Presentation on theme: "Some interesting physics in transition metal oxides: charge ordering, orbital ordering and spin-charge separation C. D. Hu Department of physics National."— Presentation transcript:
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
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
Phase diagram OOI
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.
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.
atom Crystal field e g t 2g Jahn-Teller distortion x 2 -y 2 3z 2 -r 2 xy xz, yz Mn YT
orbital? PRB. 58, 11841 Kilian and Khaliulin J. Phys. Soc. Jpn. Shiba et. al.
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.
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.