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C. D. Hu Department of physics National Taiwan University

Some interesting physics in transition metal oxides: charge ordering, orbital ordering and spin-charge separation. C. D. Hu Department of physics National Taiwan University. 1. Introduction to double-exchange interaction (DE) 2. Introduction to charge ordering

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C. D. Hu Department of physics National Taiwan University

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  1. Some interesting physics in transition metal oxides: charge ordering, orbital ordering and spin-charge separation C. D. Hu Department of physics National Taiwan University 1. Introduction to double-exchange interaction (DE) 2. Introduction to charge ordering 3. Introduction to orbital ordering and orbital dynamics 4. Interplay between double-exchange interaction, charge ordering, and orbital ordering

  2. Double-exchange interaction La1-xDxMnO3 D: divalent elements 3-d Lan(1-x)Sr1+nxMnnO3n+1 n = # of layers. 2-d

  3. Phase diagram OOI

  4. CMR: Temperature Dependence The electrical resistance depends strongly on applied magnetic field.As the temperature is increased through the ferromagnetic Curie temperature Tc, the MR ration rises sharply.

  5. Manganites Structure LaMnO3 La+3 Mn+3 O-23 Mn+3 3d4 xy, yz, zx orbitals form t2g band, localized spin 3/2 x2-y2, 3z2-r2 form eg band, mobile spin 1/2 S=3/2+1/2 -------doping----- La1-xCaxMnO3 La+3 Ca+2 Mn+4 O+23 Mn+3 3d4 xy, yz, zx orbitals form t2g band, localized spin 3/2 S=3/2.

  6. eg x2-y2 3z2-r2 YT Crystal field xy xz, yz t2g atom Jahn-Teller distortion  Mn

  7. Zener, Anderson, Hasegawa: Double-Exchange interaction

  8. Mean field picture

  9. Recent Development (PRB 64,054406(2001)) From the point of view of the total spin on a site. |S=3/2,m> and |1/2,+1/2>  |S=2,m+1/2> |S=3/2,m> and |1/2,-1/2>  |S=2,m-1/2>

  10. Slave fermion combine α or β with the localized spin. Schwinger bosons Finally

  12. Similar to one-magnon process.

  13. Saito, et. al., PRB 62,1039 (2000). Experimental results II: ARPES shape of Fermi edge(1) Different from that of Gold (metal).(2) Temperature sensitive

  14. f f f f f f f f f

  15. Charge ordering • Many compounds • cuperates • manganites • magnetites

  16. Nd doped La2-xSrxCuO4(Niemoller et. al.) ac-plane, Stripe in b-directuion

  17. Charge-ordered stripes seen in La0.33Ca0.67MnO3 by Uehara, Mori, Chen and Cheong, Nature399, 560 (1999).

  18. DV2O4 D: divalent elements New J. Phys. 7, 53. Radaelli PRL 93 157206. Tchernyshyov

  19. Orbital ordering Fe3O4 Verway transition Miles, et. al. Rev. Mod. Phys. 29, 279 cubic to monoclinic

  20. Fe3O4 Verway transition O O-2 OA-type: 1/3 Fe+2 O B-type: 1/3 Fe+2 OB-type: 1/3 Fe+3

  21. Orbital ordering Manganite, Spinel (AB2X4, MgTi2O4, FeSc2S4), R1-xAxTiO3, TiOX (X=Cl,BR), V2O3, LiNiO2, NaTiO2, Ca3Ru2O7, KCuF3, Fe3O4,

  22. Fe3O4 PRL 93, 156403. Jen, Guo, Huang PRB 66, 214422. Wright, Attfield, Radaelli

  23. Interplay between DE and OO x, y-direction tx(y) z-direction tz (PR. 93, 1498. Slater, Koster) simple cubic lattice

  24. La0.5Ca0.5MnO3 La0.5Sr1.5MnO4 PR 100, 545. Wollen, Koehler PR 100, 564. Goodenough : Mn4+, : spin, lobes: orbitals of Mn3+

  25. Summary 1. A lot of interesting phenomena. 2. Orbital dynamics is simple. 3. With the new form of DE, the system seems to be managable.

  26. PRL. 88 167204 Kim et. al.

  27. PRL. 81, 1517 x=0.3 Feathures: Drude peak and broad peak

  28. polaron? small polaron large polaron

  29. orbital? PRB. 58, 11841 Kilian and Khaliulin J. Phys. Soc. Jpn. Shiba et. al.

  30. Probing the orbital ordering Resonant x-ray scattering (RXS) : An Incident photon excites an electron to a higher level. The Electron emits a photon and falls to a lower state.

  31. La0.5Sr1.5MnO4 1s4p (PRL 80, 1932. Murakami et. al.) 1. The energy of 4p state is affected by the electrons at 3d state. 2. The energies of 4p state of Mn3+ and Mn4+ are different. 3. Intensity varies with the direction of polarization due to the Aj coupling. 4. Incident photon:  polarization. z-axis: b direction. orbitals: y2-z2 and x2-z2.

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