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Magnetic transitions of multiferroics revealed by photons

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. Multiferroicity Soft x-ray magnetic scattering Magnetic transitions and switch of spin chirality. May 9, 2007. Collaborators National Synchrotron Research Center:

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Magnetic transitions of multiferroics revealed by photons

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  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 • Multiferroicity • Soft x-ray magnetic scattering • Magnetic transitions and switch of spin chirality May 9, 2007

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

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

  4. Magnetoelectric effect Induction of magnetization by an electric field; induction of polarization by a magnetic field. - first presumed to exist by Pierre Curie in 1894on the basis of symmetry considerations M. Fiebig, J. Phys. D: Appl. Phys 38, R123 (2005) Materials exhibiting ME effect: Cr2O3 BiMnO3 BiFeO3 ….. However, the effects are typically too small to be useful in applications!

  5. (Ferro)magnetism vs. (Ferro)electricity Pauli vs. Coulomb Magnetic moment: unfilled d bands impurities (La,Sr)MnO3: spins from : 3d3 or 3d4 Exchange interactions: - superexchange TM O TM Mn double exchange

  6. Large displacement often involved in ferroelectricity Pb-O plane Ti-O plane • PbTiO3: • Pb-O covalent bond cubic 800 K Ti4+ tetragonal 300 K O Pb TC=763 K Kuroiwa et al, PRL87 217601 (2001)

  7. Ba+2 0.04 Å + - 0.05 Å 0.10 Å + O-2 Ti+4 (Ferro)magnetism vs. (Ferro)electricity Classic examples: BaTiO3 or PbTiO3 polarization from cation/anion paired diploes Ti+4 3d0 O 2p2 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 RMnO3 and RMn2O5 (R=Tb, Ho , …) TbMnO3: Kimura et al., Nature 426, 55, (2003) TbMn2O5: Hur et al., Nature 429, 392 (2004) revived interest in “multiferroicity” Magnetism and ferroelectricity coexist in materials called “multiferroics.” • TC < TN • Frustrated magnetic systems.

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

  11. T=15 K TbMnO3 antiferromagnetic TN=42 K H // b TC=27 K Kimura et al. Nature, 426, 55 (2003) collinear magnetic order, inversion symmetric TN=42 K non-collinear magnetic order, inversion symmetry broken T=35 K Kenzelmann et al., PRL 95, 087206 (2005)

  12. TbMn2O5Nature, 429, 392 (2004) antiferromagnetic TN=42 K

  13. Frustrated magnets: RMnO3, RMn2O5 TC < TN polarization governed by magnetism ? Issues: -What is the underlying mechanism of the gigantic ME effect? -What kind of spin configurations supports electric polarization? Mostovoy PRL (2006) L spiral ? collinear ?

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

  15. Symmetry properties

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

  17. Microscopic theory • Atomic displacement + antisymmetric exchange interaction Sergienko and DagottoPRB 73, 094434 (2006) Sergienko,Sen and DagottoPRL 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. Electric polarization induced by “spin current” What is spin current? Heisenberg Model:

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

  22. Magnetic transitions and switch of spin chirality in CoCr2O4

  23. CoCr2O4 field cooling 0.01 T spinel Yamasaki et al. PRL 96, 207204(2006) conical spin structure ferrimagnetic TC= 93 K TS= 26 K

  24. CoCr2O4 Yamasaki et al. PRL (2006) [001] P//[-110] q// [110] The spin-current model

  25. (4,4,0) Bragg peaks of CoCr2O4 (2,2,0) q=(2/3,2/3,0) interlayer spacing of (110) lattice planes L L110 reciprocal space (110) real space a b* (2p/a) a* (2p/a)

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

  27. Soft x-ray magnetic scattering

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

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

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

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

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

  33. Resonant X-ray magnetic scattering q electric dipole transitions Hannon et al., PRL(1988) F1,1F1,-1 scattering amplitudes As a result of spin-orbit and exchange interactions, magnetic ordering manifests itself in resonant scattering.

  34. Resonant soft x-ray scattering of CoCr2O4 X-ray absorption X-ray scattering q=(0.63, 0.63, 0) 3d 778 eV 2p3/2 Co

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

  36. reciprocal space For a given x, switch of chirality: d  - d

  37. Summary We can “see” spin order of TMO’s by using photons. • Multiferroicity • ME from an internal field determined by . • CoCr2O4 • Magnetic lock-in transition revealed with resonant soft x-ray scattering • Switch of spin chirality.

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