Title: Multiferroics 台灣大學物理系 胡崇德 (C. D. Hu) Abstract

1. Title: Multiferroics 台灣大學物理系 胡崇德 (C. D. Hu) Abstract Multiferroics is the type of material which possesses several long-range orders. These long-range orders, such as ferroelectric order, (anti)ferromagnetic order, ferroelastic order are coupled with each other and give rise to interesting physical phenomena. Experiments such as magnetic susceptibility measurement, spin-polarized neutron scattering and synchrotron radiation can give us important information of the cause of multiferrroics. Several theoretical models of the mechanism will be introduced. The emphasis will be on the "spin-current" model in which spin-orbit interaction will play the essential role. 1. Introduction. 2. Experiments. 3. Models. 4. Conclusion.

2. 1. Introduction Multiferroics: The kind of material which have several long-range orders such as antiferromagnetism and ferroelectricity. http://physics.aps.org/ articles/v2/20 Physics 2, 20 (2009) Daniel Khomskii Illustration: Alan Stonebraker

3. Ferroelectricity: Material which has net electric polarization. BiFeO3 lone-pair of 6s-electrons of Bi(3+) YMnO3 tilting of MnO5 BaTiO3 movement of Ti(4+) TbMn2O5 dimerization

4. Antiferromagnetism: Material which has no net magnetization but has long-range magnetic order. Sinusoidal Cycloidal spiral Proper screw

5. There are more than 100 multiferroic compounds. Type I multiferroics High Tc and large electric polarization, but weak coupling between electricity and magnetism. Type II multiferroics Low Tc and small electric polarization, but strong coupling between electricity and magnetism.

6. K.F. Wan, J.-M. Liu and Z.F. Ren, Advances in Physics 58, 321–448 (2009)

9. 2. Experiments RMnO3 orthorhombic c b a O: Oxygen R: Rare earth elements Mn: Manganese

10. Kimura et. al. PRB 71 224425 (2005), TN=41K, Tlock=28K.

11. Kenzelmann et. al. PRL 95, 087206 (2005) neutron scattering

13. 3. Models Why are electric polarization and magnetic order coupled? Maxwell's equations

14. A. Atomic displacement (lattice distortion) Ca3CoMnO6 Choi et. al., PRL 100, 047601 (2008) face-sharing octahedra along c-axis

15. 4+ 2+ 4+ 2+ 4+ 2+ 4+ 2+ 4+ Mn Co

16. B. Spin current model H. Katsura, N. Nagaosa and A. V. Balatsky, PRL 95, 057205 z TM1 O TM2 S1 y S2 x p V  eg eg

17. d-orbitals under crystal field of cubic symmetry

18. hybridization Hund’s coupling Sj: local spin Direction: sj: mobile spin

19. spin-orbit interaction

20. electronic origin       P

21. z Result y x spiral spin

22. spin current spin current  electric field  electric polarization AC (Aharonov-Casher) effect charge accumulation

23. Spiral Spin and Orbital Ordering The spin current model gives a very small electric polarization. It is due to cancellation of the contribution of entire energy band.

25. Conclusion 1. Multiferroics is a field of rich physics. 2. Multiferroics is a field driven by experiments. 3. The theoretical models are not complete. 4. Multiferroics is related to a lot other physical phenomena such as, lattice distortion, charge order, orbital order, spintronics, and magnetic properties.

26. Polarization and Dzyaloshinskii-Moriya interactionI. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958).Tôru Moriya, Phys. Rev. 120, 91 (1960) exchange interaction with spin-orbit coupling V SO E SO V D(/E) (t2/U), D/JSEg/g

28. Relation between multiferroics and DM

29. DM interaction Spin current i: bond direction Gauge field AC effect

30. z y x Eeff,z s jxy Mn O Mn