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 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

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 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.

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

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

11. 

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 ff

15. Charge ordering Many compounds cuperates manganites magnetites

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

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

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

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

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

21. 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,

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

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

25. 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+

26. 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.

27. PRL. 88 167204 Kim et. al.

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

29. polaron? small polaron large polaron

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

31. 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.

32. 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.