Spin-polarization coupling in multiferroic transition-metal oxides

1. Spin-polarizationcouplingin multiferroic transition-metal oxides Jung Hoon Han (SKKU) Chenglong Jia (KIAS) Shigeki Onoda (RIKEN) Naoto Nagaosa (U Tokyo)

2. 2007 호암상 수상자 정상욱 박사는 터븀망간산화물이 전기적 성질과 자기적 성질을 함께 가지는 다중강성 물질임을 확인하고 자기장을 이용, 전기편극 현상을 제어할 수 있음을 세계 최초로 입증한 업적을 평가받았다. (2007.04.04.)

3. Early indications of multiferroics Hexagonal YMnO3 Ferroelectricity along z (Tc>>RT); Domain wall for (+P,-P) AFM within xy (TN=70K); Domain wall for (+M,-M) Coupling of the FE and AFM domain walls Observed through second harmonic generation techniques Park PRB68, 104426 (2003) Nature 419, 818 (2002) Cited: 138

4. Coupling of FE and AFM domain walls Fiebig Nature419, 818 (2002) Sign change of FE is ALWAYS accompanied by sign change of AFM Sign change of AFM is NOT ALWAYS accompanied by sign change of FE

5. Control of ferroelctricity using magnetism Nature 426, 55 (2003) Cited: 248 Nature 429, 392 (2004) Cited: 152 TbMnO3 TbMn2O5

6. Control of ferroelctricity using magnetic field Cheong & Mostovoy Review Nature Materials 6, 13 (2007) Magnetic field along a switches polarization from +b to -b axis in TbMn2O3 (Hur) Magnetic field along b switches polarization from c to b axis in TbMnO3 (Kimura)

7. Connection to Spiral Magnetism The original work of Kimura demonstrated controllability of FE through applied field Connection to magnetism made clear by later neutron scattering study of Kenzelman et al. T

8. Connection to Spiral Magnetism Spin flop concomitant with the polarization re-orientation in TbMnO3 Ferroelectricity in Tb(Dy)Mn2O5 not associated with spiral magnetic order; Will not be discussed in this talk

9. Connection to Spiral Magnetism Basic theoretical idea is that one can have a coupling linear in P(olarization) and quadratic in M(agnetism) through Mostovoy PRL96, 067601 (2006) Nonzero gradient in magnetism usually due to spiral spins, which in turn arises in frustrated spin-spin interaction (triangular lattice, Kagome lattice, J3-J4-J5 interactions, etc)

10. Connection to Spiral Magnetism With spiral magnetism one can define a SENSE of ROTATION which is given by the outer product of two adjacent spins C=<Si x Sj> It is an Ising order parameter which inverts sign under inversion; Can couple to another Ising order parameter with same symmetry, P. as C*P (Can understand clamping); For collinear magnetism the sense of rotation is ill-defined

11. Two types of spin-polarization coupling Exchange-striction type: (RMn2O5) Dzyaloshinskii-Moriya type: (RMnO3 and many others)

12. Multiferroics with noncollinear magnetic and ferroelectric phase RED = magnetic ions

13. Common & uncommon features

14. Crystal Zoo TbMnO3 Arima PRL96, 097202 (2006) Ni3V2O8 Lawes PRL93, 247201 (2004) Ba0.5Sr1.5Zn2Fe12O22 Kimura PRL94, 137201 (2005) CoCr2O4 Yamasaki PRL96, 207204 (2006)

15. Crystal Zoo LiCuVO4 Naito cond-mat/0611659 CuFeO2 Kimura PRB 73, 220404 (2006) LiCu2O2 Park PRL 98, 057601 (2007) MnWO4 Taniguchi PRL 97, 097203 (2006)

16. In this talk The physics of spin-polarization coupling must be local, involving a cluster of transition metals and ligands A microscopic theory of spin-polarization coupling for arbitrary d-electron configuration is presented, assuming spin-orbit interaction as the underlying mechanism

17. Existing theories Phenomenological theories of Mostovoy & Harris provide general ground for writing down the spin-polarization coupling Microscopic derivation first given by Katsura, Nagaosa, Balatsky (2005) Physical origin: spin-orbit interaction

18. Developing a Microscopic Theory M O M O M O M O M O M O M O M A linear chain consisting of alternating M(agnetic) and O(xygen) atoms is a reasonable model for magneto-electric insulators The building block is a single M-O-M cluster. We solve this model as exactly as possible for realistic d-electron configurations: t2g, eg, mixed t2g-eg Previous theory of KNB based on t2g orbitals, although none of the realistic multiferroics are pure t2g

19. Multiferroics with noncollinear magnetic and ferroelectric phase RED = magnetic ions

20. Our Result Jia, Onoda, Nagaosa, Han, cond-mat/0701614

21. Classification of spin-orbit interactions In all instances we find non-zero Psp associated with noncollinear magnetic order Pspis reallyUNIVERSAL

22. t2g t2g t2g p Both Porb and Psp are found

23. eg eg eg p Only Psp exists due to oxygen p-orbital spin-orbit interaction Relevant to d8 NVO; d9LiCu2O2 ,LiCuVO4

24. Mixed t2g-eg: Model for TbMnO3 • Ingredients: • Orbital ordering takes place at high temperature -> • Inversion symmetry is broken; two-sublattice structure to begin with -> • Need to generalize theory for two-sublattice orbitals • (2) d4 (t2g)3 (eg)1 configuration gives rise to (t2g)-(eg) mixing and polarization • (3) Spin-orbit coupling at oxygen gives rise to polarization

25. t2g-eg mixing (C.D.Hu, cond-mat/0608470; Our work) Mixing of occupied spin-up eg state and unoccupied spin-down t2g state Gives rise to Psp Numerical estimate using realistic parameters of TbMnO3 consistent with experimentally measured polarization Same mechanism must be relevant for CuFeO2(t2g)3 (eg)2 MnWO4(t2g)3 (eg)2

26. Loss of Inversion Symmetry A new term along the cluster axis due to lack of inversion symmetry; No spin-orbit interaction is required

27. Two-sublattice structure gives further peaks at Spin-current type of polarization is the only UNIFORM POLARIZATION Relevance for X-ray scattering For a helical spin pattern at wavevector Q, there arises lattice modulations due to induced polarization at various wavevectors;

28. Summary A general theory of magnetism-induced dipole moment is presented The mechanisms can be classified according to t2g, e g, and mixed t2g-e gconfigurations One can identify the origin of improper ferroelectricity in diverse d-electron configurations as follows:

29. Abstracting away Spiral spin phase supports an additional DISCRETE order parameter having to do with the sense of spin rotation This OP can couple to uni-directional polarization P Can we envision a phase without magnetic order, but still has the remnant of chirality? T, frustration Magnetic Chiral Paramgnetic Ferroelectric

30. Known examples Nersesyan et al proposed a spin ladder model (S=1/2) with nonzero chirality in the ground state Nersesyan PRL 81, 910 (1998) Arrows indicate sense of <SixSj*z>=<SixSjy– SiySjx>=Jij

31. Known examples Nersesyan’s model equivalent to a single spin chain with both NN and NNN spin-spin interactions

32. Known examples Later DMRG found chiral phase not for S=1/2, but for S=1 Hikihara JPSJ 69, 259 (2000) Chiral ground state carries nonzero expectatation value of <SixSjy– SiySjx> No mention of the structure of the ground state in Hikihara’s paper; only numerical reports Spin-1 chain has a well-known exactly solvable model established by AKLT

33. Zittartz’s work Meanwhile, completely independent of Nersesyan and Hikihara and much earlier, Zittartz found exact ground state for the class of anisotropic spin interaction models Klumper ZPB 87, 281 (1992) Both the NNN interaction (considered by Nersesyan, Hikihara) and biquadratic interaction (considered by Zittartz) tend to introduce frustration and spiral order Zittartz’s ground state may support nonzero chirality (We are working on it)

34. 2D Examples? We consider the modification of the antiferromagnetic XY model on the triangular lattice In the spin language this is equivalent to putting a bi-quadratic interaction, and =0 in Zittartz’ model We did Monte Carlo (MC) on the classical J1-J2 model

35. Order Parameters Order parameters referring to magnetic, nematic, and chiral orders are defined

36. Magnetic, Nematic, Chiral

37. Phase Diagram T paramagnetic nematic magnetic X=1 X=0 The interaction strengths are parameterized as follows Qualitatively the phase diagram looks like Nematic phase also appears to be chiral

38. Lesson? Perhaps a spin system with a sufficiently large frustrating interaction will support a chiral phase, and hence a ferroelectricity, without having the magnetic order