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.
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. Material which has no net magnetization but has long-range
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, (2008)
face-sharing octahedra along c-axis

15.
Mn Co

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

17. d-orbitals under crystal field of cubic symmetry

18. Sj: local spin Direction: sj: mobile spin
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  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 interaction I. Dzyaloshinskii, J. Phys. Chem. Solids 4, 241 (1958). Tôru Moriya, Phys. Rev. 120, 91 (1960)
exchange interaction with spin-orbit coupling E SO V 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