Spin-reorientation magnetic transitions in Mn-doped SmFeO₃

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 Γ₄ → Γ₂ transition. This work reports the successful synthesis of the new single-crystal perovskite SmFe_0.75Mn_0.25O₃ and finds interesting spin reorientations above and below room temperature. In addition to the spin reorientation of the Γ₄ → Γ₂ magnetic phase transition observed at around T_SR2 = 382 K, a new spin reorientation, Γ₂ → Γ₁, was seen at around T_SR1 = 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. M–T and M–H 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). Up to now, RFeO₃ compounds have been investigated for future applications such as inertia-driven spin switching (Kimel et al., 2009), laser-induced spin reorientation (SR) (de Jong et al., 2011), ultrafast manipulation of spins through thermally induced SR transition (de Jong et al., 2012), temperature and magnetic field control of SR (Cao et al., 2014; Hong et al., 2011; Cao et al., 2016; Zhao et al., 2015; Wu et al., 2014; Wang et al., 2016; Yuan et al., 2013) and large rotating-field entropy change (Cao et al., 2016; Huang et al., 2013). The RMnO₃ family also draws a lot of attention due to spontaneous electric polarizations induced by noncollinear spiral magnetic order (Kenzelmann et al., 2005), a collinear E-type antiferromagnetic structure (Okuyama et al., 2011) and strong antiferromagnetic pinning effects (Jin et al., 2015). In RFeO₃ and RMnO₃ compounds, below their Néel temperatures (T_N), 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; Moriya, 1960). Magnetoelectric (ME) coupling, which breaks spatial inversion and time-reversal symmetries (Mostovoy, 2006), has been the focus of extensive research to explore the mutual control of electric and magnetic degrees of freedom (Cao et al., 2016; Fina et al., 2010). Various magnetic phase transitions also occur in the presence of ME processes (Hemberger et al., 2007; Kimura et al., 2005) 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). 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). 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). 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) and DyFeO₃ (White, 1969).

SmFeO₃ has attracted much attention due to its intriguing behaviours, like fast magnetic switching (Jeong et al., 2012), temperature-induced spin switching (Cao et al., 2014), the highest SR temperature (T_SR) among the RFeO₃ system and its curious ferroelectric properties (Lee et al., 2011; Kuo et al., 2014). SmMnO₃ is one of the A-type antiferromagnetic (AFM) RMnO₃ compounds, showing negative magnetization (Cheng et al., 2011) and magnetocapacitive effects (Jung et al., 2010) as reported recently. In addition, the RFe_xMn_1−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; Mandal et al., 2013, 2011; Hong et al., 2011). Typically, the usual way to control the temperature and configuration of the SR transition is to dope other lanthanides into RFeO₃, such as Sm_1−xDy_xFeO₃ (Zhao et al., 2015) and Dy_0.5Pr_0.5FeO₃ (Wu et al., 2014). 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 SmFe_xMn_1−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 SmFe_0.75Mn_0.25O₃ and the continuously tunable phase transition as observed from the temperature dependence of the magnetization (M–T) under external applied fields and hysteresis loops (M–H).

2. Experimental

The SmFe_0.75Mn_0.25O₃ (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(a) shows the Rietveld refinement of powder X-ray diffraction (XRD) data from the single crystal of SmFe_0.75Mn_0.25O₃ performed using the AutoFP (Cui et al., 2015) and FULLPROF (Rodríguez-Carvajal, 2001) 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 (R_wp = 0.133). Fig. 1(b) shows the clear Laue diffraction spots, indicating the high quality of our SmFe_0.75Mn_0.25O₃ 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 (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 shows the temperature dependence of the ZFC and FC magnetizations measured under a field of H = 0.01 T for the SmFe_0.75Mn_0.25O₃ single crystal (sample shown in the inset) along the the a and c axes, respectively. The second-order transition starting from T_SR2 = 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, , to canting antiferromagnetism along the c axis with weak ferromagnetism along the a axis, . Another unique and new feature of the M–T curve is that at T_SR1 = 212 K, the SmFe_0.75Mn_0.25O₃ single crystal undergoes a second SR transition at a lower temperature with weak ferromagnetism along the a axis , changing to complete antiferromagnetism with no net magnetization, . This kind of SR behaviour has never been reported in the literature to the best of our knowledge.

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 Γ₂ 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 SmFe_0.75Mn_0.25O₃ 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 T_SR1 = 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), for which the SR transition temperature (T_SR = 37 K) is much lower than that of our single crystal here.

To investigate the SR transition further, the M–H curves were measured at different temperatures along the a and c axes, repectively. Figs. 3(a) and 3(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 T_SR1 = 212 K. Fig. 3(c) and inset show the uncompensated ferromagnetism component along the a axis, while Fig. 3(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 M–H, as shown in Fig. 3(e), while the c axis shows a ferromagnetism component in Fig. 3(f) and its inset. Inflexion behaviours are observed in Figs. 3(d) and 3(e) when the magnetic fields reach certain critical values, which suggests a field-induced SR. Therefore, according to Fig. 3, we can confirm that the weak ferromagnetism aligns along the c axis when the temperature is below T_N (around 600 K), and changes its direction to the a axis when the temperature drops below T_SR2 = 382 K, before disappearing in any direction below T_SR1 = 212 K, as shown in Fig. 2. Therefore, such a double SR transition induced by temperature is extraordinary for a single-phase rare earth perovskite.

Figure 3 M–H 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(a) shows the M–T curves along the c axis when we change the magnitude of the external magnetic field. Upon increasing the magnetic field, T_SR2 moves to a lower temperature in a linear-like fashion. For example, we can see that the value of T_SR2 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, T_SR1 is found to be almost constant regardless of the magnitude of the external field. Fig. 4(b) shows the measured M–H curves at different temperatures ranging from 215 to 380 K. This diagram shows the evolution of the M–H curves with a change of slope around T_SR2 at different temperatures, illustrating an intermediate state between two different magnetic configurations, corroborating the details of Fig. 4(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(a) and 4(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(c) shows that the spin reorientation temperature T_SR2 will move to the high-temperature region, as indicated by the green arrow. When the magnetic field exceeds 0.5 T, T_SR2 moves above 400 K, which is beyond our temperature detection limit. Fig. 4(d) shows the M–H curves along the a axis at temperatures ranging from 385 to 397 K. The collected data show another linearly increasing behaviour for T_SR2 versus magnetic field, consistent with that of the M–T curve in Fig. 4(c). In addition, T_SR1 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 (a) M–T curves along the c axis at different magnetic fields from 0.01 to 5 T. (b) M–H curves along the c axis at different temperatures from 215 to 380 K. (c) M–T curves along the a axis at different magnetic fields from 0.01 to 2 T. (d) M–H 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). 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):

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

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

where

and

The equilibrium values of θ can be acquired as

From equation (7), we can see that θ is zero when s = s_c1 and will increase with increasing s. This implies rotation of the spin system. When s reaches another critical value of s = [s_c1² + (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).

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 s ≤ s_c1 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 s_c1 where the free energy F(Γ₂₄) crosses F(Γ₄). When s finally surpasses [s_c1² + (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 s_c2, 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 s_c1 and s_c2. For an un-doped RFeO₃ system, if s_c1 ≤ s_c2, a Γ₄ to Γ₂ SR transition will be seen, and if s_c1 ≥ s_c2, a Γ₄ to Γ₁ SR transition will occur (Yamaguchi, 1974). Indeed, if s never reaches s_c1 or s_c2 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 s_c2 at high temperature where the spin structure transforms to the Γ₁ configuration (Hornreich et al., 1975).

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). 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 T_SR1 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 T_SR1 and T_SR2. 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 T_SR2 and T_N.

5. Conclusions

In summary, we have successfully synthesized a single crystal of SmFe_0.75Mn_0.25O₃, 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 Γ₂ 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.