Haotian Zhai(翟浩天) Tian Gao(高湉) Xu Zheng(郑旭) Jiali Li(李佳丽)Bin Chen(陈斌) Hongliang Dong(董洪亮) Zhiqiang Chen(陈志强) Gang Zhao(赵钢)Shixun Cao(曹世勋) Chuanbing Cai(蔡传兵) and Vyacheslav V.Marchenkov

1Department of Physics,Shanghai University of Electric Power,Shanghai 200090,China

2Center for High Pressure Science and Technology Advanced Research,Shanghai 201203,China

3Shanghai Key Laboratory of High Temperature Superconductors,Shanghai University,Shanghai 200444,China

4M.N.Mikheev Institute of Metal Physics,Ekaterinburg 620108,Russia

5Ural Federal University,Ekaterinburg 620002,Russia

Keywords: rare earth orthoferrite,magnetocrystalline anisotropy,magnetic ordering,magnetic hysteresis

1. Introduction

In recent years,RFeO3(Rmeans rare-earth elements)family has regained attention owing to its rich physical content and the fascinating potential applications,such as precession excitation induced by terahertz pluses,ambient multiferroics,laser-induced ultrafast spin reversal,ultrafast photomagnetic excitation, etc.[1-5]RFeO3ferrites usually crystallize in a distorted perovskite structure and contain two sets of magnetic sublattices,R3+and Fe3+ions. Three types of magnetic interactions are identified in this kind of rare-earth orthoferrites, Fe3+-Fe3+,R3+-R3+, and Fe3+-R3+,[6,7]which make the magnetic behaviors complex and interesting. The magnetic moment of Fe3+mainly comes from the unpaired electrons on the 3d shell. The antiferromagnetic(AFM)coupling of the neighboring Fe3+ions is generated by the Fe-O-Fe super-exchange interaction.[8]However, the canted FeO6octahedra could induce a weak ferromagnetic(FM)moment due to the so-called antisymmetric Dzyaloshinskii-Moriya (DM)interactions.[9,10]On cooling,RFeO3may undergo two spin reorientation (SR) transitions originated fromR-RandR-Fe interactions.[11]PrFeO3and NdFeO3come into aΓ2(Fx, Cy,Gz)phase fromΓ4(Gx,Ay,Fz)phase in the temperature ranges of 6.5-10 K and 107-170 K,respectively.[12,13]Here,F means the weak FM moment because of the canted AFM ordering due to DM interactions, A, C and G mean the AFM orderings of A-, C- and G-type, respectively. That is, the resultant FM vector points along thec-direction of the crystal inΓ4state,and thea-direction inΓ2state.The strong interaction between the 3d outer electrons of Fe3+and 4f electrons ofR3+is the main source for the magnetic configuration and magnetic phase transitions. However,the interaction mechanisms of Fe-Fe,R-RandR-Fe are unclear till now.

Researchers have tried many kinds of physical fields(such as optical pulse, temperature, magnetic field, etc) to regulate the SR ofRFeO3ferrites,[14]so that they can have a deeper understanding to the behavior of 4f and/or 3d electrons. From the perspective of the intrinsic energy of the crystal, the competition between magnetic energy and anisotropy becomes more intense during the SR process, and it is more sensitive to external influence factors. In 2004, Kimelet al. reported the inverse Faraday effect and thermal effect of short laser pulses induced by ultrafast spin reversal in TmFeO3single crystal.[2]The magnetic field induced gigantic magnetoelectric and ferroelectric phenomena in DyFeO3have also been studied.[15]In addition,terahertz time-domain spectroscopy has been used to describe the SR of ErFeO3,YFeO3,and NdFeO3single crystals.[16-18]Temperature induced SR transitions in SmFeO3, TbFeO3, and Ho0.5Pr0.5FeO3single crystals were detailedly studied.[8,19,20]The investigation of physical mechanism of SR transition in rare-earth orthoferrites can provide a deeper understanding of the the behavior of the 4f and 3d electrons. Besides, multiple magnetic transitions study may help to find new multiferroic and other spintronic materials.

In this work,magnetocrystalline anisotropy and dynamic spin reorientation of half-doped Nd0.5Pr0.5FeO3single crystal were detailedly studied. The anisotropic magnetic interactions and multiple magnetic phase transitions reflect the complex magnetic structure. The magnetic phase diagram of Nd0.5Pr0.5FeO3single crystal was finally obtained.

2. Experimental details

The Nd0.5Pr0.5FeO3single crystals were grown by the optical floating-zone furance(FZ-T-10000-H-VI-P-SH,Crystal System Inc). The preparation process has been described in detail in the previous literature.[21]The crystal morphology and compositional homogeneity were verified by x-ray diffraction (XRD). The orientation and quality of the crystal were determined by Laue back-reflection. Measurements of the magnetization as a function of magnetic field and temperature were conducted by using the physical property measurement system(PPMS-9,Quantum Design)with vibrating sample magnetometer option. In zero-field-cooling (ZFC) measurements, the crystal was cooled down to 2 K without external magnetic field,and then an external magnetic field was applied to conduct measurements during the process of heating to 300 K.The magnetic field dependence of magnetization was measured at selected temperatures after ZFC.

3. Results and discussion

The room temperature powder XRD data of Nd0.5Pr0.5FeO3single crystal were refined by Rietveld method in the FullProf program.[19]As shown in Fig.1(a),the diffraction patterns demonstrate the single-phase orthorhombic perovskite structure with space groupPbnmand no impure phase was detected. The lattice parameters are obtained to bea=5.46650 ˚A,b=5.58270 ˚A, andc=7.77310 ˚A. The spin-lattice interaction dictates the spin configuration and the canted FeO6octahedra, as shown in Fig. 1(b) made by the VESTA software. The clear Laue diffraction spots can easily be observed. Both the XRD pattern and Laue photography confirm the high quality of the single crystal, and the cutting planes are precisely perpendicular to the orthorhombica-,b-,andc-directions(Pbnmsetting),respectively.

Fig. 1. (a) The rietveld refinement of the powder XRD patterns for Nd0.5Pr0.5FeO3. It shows the experimental, calculated, and difference intensities along with the Bragg positions. (b) The simulated crystallography structure and the Laue photographs along the a-, b-, and cdirections of the Nd0.5Pr0.5FeO3 single crystal.

Figure 2 displays the temperature dependence of magnetization measured with an applied magnetic fieldH=0.01 T alonga-,b-, andc-directions of the Nd0.5Pr0.5FeO3single crystal. The visible magnetic anisotropy illustrates the complex magnetic interactions. As the temperature goes down from 300 K to 2 K, the sample shifts from aΓ4phase to aΓ2phase through a SR transition. To determine the phase transition parameters,we evaluated the derivations of the magnetization data atH=0.01 T alonga- andc-directions of the Nd0.5Pr0.5FeO3single crystal,the plotted curves are shown in Fig.3. The sample undergoes the SR transition in the temperature window from 45 K to 66 K as marked by green dotted lines. Above～66 K, the sample shows the spin characteristics ofΓ4phase. That is, it possesses FM moments atcdirection,G-and A-type AFM properties ata-andb-direction,respectively. Similar phenomena have been observed in the NdFeO3and PrFeO3orthoferrites.[12,13]Once a temperature below 45 K is achieved, the Fe3+spins shift to aΓ2state,

where the magnetic structure is changed to FM order, C-type AFM, and G-type AFM order ata-,b-, andc-direction, respectively. In the temperature window of 45-66 K,it exhibits a mixed feature ofΓ4phase andΓ2phase, and illustrates the dynamic transition process of the two phases,which is marked asΓ24(Gxz, Fxz) phase. One can see the color area marked asΓ2,Γ24, andΓ4in Fig. 2. In addition, the maximum value of magnetization ata-direction inΓ2state is much larger than that ofΓ4state atc-direction. As marked by the blue dotted line,the maximum value of magnetization atc-direction inΓ4state is～0.76 emu/g,and it changes to～3.12 emu/g ata-direction inΓ2state. The maximum value of magnetization inΓ2state has increased by～311% compared to the value inΓ4state.Therefore, we reasonably believe that the abnormal increase of magnetization at low temperatures is dominated by a new mechanism of magnetic interaction. It is interesting that the magnetization along theb- andc-direction inΓ2state continuously rises with temperature decreasing to the lowest temperature. As reported in previous literature,[13]the upwarping behavior at low temperatures in NdFeO3system is related to the increasingly polarization of magnetic rare-earth ions, and the effective moment of the Nd sublattice is antiparallel to that of the Fe sublattice and increases faster when the temperature reaches a compensation point. Furthermore, an enlarged latent plateau around～54 K alongb-direction is displayed in the figure inset,where the dynamic spin rotation from A-type AFM to C-type AFM state is visibly observed.

Fig.2.Temperature dependence of magnetization along the a-,b-and cdirection of Nd0.5Pr0.5FeO3 single crystal,measured in an external feild H=0.01 T.Γ2,Γ24 and Γ4 phases can be distinguished by the shaded areas. The inset is the zoom-in for the spin reorientation transition along the b-direction.

The SR transition temperature window is 6.5 K to 10 K for PrFeO3and 107 K to 170 K for NdFeO3.[12,13]As a mixture of PrFeO3and NdFeO3, half-doped Nd0.5Pr0.5FeO3performs the SR transition fromΓ4toΓ2state in the temperature window of 45 K to 66 K, which is exactly the intermediate region between the SR transitions of the two matrixes. The dynamic rotation process of spins is symbolically depicted in the insets of Fig. 3. It is commonly believed that the weak macroscopic FM moment(MFe=S1+S2)is induced by the antisymmetric DM interactions. Here,S1andS2are represented as two pairs of spins for Fe3+in the G-type AFM state.While cooling the sample below its N´eel temperature,MFecontinues to rotate from thec-direction inΓ4phase towards thea-direction inΓ2phase and always stays in theac-plane through the metastableΓ24(Gxz, Fxz) phase. As the temperature drops to～17 K, the magnetization is further enhanced and an anomaly occurs ata-direction in Fig.3,which implies a kind of new magnetic interactions and can account for the 311% increase in magnetization as displayed in Fig. 2. The increasing magnetization at～17 K may be linked to the transition from low-spin(S=1/2)to high-spin(S=5/2)state of Fe3+.[22,23]The volume change of Fe3+gives rise to the conflict of atomic Hund rules due to the changed crystal field and results in a further enhancement of the total moment(see the insets of Fig. 3). Another possible source of the unexpected anomaly at～17 K is theR3+-R3+and/orR3+-Fe3+interactions. More in-depth experimental research will be performed in other works.

Fig. 3. The calculated derivations of the magnetization data at H =0.01 T along a- and c-direction of Nd0.5Pr0.5FeO3 single crystal. The temperature window of dynamic spin reorientation is marked with green dotted lines. Insets illustrate the simplified spin configuration for Fe3+and R3+. The two pairs of spins for Fe3+ are visualized as S1 and S2 in the G-type AFM state,MFe represents the resultant FM moment of Fe3+, Mtotal represents the total FM moment of Fe3+ and/or R3+ at T ＜～17 K.

Figures 4(a)-4(b) show the magnetization curves under different magnitude fields alonga-andc-direction of the single crystal. In order to make the phase transition legible, the coordinate takes in the form of logarithm. It is clear that the magnetic phase transitions are particularly sensitive to the applied magnetic field. In Fig. 4(a), the SR temperature (TSR),marked by the green and red dotted lines, moves to higher temperatures with the increasing magnetic field applied atadirection. Figure 4(b)shows thatTSRmoves to the lower temperature region under a higher applied field paralleled tocdirection. According to the slope change of the magnetization curves,the phase boundaries can be depicted.The correspondingT-Hphase diagrams for Nd0.5Pr0.5FeO3single crystal are shown in Figs. 4(c) and 4(d). TheTSRvariation reflects the competition effects ofΓ4andΓ2phases and confirms the inverse effects of magnetic field on magnetic moment ata-andc-direction. Specifically, theΓ4state will be stabilized alongc-direction by the magnetic field, so the rotation of moments towards basal-plane will be transferred to a lower temperature,resulting in a decrease ofTSR. While the rising magnetic field is applied parallelly toa-direction, it will accelerate the rotation process of moments toa-direction, which yields the increase ofTSR. Furthermore,one can see that theTSRalongadirection is evidently higher than that alongc-direction under the identical conditions, which is owing to an asynchronous characteristic of theM(T)curves.[24]

Fig. 4. (a)-(b) Temperature dependence of magnetization at various magnetic field along the a- and c-direction of Nd0.5Pr0.5FeO3 single crystal. Γ2, Γ24 and Γ4 phases are separated by green and red dotted lines, respectively. (c)-(d) The corresponding phase diagrams for Nd0.5Pr0.5FeO3 single crystal. The phase boundaries are ascertained according to the slope change of the magnetization curves.

The isothermal magnetization loops are characterized to certify the nature of the magnetic state, selected results are shown in Figs. 5(a) and 5(b). In accord with theM(T) data in Figs. 2 and 4, the S-shaped hysteresis loops ata- andcdirection show weak FM features because of the multiple magnetic phase transitions of Fe3+and/orR3+,and the unsaturated magnetization is a typical characteristic of AFM state. The FM moment along the direction of thec-axis at high temperatures(T ≥100 K)is attributed to the canted magnetic moment of Fe3+,which rotates in the direction of thea-axis when the temperature drops below 40 K. In addition, one can see the residual magnetization at 10 K in Fig.5(a)is much larger than the values in Fig.5(b). This is due to the occurrence of a new FM phase at～17 K as discussed above. The insets of Fig.5 are enlargements of the magnetization curves at low magnetic fields, where we can read the coercivity and residual magnetization clearly. In the inset of Fig.5(a), the coercivity is observed to be zero atT ＜60 K.From 60 K to up,the coercive force gradually increases. At 300 K, the square shape hysteresis loop with a coercivity of～0.08 T is detected. The coercivity above the SR transition temperature is higher than that below it, which illustrates the stronger anisotropy in theΓ4state. Therefore, the magnetic excitation is closely related to the external temperature and applied magnetic field.

To further represent the nature of phase transitions for Nd0.5Pr0.5FeO3single crystal,we calculated the arrott plots by the isothermal magnetization data, as displayed in Figs. 5(c)and 5(d). The vertical coordinates are shown in logarithmic form for clear. The typical S-shape and the negative slope around～60 K imply a phase transition of first-order,which is believed to be related to the SR transition. By applying an external magnetic field, the temperature of the first-order phase transition in the direction ofa-axis moves to the higher temperatures,while that in the direction ofc-axis gradually moves to the lower temperatures.AboveTSR,the crystal is in theΓ4state with the resultant FM vector pointing along thec-direction of the crystal,and the phase transition of first-order is stimulated by a magnetic field alonga-direction.While the magnetic field is applied alongc-direction,there is no phase transition except that the magnetization is enhanced.

Fig.5.(a)-(b)Isothermal magnetization hysteresis loops up to 7 T were measured at various temperatures along the a-and c-direction of the Nd0.5Pr0.5FeO3 single crystal. Figure insets are the enlarged curves in the low magnetic fields region. (c)and(d)show the corresponding arrott plots.

4. Conclusion

The excellent quality single crystals of half-doped Nd0.5Pr0.5FeO3have been successfully grown by using the optical floating zone furnace. The crystal structure was characterized by XRD pattern and Laue back-reflection. The magnetic anisotropy and multiple phase transitions were detected by PPMS-9T under various temperatures and magnetic fields.Below 300 K, the weak FM moment is caused by the famous DM interactions due to the distortion of FeO6octahedra, which rotates from thec-direction to thea-direction of the single crystal (Pbnmsetting) in the temperature window from 66 K to 45 K.The dynamic SR transitionΓis verified to be first-order by arrott plots in various magnetic fields.

Acknowledgments

The authors thank Dr. Yiming Cao(Qujing Normal University)for the valuable discussion on crystal structure.

The data that support the findings of this study are available from the corresponding author upon reasonable request.