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Spin-polarization coupling in multiferroic transition-metal oxides

Spin-polarization coupling in multiferroic transition-metal oxides. Shigeki Onoda (U. Tokyo) Chenglong Jia (KIAS) Jung Hoon Han (SKKU) Naoto Nagaosa (U. Tokyo). Multiferroics with noncollinear magnetic and ferroelectric phase. RED = magnetic ions. Common & uncommon features. In this talk.

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Spin-polarization coupling in multiferroic transition-metal oxides

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

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

  3. Common & uncommon features

  4. In this talk A microscopic theory of spin-polarization coupling for arbitrary d-electron configuration is presented

  5. 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

  6. 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

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

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

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

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

  11. 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

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

  13. t2g-eg mixing (C.D.Hu, cond-mat/060470; 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 may be relevant for CuFeO2(t2g)3 (eg)2 MnWO4(t2g)3 (eg)2

  14. 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;

  15. 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:

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