Figure 1
(a) X-ray diffraction pattern and (b) Laue back-scattering photography of SmFe0.75Mn0.25O3 single crystal along the (001), (010) and (100) crystallographic axes.

Fig. 2[link] shows the temperature dependence of the ZFC and FC magnetizations measured under a field of H = 0.01 T for the SmFe0.75Mn0.25O3 single crystal (sample shown in the inset) along the the a and c axes, respectively. The second-order transition starting from TSR2 = 382 K is the first spin reorientation, where the Fe3+ spins reorient from a configuration of canting antiferromagnetism along the a axis with weak ferromagnetism along the c axis, [\Gamma_4 (G_x, A_y, F_z)], to canting antiferromagnetism along the c axis with weak ferromagnetism along the a axis, [\Gamma_2 (F_x, C_y, G_z)]. Another unique and new feature of the MT curve is that at TSR1 = 212 K, the SmFe0.75Mn0.25O3 single crystal undergoes a second SR transition at a lower temperature with weak ferromagnetism along the a axis [\Gamma_2 (F_x, C_y, G_z)], changing to complete antiferromagnetism with no net magnetization, [\Gamma_1 (A_x, G_y, C_z)]. This kind of SR behaviour has never been reported in the literature to the best of our knowledge.

[Figure 2]
Figure 2
Temperature-dependent magnetizations of SmFe0.75Mn0.25O3 along the a and c axes under magnetic field H = 0.01 T. Three slightly canted antiferromagnetic phases Γ1, Γ2 and Γ4 can be distinguished by the shaded areas. The inset shows the SmFe0.75Mn0.25O3 single-crystal sample.

The transition over the whole temperature range might be called a Γ4 [\to] Γ2 [\to] Γ1 double SR transition. Since pure SmFeO3 possesses a spin configuration from Γ4 to Γ2 due to the Sm3+–Fe3+ interaction at rather high temperatures (450–480 K), it is reasonable to have such a spin configuration transition in SmFe0.75Mn0.25O3 at a lower temperature of 361–382 K. The most interesting finding here is the spin configuration from Γ2 to Γ1 due to Mn3+ doping in SmFeO3 that gives a vanishing effective moment vector below TSR1 = 212 K. It is known that there is no SR in the whole family of the RMnO3 system. In addition, it is very rare for a rare earth orthoferrite to possess a Γ1 spin configuration, with the exception of DyFeO3 (Fu et al., 2014[Fu, X., Liu, X. & Zhou, J. (2014). Mater. Lett. 132, 190-192.]), for which the SR transition temperature (TSR = 37 K) is much lower than that of our single crystal here.

To investigate the SR transition further, the MH curves were measured at different temperatures along the a and c axes, repectively. Figs. 3[link](a) and 3[link](b) show the standard linear AFM behaviour at 50, 100 and 150 K with a change of slope, which corresponds to the feature of Γ1 spin configuration below TSR1 = 212 K. Fig. 3[link](c) and inset show the uncompensated ferromagnetism component along the a axis, while Fig. 3[link](d) shows AFM-like behaviour but with noticeable kinks along the c axis. Above 382 K, the AFM-like and kink behaviour is more obviously seen in the a axis MH, as shown in Fig. 3[link](e), while the c axis shows a ferromagnetism component in Fig. 3[link](f) and its inset. Inflexion behaviours are observed in Figs. 3[link](d) and 3[link](e) when the magnetic fields reach certain critical values, which suggests a field-induced SR. Therefore, according to Fig. 3[link], we can confirm that the weak ferromagnetism aligns along the c axis when the temperature is below TN (around 600 K), and changes its direction to the a axis when the temperature drops below TSR2 = 382 K, before disappearing in any direction below TSR1 = 212 K, as shown in Fig. 2[link]. Therefore, such a double SR transition induced by temperature is extraordinary for a single-phase rare earth perovskite.

[Figure 3]
Figure 3
MH curves for the SmFe0.75Mn0.25O3 single crystal along the a and c axes at temperatures of (a), (b) 50 K, 100 K and 150 K, (c), (d) 250 K and 300 K, and (e), (f) 390 K. The insets of (c) and (f) show enlargements of the plots at small magnetic field.

Fig. 4[link](a) shows the MT curves along the c axis when we change the magnitude of the external magnetic field. Upon increasing the magnetic field, TSR2 moves to a lower temperature in a linear-like fashion. For example, we can see that the value of TSR2 decreases to 263 K under H = 5 T. Thus, we believe that when the magnetic field is high enough, the Γ2 spin configuration will be totally suppressed. On the other hand, TSR1 is found to be almost constant regardless of the magnitude of the external field. Fig. 4[link](b) shows the measured MH curves at different temperatures ranging from 215 to 380 K. This diagram shows the evolution of the MH curves with a change of slope around TSR2 at different temperatures, illustrating an intermediate state between two different magnetic configurations, corroborating the details of Fig. 4[link](a). Here, the magnetic order would be stabilized in a Γ4 spin configuration with a moment along the c axis after the intermediate state. Furthermore, we also observe from both Figs. 4[link](a) and 4[link](b) that, with increasing magnetic field, the inflection points move to low temperature. On the other hand, when we apply the external magnetic field along the a axis, Fig. 4[link](c) shows that the spin reorientation temperature TSR2 will move to the high-temperature region, as indicated by the green arrow. When the magnetic field exceeds 0.5 T, TSR2 moves above 400 K, which is beyond our temperature detection limit. Fig. 4[link](d) shows the MH curves along the a axis at temperatures ranging from 385 to 397 K. The collected data show another linearly increasing behaviour for TSR2 versus magnetic field, consistent with that of the MT curve in Fig. 4[link](c). In addition, TSR1 remains constant with varying magnetic field, as indicated by the vertical dashed line. To sum up, the Γ4 to Γ2 SR transition temperature can be easily controlled by magnetic field, whereas the Γ2 to Γ1 transition temperature is insensitive to the magnetic field.

[Figure 4]
Figure 4
(a) MT curves along the c axis at different magnetic fields from 0.01 to 5 T. (b) MH curves along the c axis at different temperatures from 215 to 380 K. (c) MT curves along the a axis at different magnetic fields from 0.01 to 2 T. (d) MH curves along the a axis at different temperatures from 385 to 397 K. The insets in (b) and (d) show the linear temperature dependence of TSR2 along the c and a axes, respectively.

4. Discussion

As mentioned, the rare earth orthoferrites have two kinds of magnetic ion, M3+ and R3+. So there are three kinds of magnetic interaction, M3+M3+, M3+R3+ and R3+R3+. These three interactions all consist of isotropic, antisymmetric and anisotropic-symmetric super-exchange interactions, which inevitably makes the magnetic properties of RFeO3 complex. Further, the antisymmetric and anisotropic-symmetric super-exchange interactions of M3+R3+ are responsible for the temperature-induced SR (Yamaguchi, 1974[Yamaguchi, T. (1974). J. Phys. Chem. Solids, 35, 479-500.]). In our case, the interaction becomes even more complicated due to the doping Mn3+ ions and intriguingly introduces all three spin configurations allowed in RFeO3. By minimizing the free energy in the Γ4 to Γ2 SR transition with respect to θ and Φ (θ is the rotation angle of the easy axis in the ac plane and 2Φ represents the angle between two sublattices of the R3+ spins), one can obtain the following equation (Yamaguchi, 1974[Yamaguchi, T. (1974). J. Phys. Chem. Solids, 35, 479-500.]):

[\eqalignno{ & \left ( J_B - J_C \right ) \left ( {\hat J} + {\hat {J^\prime}} \right )^2 \left ( s_0 + \, s \cos \Phi \right ) \, s \sin \Phi + \left ( J_D + J_B \right) \left ( {\hat J} - {\hat {J^\prime}} \right )^2 \cr & \times \left ( s_0 ^\prime \sin \theta - \, s \sin \Phi \right ) \, s \cos \Phi = 0 , & (1)}]

[\eqalignno{ & \cos \theta \biggl \{ \left [ 2 (D - E) + {{\left ( D_z - C_z \right )^2} \over {2 \left ( J_D - J_C \right )}} - {{\left ( B_x - C_x \right )^2} \over {2 \left ( J_B - J_C \right )^2}} \right ] \sin \theta \cr & + 2s_0 ^\prime \biggl [ {{ ( {\hat J} - {\hat {J^\prime}} )^2} \over {\left ( J_B - J_C \right )}} \biggr ] \, s \sin \Phi \biggr \} = 0 & (2)}]

where s is the ratio of the mean values of the R3+ and M3+ spins, 〈SR〉/〈SM〉, which is the only parameter depending directly on temperature. The other parameters in equations (1)[link] and (2)[link] are different exchange constants. These two equations give the following three sets of solutions, (I), (II) and (III).

[({\rm I}) \quad \sin \Phi = 0 . \eqno (3)]

In this case, the stable angle of θ is 0 and this gives the Γ4 configuration in the high-temperature phase (382 K < T < TN).

[({\rm II}) \quad s \cos \Phi = s_{c1} . \eqno (4)]

where

[s_{c1} = {{-s_0 [( {\hat J} + {\hat {J^\prime}} )^2 / (J_D + J_B)]} \over {[ {{ ({\hat J} + {\hat {J^\prime}})^2} / {(J_D + J_B)}}] + [(A s_0^\prime - 1) ({\hat J} - {\hat {J^\prime}})^2 / (J_B - J_C) ]}} , \eqno(5)]

and

[\eqalignno{&A = \cr & {{-2s_0^\prime [ ({\hat J} - {\hat {J^\prime}})^2 / ( J_B - J_C) ]} \over { 2(D - E) + [(D_z - C_z)^2 / 2(J_D - J_C)] - [(B_x - C_x)^2 / 2(J_B - J_C)^2 ]}} . \cr &&(6)}]

The equilibrium values of θ can be acquired as

[\theta = \sin^{-1} \{ [ A (s^2 - s_{c1}^2)^{1/2} ] \} . \eqno (7)]

From equation (7)[link], we can see that θ is zero when s = sc1 and will increase with increasing s. This implies rotation of the spin system. When s reaches another critical value of s = [sc12 + (1/A2)]1/2, θ will take a value of π/2. This process corresponds to the continuous SR intermediate range (361 K ≤ T ≤ 382 K).

[{\rm (III)} \quad \cos \theta = 0 . \eqno (8)]

This indicates that the easy axis has rotated to the c axis and the system is in the Γ2 phase. Briefly, the case when s = 0 corresponds to the state at the Néel temperature. At high temperature s is small, and when ssc1 the free energy F(Γ4) is lower and the spin system will be stabilized in the Γ4 configuration due to the anisotropic energy of the Fe3+ single ions. As the temperature decreases, the sublattice moments of Sm3+ and Fe3+ will increase and s gradually approaches sc1 where the free energy F(Γ24) crosses F(Γ4). When s finally surpasses [sc12 + (1/A2)]1/2, the free energy F(Γ2) becomes lowest, thus favouring the Γ2 configuration. This is the typical continous SR transition in most RFeO3 systems, but in the Mn3+-doped SmFeO3 single crystal the situation will become more complicated. Once the first SR transition is complete, the Mn3+ ions will be ordered with decreasing temperature and this will consequently influence the distribution of the free energy along the three main axes and s as well. When s reaches another critical value sc2, the free energy of the Γ1 configuration is smaller than that of Γ2 and Γ4, and the corresponding temperature is 212 K for our case.

So far, we have discussed two criticial values of s, namely sc1 and sc2. For an un-doped RFeO3 system, if sc1sc2, a Γ4 to Γ2 SR transition will be seen, and if sc1sc2, a Γ4 to Γ1 SR transition will occur (Yamaguchi, 1974[Yamaguchi, T. (1974). J. Phys. Chem. Solids, 35, 479-500.]). Indeed, if s never reaches sc1 or sc2 in the whole temperature range, no SR takes place, and this is the case for LaFeO3 and YFeO3. With the appropriate concentration of Mn3+, the influence of the Mn3+ sublattice will make s grow more rapidly as the temperature decreases and s will reach sc2 at high temperature where the spin structure transforms to the Γ1 configuration (Hornreich et al., 1975[Hornreich, R. M., Komet, Y., Nolan, R., Wanklyn, B. M. & Yaeger, I. (1975). Phys. Rev. B, 12, 5094-5104.]).

The energy of an antiferromagnetic system in a magnetic field is lower when the antiferromagnetic vector is perpendicular to the direction of the field than when the two are parallel (Johnson et al., 1980[Johnson, C. E., Prelorendjo, L. A. & Thomas, M. F. (1980). J. Magn. Magn. Mater. 15-18, 557-558.]). A magnetic field applied along the antiferromagnetic axis of the Fe3+ system in the rare earth orthoferrites acts to cause reorientation of the Fe3+ antiferromagnetic vector to a perpendicular alignment. It is the competition between this Zeeman energy and the magnetic anisotropy energy of the Fe3+ system that determines the spin reorientation. In our case, since the antiferromagnetic vector of the Γ1 configuration is along the b axis, one would not expect a field-induced change in the SR temperature TSR1 when the external field is along the c or a axis. Accordingly, a field-modified spin reorientation is seen when the external field is along the c axis rather than the a axis, as the antiferromagnetic vector of the Γ2 configuration is along the c axis when the temperature is between TSR1 and TSR2. Weak magnetism along the c-axis direction can be induced by applying an external field along the c axis. The Γ4 configuration has its antiferromagnetic vector along the a axis, and an external field along the a axis can induce another Γ2 spin configuration when the temperature is between TSR2 and TN.

5. Conclusions

In summary, we have successfully synthesized a single crystal of SmFe0.75Mn0.25O3, which has a single-phase perovskite structure, by the optical floating-zone method. The magnetic properties along different crystallographic axes have been studied in detail. Interesting double spin reorientation transitions Γ4 [\to] Γ2 [\to] Γ1 were observed above and below room temperature. Field-induced spin reorientation has been investigated along the c and a axes in detail, showing the linear dependence and independence of SR temperatures versus magnetic field. Delicate interactions between the magnetic sublattices of Sm3+, Fe3+ and Mn3+ make this unique compound highly sensitive to magnetic field and to temperature. Due to its intriguing magnetic characteristics, novel magnetic switching devices could be designed based on this finding.

Funding information

Funding for this research was provided by: National Key Basic Research Program of China (award Nos. 2015CB921600, 2016YFB0700201); National Natural Science Foundation of China (award Nos. 51672171, 11574194, 51372149, 11274222); Eastern Scholar Program from Shanghai Municipal Education Commission; Shanghai Materials Genome Institute from the Shanghai Municipal Science and Technology Commission (award No. 14DZ2261200).

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IUCrJ
Volume 4| Part 5| September 2017| Pages 598-603
ISSN: 2052-2525