1. Magnetic transitions of multiferroics revealed by photons 黃迪靖 同步輻射研究中心 清華大學物理系 May 9, 2007 Multiferroicity Soft x-ray magnetic scattering Magnetic transitions and switch of spin chirality

2. Collaborators National Synchrotron Research Center: J. Okamoto, K. S. Chao, H. H. Wu, H.-J. Lin, and C. T. Chen National Tsing Hua Univ. : C. Y. Mou Rutgers Univ. : S. Park, J. Y. Choi, and S-W. Cheong Acknowledgement C. D. Hu, National Taiwan University 趙國勝 吳雪鴻 林宏基 陳建德 牟中瑜 胡崇德

3. Magnetism: ordering of spins Ferroelectricity: polar arrangement of charges Magnetization can be induced by H field Electric polarization can be induced by E field

4. Induction of magnetization by an electric field; induction of polarization by a magnetic field. - first presumed to exist by Pierre Curie in 1894 on the basis of symmetry considerations However, the effects are typically too small to be useful in applications! Magnetoelectric effect Materials exhibiting ME effect: Cr 2 O 3 BiMnO 3 BiFeO 3 ….. M. Fiebig, J. Phys. D: Appl. Phys 38, R123 (2005)

5. (Ferro)magnetism vs. (Ferro)electricity (La,Sr)MnO 3 : spins from : 3d 3 or 3d 4 Magnetic moment: - unfilled d bands impurities Pauli vs. Coulomb Exchange interactions: superexchange double exchange Mn TM O

6. Large displacement often involved in ferroelectricity PbTiO 3 : Pb-O covalent bond cubic 800 K tetragonal 300 K Pb-O planeTi-O plane Pb O Kuroiwa et al, PRL87 217601 (2001) T C =763 K Ti 4+

7. (Ferro)magnetism vs. (Ferro)electricity Classic examples: BaTiO 3 or PbTiO3 polarization from cation/anion paired diploes - O -2 Ba +2 0.10 Å 0.05 Å 0.04 Å + + Ti +4 Ti +4 3d 0 O 2p 2 Filled or empty d band, no room for magnetism!

8. Two contrasting order parameters Magnetization: time-reversal symmetry broken Polarization: inversion symmetry broken

9. Recently discovery in the coexistence and gigantic coupling of antiferromagnetism and ferroelectricity in frustrated spin systems such RMnO 3 and RMn 2 O 5 (R=Tb, Ho, …) revived interest in “multiferroicity” T C < T N Frustrated magnetic systems. TbMnO 3 : Kimura et al., Nature 426, 55, (2003) TbMn 2 O 5 : Hur et al., Nature 429, 392 (2004) Magnetism and ferroelectricity coexist in materials called “multiferroics.”

10. Normal antiferromagnet geometrically frustrated magnetization ? FM AFM frustrated spin chains spin frustration J >0

11. T=35 K T=15 K T N =42 K T C =27 K TbMnO 3 antiferromagnetic T N =42 K Kenzelmann et al., PRL 95, 087206 (2005) collinear magnetic order, inversion symmetric non-collinear magnetic order, inversion symmetry broken Kimura et al. Nature, 426, 55 (2003) H // b

12. TbMn 2 O 5 Nature, 429, 392 (2004) antiferromagnetic T N =42 K

13. Issues: -What is the underlying mechanism of the gigantic ME effect? - What kind of spin configurations supports electric polarization? Mostovoy PRL (2006) Frustrated magnets: RMnO 3, RMn 2 O 5 T C < T N  polarization governed by magnetism ? spiral ? collinear ? 

14. Phenomenological Ginzburg-Landau approach Lowest order in the expansion of the free energy: magnetization at modulation vector internal field from spins

15. Symmetry properties

16. Phenomenological Ginzburg-Landau approach Mostovoy PRL(2006) noncollinear spins, e.g. spiral Okamoto et al., PRL 98, 157202 (2007)

17. Microscopic theory Atomic displacement + antisymmetric exchange interaction Sergienko and Dagotto PRB 73, 094434 (2006) Sergienko,Sen and Dagotto PRL 97, 227204(2007) Spin current Katsura et. al., PRL 95, 057205 (2005) Jia et. al. PRB 74, 224444

18. How to induce polarization without involving atomic displacement? Essential Physics: Motion of magnetic moments induces electric dipoles! – the intrinsic Aharonov-Casher Effect Einstein and Laub (1908): A magnetic dipole moment m that moves with constant velocity should develop an electric dipole moment

19. Hirsch, PRL 83, 1834 (1999)

20. What is spin current? Heisenberg Model: Electric polarization induced by “spin current”

21. The spin-current model Katsura et. al., PRL 95, 057205 (2005)

22. Magnetic transitions and switch of spin chirality in CoCr 2 O 4

23. Yamasaki et al. PRL 96, 207204(2006) CoCr 2 O 4 ferrimagnetic T C = 93 K conical spin structure T S = 26 K spinel field cooling 0.01 T

24. P//[-110] [001] q// [110] CoCr 2 O 4 Yamasaki et al. PRL (2006) The spin-current model

25. a* (2  /a) b* (2  /a) a interlayer spacing of (110) lattice planes q=(2/3,2/3,0) real space reciprocal space (2,2,0) (4,4,0) Bragg peaks of CoCr 2 O 4    (110)

26. Tomiyasu et al. PRB (2006) (2- , 2- , 0)  =0.63 Yamasaki et al. PRL (2006) Correlation length (nm) P

27. Soft x-ray magnetic scattering

28. Elastic x-ray scattering scattering form factor momentum transfer A volume element at will contribute an amount to the scattering field with a phase factor. Fourier transform of charge distribution. Bragg condition: q = modulation vector of charge, spin, or orbital order elastic scattering Fourier transform of spin distribution.

29. Scattering accumulates microscopic effects and reveals macroscopic properties. X-ray scattering magnetization at modulation vector

30. Elastic x-ray scattering scattering form factor momentum transfer A volume element at will contribute an amount to the scattering field with a phase factor. Fourier transform of charge distribution. Bragg condition: q = modulation vector of charge, spin, or orbital order elastic scattering Fourier transform of spin distribution. Detectable with x-ray?

31. X-ray magnetic scattering : spin density Relevant interactions: Spin-orbit interactions:

32. kinetic energy m.Bm.B SO Non-resonant for   ~ 600 eV X-ray magnetic scattering Resonant Blume, J. Appl. Phys. (1985)

33. Resonant X-ray magnetic scattering electric dipole transitions F 1,1 F 1,-1 q scattering amplitudes Hannon et al., PRL(1988) As a result of spin-orbit and exchange interactions, magnetic ordering manifests itself in resonant scattering.

34. X-ray absorption X-ray scattering q=(0.63, 0.63, 0) 3d 2p 3/2 Co 778 eV Resonant soft x-ray scattering of CoCr 2 O 4

35. [001] q // [110] P // [-110]

38. reciprocal space For a given x, switch of chirality:   

39. We can “see” spin order of TMO’s by using photons.  Multiferroicity ME from an internal field determined by. Summary   CoCr 2 O 4 Magnetic lock-in transition revealed with resonant soft x-ray scattering Switch of spin chirality.