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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

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Double-exchange interaction La 1-x D x MnO 3 D: divalent elements 3-d La n(1-x) Sr 1+nx Mn n O 3n+1 n = # of layers. 2-d

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Phase diagram OOI

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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.

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Manganites Structure LaMnO 3 La +3 Mn +3 O -2 3 Mn +3 3d 4 xy, yz, zx orbitals form t 2g band, localized spin 3/2 x 2 -y 2, 3z 2 -r 2 form e g band, mobile spin 1/2 S=3/2+1/2 -------doping----- La 1-x Ca x MnO 3 La +3 Ca +2 Mn +4 O +2 3 Mn +3 3d 4 xy, yz, zx orbitals form t 2g band, localized spin 3/2 S=3/2.

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atom Crystal field e g t 2g Jahn-Teller distortion x 2 -y 2 3z 2 -r 2 xy xz, yz Mn YT

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Zener, Anderson, Hasegawa: Double-Exchange interaction

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Mean field picture

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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>

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

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Similar to one-magnon process.

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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

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f f f f f f f ff

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Charge ordering Many compounds cuperates manganites magnetites

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Nd doped La 2-x Sr x CuO 4 (Niemoller et. al.) ac-plane, Stripe in b-directuion

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Charge-ordered stripes seen in La 0.33 Ca 0.67 MnO 3 by Uehara, Mori, Chen and Cheong, Nature399, 560 (1999).

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DV 2 O 4 D: divalent elements New J. Phys. 7, 53. Radaelli PRL 93 157206. Tchernyshyov

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cubic to monoclinic Miles, et. al. Rev. Mod. Phys. 29, 279 Orbital ordering Fe 3 O 4 Verway transition

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O O -2 O A-type: 1/3 Fe +2 O B-type: 1/3 Fe +2 O B-type: 1/3 Fe +3

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Orbital ordering Manganite, Spinel (AB 2 X 4, MgTi 2 O 4, FeSc 2 S 4 ), R 1-x A x TiO 3, TiOX (X=Cl,BR), V 2 O 3, LiNiO 2, NaTiO 2, Ca 3 Ru 2 O 7, KCuF 3, Fe 3 O 4,

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Fe 3 O 4 PRL 93, 156403. Jen, Guo, Huang PRB 66, 214422. Wright, Attfield, Radaelli

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

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La 0.5 Ca 0.5 MnO 3 La 0.5 Sr 1.5 MnO 4 PR 100, 545. Wollen, Koehler PR 100, 564. Goodenough : Mn 4+, : spin, lobes: orbitals of Mn 3+

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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.

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PRL. 88 167204 Kim et. al.

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

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polaron? small polaron large polaron

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

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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.

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La 0.5 Sr 1.5 MnO 4 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 Mn 3+ and Mn 4+ 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: y 2 -z 2 and x 2 -z 2.

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