Observation of re-entrant spin reorientation in TbFe1−xMnxO3

We report a spin reorientation from Γ4(Gx, Ay, Fz) to Γ1(Ax, Gy, Cz) magnetic configuration near room temperature and a re-entrant transition from Γ1(Ax, Gy, Cz) to Γ4(Gx, Ay, Fz) at low temperature in TbFe1−xMnxO3 single crystals by performing both magnetization and neutron diffraction measurements. The Γ4 − Γ1 spin reorientation temperature can be enhanced to room temperature when x is around 0.5 ~ 0.6. These new transitions are distinct from the well-known Γ4 − Γ2 transition observed in TbFeO3, and the sinusoidal antiferromagnetism to complex spiral magnetism transition observed in multiferroic TbMnO3. We further study the evolution of magnetic entropy change (−ΔSM) versus Mn concentration to reveal the mechanism of the re-entrant spin reorientation behavior and the complex magnetic phase at low temperature. The variation of −ΔSM between a and c axes indicates the significant change of magnetocrystalline anisotropy energy in the TbFe1−xMnxO3 system. Furthermore, as Jahn-Teller inactive Fe3+ ions coexist with Jahn-Teller active Mn3+ ions, various anisotropy interactions, compete with each other, giving rise to a rich magnetic phase diagram. The large magnetocaloric effect reveals that the studied material could be a potential magnetic refrigerant. These findings expand our knowledge of spin reorientation phenomena and offer the alternative realization of spin-switching devices at room temperature in the rare-earth orthoferrites.

new magnetic phase and reveal the mechanism of new spin reorientation in TbFe 1−x Mn x O 3 system, from which some remarkable behaviors expected to be found due to competitive magnetic phases that do not exist in both TbMnO 3 and TbFeO 3 .
In this work, we synthesized a series of TbFe 1−x Mn x O 3 and reported their special magnetic phase transitions by performing magnetization and neutron powder diffraction (NPD) measurements. We demonstrate that the phase transition of Γ 4 → Γ 1 → Γ 4 exists in TbFe 0.75 Mn 0.25 O 3 single crystal, rather than the common transition of Γ 4 → Γ 2 as observed in TbFeO 3 and other orthoferrites. From a practical point of view, Γ 4 → Γ 1 (weak magnetic moment to zero net moment) transition may find use even with easily-obtained polycrystalline samples whereas we need to grow single crystals to observe Γ 4 → Γ 2 (weak magnetic moment along c to a direction) transition. The magnitude of the magnetocaloric effect is found to be large and strictly resembles the observed magnetic features. The evolution of entropy change versus Mn doping are presented and discussed with in the scenario of Mn substitution-induced anisotropic interaction.

Results
Magnetometry and neutron diffraction measurements. The x-ray diffraction patterns for the TbFe 1−x Mn x O 3 with x = 0.25 are plotted in Fig. 1(a). The Rietveld refinement results show that the sample has a distorted orthorhombic perovskite structure (Pbnm) and no additional phases are identified. Figure 1 increase slowly for H || a and H || b with the decreasing temperature. This resembles the phase transition of Γ 4 → Γ 1 spin reorientation at T SR = 254 K. Thus, we speculate that the magnetic structure transforms from the canted antiferromagnetism with weak ferromagnetism along the c axis (G x , A y , F z ) to the major G-type antiferromagnetic vector along the b axis (A x , G y , C z ). In this case, there is no net magnetic moment along the c axis in the wide range of temperature between 16 and 254 K. Interestingly, as temperature decreases below 16 K, the magnetic moment along the c axis turns to be negative with a possible (G x , A y , F z ) configuration in negative magnetization state. The moment configuration speculated from the magnetometry is shown as the arrows in Fig. 1(b). The arrows show the evolution of magnetization arising from Tb (blue arrows) and Fe/Mn (orange arrows), respectively. The net moments of Tb and Fe tend to keep aligning along c-axis and parallel to the direction of applied field, which is responsible for the weak ferromagnetism above T SR 1 . Nevertheless, due to the d − f interactions of Fe/Mn and Tb ions, the larger net moment of Tb ions become antiparallel to those of Fe ions and the direction for applied field below T SR 2 in ZFC mode, leading to a negative magnetization state. However, in FC mode, both the net moments of Tb and Fe ions keep parallel to the direction of applied field, resulting in large net magnetization below T SR 2 . To confirm our speculation on the nature of the intriguing spin reorientation transition phenomena, the NPD experiments were performed and the results are shown in Fig. 2(a-c) for T = 8, 40, and 300 K, respectively. All the structural Bragg peaks show no position shift or split, indicating the absence of structural phase transition at the different temperatures. Symmetry analysis was performed based on the crystal structure of TbFe 1−x Mn x O 3 (x = 0.25), which is an orthorhombically-distorted perovskite structure with space group Pbnm. The lattice parameters for this crystal structure are a = 5.284 Å, b = 5.603 Å and c = 7.530 Å. For our orthoferrites, the k = 0 propagation vector was adopted as usual. According to the symmetry theory proposed by White 32 and Bertaut 20 , Γ 5 and Γ 8 are incompatible with a net moment on the iron sites. Γ 3 is not consistent with the observed strong antiferromagnetic coupling between nearest iron neighbors. So Γ 1 , Γ 2 and Γ 4 could be possible magnetic structure for this compound.
Then Rietveld refinements were performed to test these possibilities with the orthorhombic Pbnm structure. The results show that the data obtained at 8 and 300 K fit well with the magnetic structures of Γ 4 (G x , A y , F z ), and the data obtained at 40 K fit well with Γ 1 (A x , G y , C z ). The derived structures of Fe/Mn are schematically drawn in Fig. 3(a-c), respectively. Arrows of A-D represent four types of location of Fe(Mn) ions, and the corresponding refined magnetic moments along different crystallographic axes are given in supplemental material 33 . Figure 3(a) illustrates an orthorhombic perovskite with Fe/Mn having G-type AFM spin order along the a axis, A-type AFM spin order along the b axis, and F-type FM spin order along the c axis, consistent to the (G x A y F z ) configuration at room temperature in Bertaut's notation 20 . This type of commensurate spin order is observed to decline at T SR 1 = 254 K and totally collapse at ′ T SR 1 = 245 K, resulting in a new antiferromagnetic phase with no net magnetization along any direction 32 . This intriguing magnetic phase configuration is found to be A x G y C z as shown in Fig. 3(b), instead of the common F x C y G z reported for most RFeO 3 systems. This transition at T SR 1 is characterized by the relative change of the (011) intensity and the (101) magnetic Bragg peaks around |Q| = 1.4A −1 as shown in Fig. 2(b,c), implying that the moments of Fe 3+ rotate from the a to b axis upon cooling as indicated in Fig. 3 c remains vanished till T SR 2 = 16 K, then a sudden increase arises at T SR 2 . This sharp transition from Γ 1 back to Γ 4 is accomplished within 1 K and the results are confirmed by NPD. The ordering of Tb 3+ has not been observed at T ≥ 8 K in our present measurement and further research at lower temperature is required. The T SR 1 at 254 K is believed to be driven by both Fe-Fe and Tb-Fe/Mn sub-lattice interactions, while T SR 1 at 16 K arises from the enhanced interactions of Tb-Fe/Mn sub-lattice 5 .

Spin reorientation at T SR
1 . Since Γ 4 configuration is characterized by the net moments along the c axis, the magnetic phase transition of Γ 4 → Γ 1 may undergo a transformation of the Fe 3+ sublattice from weak ferromagnetism to complete antiferromagnetism upon the decreasing temperature. In order to reveal the relationship between Mn substitution and the changes in the anisotropy fields on the sublattices, a formula is developed by Holmes et al. 23 . Based on molecular field theory, the doping concentration dependence of T SR 1 obeys the following equation for x ≥ x c .
where k′ is a positive constant related to the second-order anisotropy fields in the b-a, b-c, c-a planes. x c characterizes a critical doping concentration from a hypothesis that at x = x c , the Γ 4 → Γ 1 spin reorientation first appears at T = 0 K. This formula reveals that Mn substitutions can be used to shift the Γ 4 → Γ 1 spin reorientation to be near or above room temperature. Figure 4 shows the experimental and fitting results for TbFe 1−x Mn x O 3 . Corresponding Eq. (1) with x = 0 ~ 0.6 and parameters x c ≈ 0.0080 and k′ = 0.0060 is adopted for this system. Since the Eq. (1) is only valid at low doping concentration, we can obtain good fitting up to x = 0.5. As shown in Fig. 4, T SR 1 could be taken as the onset point of the first spin reorientation transition, and T SR 1 can be enhanced to 299 K at x = 0.5. For x > 0.6, the spin reorientation transition phenomenon was not observed up to their Néel temperatures (T N ). Moreover, the T N in Mn-rich TbFe 1−x Mn x O 3 becomes much lower than that of the TbFeO 3 (T N = 650 K), since Mn doping could weaken both the Tb 3+ -Fe 3+ interaction and the Fe 3+ -Fe 3+ interaction. In the high temperature Γ 4 region of TbFe 1−x Mn x O 3 , the Tb 3+ -Fe 3+ interaction is much stronger than that of Fe 3+ -Fe 3+ interaction and the former one causes the parallel aligns between the moments of Tb 3+ and Fe 3+ to give rise to the net moments along c axis 5 . This scenario is supported from the magnetization behavior along c axis as indicated   in Fig. 1(b). As a consequence, the substitution of Mn for Fe breaks the original Tb 3+ -Fe 3+ interaction, leading to the shift of T SR 1 towards higher temeprature 34 .
Spin reorientation at T SR 2 . Compare with the Γ 4 → Γ 1 spin reorientation at T SR 1 , the Γ 1 → Γ 4 spin reorientation at T SR 2 presents more complex magnetic phase since the ordering degree and interaction between magnetic ions get larger and stronger at low temperature. We herein take TbFe 0.75 Mn 0.25 O 3 as a representative of TbFe 1−x Mn x O 3 system to discuss the characteristic of re-entrant Γ 1 → Γ 4 spin reorientation. Figure 5(a) shows a phase diagram of magnetic field versus temperature for x = 0.25, and the data points of crossover field H cro were obtained from the isothermal M-H curves, in which H cro is taken as the cross point between M a -H and M c -H curves (i.e. when M a = M c at a given temperature) from H = 0 kOe to 70 kOe. As the applied field increases, the M− T curves of the same system show dramatically different characteristics. The solid data points at the phase boundaries represent the second spin reorientation transition temperature T SR 2 for x = 0.25 sample, which divides the diagram into three magnetic phases, i.e., the first low temperature phase (LT 1 ), the second low temperature phase (LT 2 ), and intermediate temperature phase (IT). Both LT 1 and LT 2 phases are characterized as Γ 4 type, and IT is of Γ 1 type. LT 1 presents a weak ferromagnetic phase with Γ 4 type while LT 2 regions show the negative magnetization behavior with Γ 4 type. This phase diagram illustrates the phase transition Γ 1 → Γ 4 can be modified by the external field at low temperature, resulting in rich variation of magnetocrystalline anisotropy.

Discussion
Several factors may affect the spin reorientation transition phenomena: single ion anisotropy, DM interaction, exchange interaction, and magnetic anisotropy 35 . For a rare-earth ion, 4f orbital electrons make it special in bonding and the compounds have large single ion anisotropy. Consequently, the giant magnetocrystalline anisotropy and sharp spin reorientation can be attributed to the single ion anisotropy of Tb 3+ with large angular momentum. For a spin-canted system [36][37][38][39] , a ubiquitous antisymmetric interaction D ⋅ (S 1 × S 2 ) exists, which is linear with respect to the spin-orbit coupling and exchange interaction. The magnitude of D can be expressed roughly as D ≈ (Δ g)/(g)J super , where g is the gyromagnetic ratio, Δ g is its deviation from the value for a free electron, and J super is the strength of superexchange interaction. According to the magnetocaloric and NPD data, we can regard the magnetic entropy change between the a and c axes as a measurement of magnetocrystalline anisotropy energy and analyze the superexchange interactions in our TbFe 1−x Mn x O 3 system.
In order to illustrate the variation of magnetocrystalline anisotropy energy versus Mn doping concentration, we estimate that the magnetic entropy change ( c ) between the a and  40,41 , the magnetic entropy change in a thermodynamic process can be estimated using the following equation We take the Δ T = 1 K (or no more than 5 K at higher temperature) and Δ H = 1 kOe and the computed results are illustrated in Fig. 6(a-f). From Eq. (2), the magnetic entropy change is a function of both temperature and magnetic field. Therefore, by changing temperature and magnetic field, the direction of magnetization vector will rotate due to the magnetocrystalline anisotropy field, and the distribution of anisotropy energy will also vary. Hereafter, we denote the magnetocrystalline anisotropy energy as E ani . It is noted that the − Δ S M value decreases from x = 0 to x = 0.5 and then increases to x = 1, suggesting a similar tendency for the E ani . The evolution of − Δ S M versus doping concentration x implies that the superexchange interaction weakens along the c axis while enhances along the a or b axes for 0 ≤ x ≤ 0.5, and the reversed case holds for 0.5 ≤ x ≤ 1.
In TbFe 0.75 Mn 0.25 O 3 , the hard axis is along the c direction, and the easy magnetization vector is along a direction as shown in Fig. 6. This contour plot of − Δ S M reveals the state of E ani , which may affect both the magnitude and the direction of magnetization vectors. Furthermore, it is noted that the magnitude of net magnetic moment is usually small but its direction is often a decisive factor when considering the exchange coupling interactions in a system 42 . According to our NPD experiment, the Tb 3+ ions are in paramagnetic state at T ≥ 8 K. Therefore, the Tb-Fe(Mn) interactions should be very weak so that they can hardly be influenced by the crystal field. As the applied field increases, ZFC magnetizations in Γ 4 phase become increasing larger, as shown by the ZFC-FC convergence near the Γ 4 − Γ 1 transition (Fig. 5b-d). Thus, the effect of the external field plays a determining role on Γ 4 − Γ 1 transition which to be explored in future.
According to the NPD experimental results 15,29 , the evolution of spin configurations versus doping content x is schematically illustrated in the upper panels of Fig. 7(a-c). In the lower panels of Fig. 7(e,f), the spin glass (SG) transition T SG occurs at 16 and 6.5 K along the c axis under H = 100 Oe in both TbFe 0.75 Mn 0.25 O 3 and TbMnO 3 single crystals, respectively. However, the SG state is not detected along any axis down to 1.9 K in TbFeO 3 single crystal from Fig. 7(d), nor a and b axes in TbFe 0.75 Mn 0.25 O 3 and TbMnO 3 single crystals. The observation of SG behavior is attributed to the competition between AFM and FM component, leading to a spin frustration in Fig. 7(e,f). The M-O-M bond angle (M = Fe or Mn), namely, superexchange interaction angle, is usually reduced from 180° due to the cooperative octahedral rotations in the orthorhombic perovskites. In RMO 3 systems 43 , the easy magnetization axis may rotate below T N because of the coupling between magnetic moments of rare earth R ions and the spin of transition metal M ions. As the major controlling factor of the superexchange interaction, the coupling of M-O-M is much stronger than that of R-O-M, which should be neglected. In TbFe 1−x Mn x O 3 system, the Fe-O-Fe interaction can be partially replaced by Fe-O-Mn upon Mn 3+ doping. In Fig. 7(b,c), the spin frustration along c axis causes the anisotropic superexchange interaction decreasing along the c axis by Mn substitution, which means the entropy change between the a and c axis gets weaker as x increases in a Fe-rich TbFe 1−x Mn x O 3 system. The mechanism of SG phenomena is as follows.
Since the ionic radius of Fe 3+ is equal to Mn 3+ in high spin state (Fe 3+ : S = 5/2, 5.9 μ B /at., r = 0.645 Å and Mn 3+ : S = 2, 4.9 μ B /at., r = 0.645 Å), the crystal distortion caused by ionic radius difference can be ignored. It should be pointed out that the hybridization between inter-site t and e orbitals is orthogonal for a 180° M-O-M chemical bonding. The sketches of Fig. 8(a-c) describe the different effects of Mn 3+ and Fe 3+ ions on the orbital hybridization. According to Goodenough-Kanamori rule 44 , the superexchange interaction between two adjacent transition-metal ions is delivered by a virtual charge transfer. The Fe 3+ and Mn 3+ ions present different configurations for the outer shell electrons, i.e., t 3 e 2 for Fe 3+ and t 3 e 1 for Mn 3+ , respectively. In RFeO 3 , five outer shell electrons of Fe 3+ ions lead to half-filled e g (σ -bond component) and t 2g (π -bond component) orbitals. Therefore, the superexchange interactions between the two Fe 3+ ions only result in an AFM coupling, in accordance to Hund's rules. For Mn 3+ ions, there are three kinds of coupling, i.e., t 3 -O-t 3 , e 1 -O-e 1 and t 3 -O-e 1 . The superexchange interactions over the half-filed t 3 -O-t 3 induce an AFM coupling. Nevertheless, the hybridization between t 3 -O-e 1 and e 1 -O-e 1 might provide an FM coupling in the system, which experimentally confirms that the spiral spin states in TbMnO 3 originate from spin frustration 29 . The above argument can help us explain the SG phenomena in Fig. 7(b,c).  Now we look at the Mn-rich TbFe 1−x Mn x O 3 system. As illustrated in Fig. 8(b,c), the Mn substitution gives rise to the FM component in TbFe 1−x Mn x O 3 system with two consequences. One is the appearance of spin-glass state in Fig. 7(b,c), and the other one is the variation of anisotropic − Δ S M . In TbFe 1−x Mn x O 3 (x > 0.5), Mn 3+ substitution can induce more FM component and lead to a stronger lattice distortion in the system. These factors induce a spin frustration state and result in the reduction of superexchange interaction. In RMnO 3 system, the occupied e g orbital wavefunction of Mn is given by Eq. (3) where θ is the respective orbital component (Fig. 8(d)). The ground state of the system is given by any normalized linear combination of the two e g orbitals in Eq. (3). In TbMnO 3 , the Jahn-Teller distortion of MnO 6 octahedral is a mode of elongating along one axis but shrinking in the other two axes. Since the rare-earth ferrites belong to Jahn-Teller inactive system, θ becomes smaller with doping from x = 1 to 0.5, and the shape of wavefunction |φ > will be stretched. Therefore, the distance of Mn(Fe)-Mn(Fe) along the c axis between the Mn(Fe)O 6 octahedra should be longer than that in TbMnO 3. Thus the superexchange interaction in TbFe 1−x Mn x O 3 is suppressed along the c axis. Additionally, the application of external magnetic field can increase the lattice distortion and enhance the DM interaction 45,46 . The above discussions can account for the variation of − Δ S M for 0.5 ≤ x ≤ 1.
In summary, we observed a re-entrant spin reorientation of type Γ 4 → Γ 1 → Γ 4 in TbFe 0.75 Mn 0.25 O 3 perovskite system. Through neutron powder diffraction and magnetization measurements, we have observed the recurrent magnetic phase transitions at 254 and 16 K. With Mn doping, the spin configurations can be modified and the spin glass state emerges due to the competition between AFM and FM components. Furthermore, the first spin reorientation temperature increases from 8.5 K for x = 0 to 299 K for x = 0.5 TbFe 1−x Mn x O 3 sample, which might be useful for developing spin-switching devices. We have found a rich phase diagram of magnetization by tuning the applied magnetic field and temperature. In the framework of Goodenough-Kanamori rule, we analyze the evolution of − Δ S M versus Mn doping to reveal the unusual spin reorientation and abundant magnetic phase diagram. It is found that the − Δ S M decreases for 0 ≤ x ≤ 0.5 and increases for 0.5 ≤ x ≤ 1. The evolution of − Δ S M is attributed to the change of anisotropic interactions tuned by Mn doping concentration. Furthermore, in an ongoing project we have discovered similar results in Mn doped HoFeO 3 and DyFeO 3 , with Mn dopants in RFeO 3 triggering a rare phase transition from normal Γ 4 → Γ 2 to re-entrant Γ 4 → Γ 1 → Γ 4 spin reorientation.

Methods
A series of Mn doped terbium orthoferrites TbFe 1−x Mn x O 3 (x = 0, 0.10, 0.25, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1) polycrystalline samples were first synthesized by traditional solid state reaction method. Single crystals of x = 0, 0.10, 0.25 and 1 were then grown by using a four-mirror optical floating-zone furnace (FZ-T-10000-H-VI-P-SH, Crystal System Corp.). The phase purity, crystal quality, and crystallographic orientation were checked by powder X-ray diffraction (XRD) and back-reflection Laue XRD experiment, respectively. Magnetization measurements were performed on vibrating sample magnetometer (VSM) attached to a physical property measurement system (PPMS-9), and both zero-field-cooling (ZFC) and field-cooling (FC) modes were used. The NPD experiments at 8, 40, and 300 K were carried out on the thermal triple-axis spectrometer SV30 located at China Advanced Research Reactor (CARR) in China Institute of Atomic Energy, and the neutron powder diffractor at the Institute of Nuclear Physics and Chemistry, China Academic of Engineering Physics. The structural data analyses of XRD and NPD were performed by FullProf program using Rietveld method 47 , and the magnetic symmetry analysis was performed with BasIReps.