1. S. Maekawa (IMR, Tohoku University) Spin, Charge and Orbital and their Excitations in Transition Metal Oxides Contents: i) Spin-charge separation in one-dimensional cuprates, ii) Non-linear optical response due to spin-charge separation, iii) Orbital in High Tc cuprates, iv) Anomalous transport properties due to orbital, v) Thermo-electric response due to spin and orbital, (Hong Kong, Dec. 18, 2006)

2. Internal degrees of freedom of electron SpinMagnet ChargeElectric Current z x y Oxygen d(3z 2  r 2 ) d(x2y2)d(x2y2) d(xy)d(yz)d(zx) Orbital (Shape of wave function: Shape of electron)

3. Hong Kong Conference December 18, 2006 Anomalous Electronic Lattices in Cobaltates S. Maekawa, W. Koshibae and N. Bulut (IMR, Tohoku University, Sendai)

4. Co - Oxides in triangular lattice (Na x CoO 2 and Na x CoO 2 ・ yH 2 O) i) Review of Unconventional properties ii) Orbital degeneracy in the frustrated lattice crystal lattice vs. electron lattice unconventional properties

5. x Co 3+ (3d 6 ) and (1  x) Co 4+ (3d 5 ) in CoO 6 units CoO 6 octahedron Crystal Structure CoO 2 layer edge-shared CoO 6 units Na layer CoO 2 layer Na layer CoO 2 layer In Na x CoO 2,

6. K. Takada, H. Sakurai, E. Takayama- Muromachi, F. Izumi, R.A. Dilanian, T. Sasaki, Nature 422, 53 (2003). Superconductivity in water-intercalated Na x CoO 2 ·yH 2 O Na layer CoO 2 layer H2OH2O

8. In cubic CoO 6 units, Co 3+ egeg t2gt2g Co 4+ Co 3+ (3d 6 ) S = 0 Co 4+ (3d 5 ) S = 1/2 z x y d(3z 2  r 2 ) d(x2y2)d(x2y2) d(xy)d(yz)d(zx) 5 - 3d orbitals egeg t2gt2g Na x CoO 2 :

9.  Anomalous physical properties in CoO 2 layer: i.Giant Hall effect at T  R.T. Na x CoO 2 (Y. Wang, et al., cond-mat/0305455) ii.Ferromagnetism [Bi 2  x Pb x Sr 2 O 4 ] y CoO 2, T c  3.2 K (I. Tsukada et al., J. Phys. Soc. Jpn. 70, 834 (’01).) iii.Giant thermopower at T  R.T. Na x CoO 2 (I. Terasaki, Y. Sasago, and K. Uchinokura, PRB56, 12685(’97).) [Bi 2  x Pb x Sr 2 O 4 ] y CoO 2 (T. Yamamoto et al., Jpn. J. Appl. Phys. 39, L747 (’00).) Ca 3 Co 4 O 9 (A. C. Masset et al., PRB62, 166 (’00).) iv.Superconductivity Na x CoO 2 ·yH 2 O (K. Takada et al., Nature 422, 53 (’03).) v.Charge ordering Na x CoO 2 (Foo et al., cond-mat/0312174) vi.Antiferromagnetism Na 0.5 CoO 2 (T. Uemura et al.)

10. I. Terasaki, Y. Sasago, and K. Uchinokura, PRB56, 12685(’97). Y. Wang et al., cond-mat/0305455

11. Novel physics in CoO 2 layer with triangular structure 1.Kagomé lattice hidden in CoO 2 layer (WK and SM: PRL 91, 257003 (’03), NB, WK and SM: PRL 95, 037001 (05)) 2.Anomalous physical properties: - Superconductivity (G. Khaliullin, WK and SM: PRL93, 176401(’04)) - Hall effect (WK, A. Oguri and SM: unpublished) - Thermopower and Nernst effect (WK and SM: PRL 87, 236603 (’01). ) t 2g orbital degeneracy in edge-shared CoO 6 units

12. CoO 2 layer Edge shared octahedra 90 degrees O Co x y z 2px2px d(xy) d(zx) +      + +   2px2px d(xy) +          OK to GO ! NO GO ! OK to GO ! Kagomé in triangular lattice

13. Martin Indergand, Yasufumi Yamashita, Hiroaki Kusunose, Manfred Sigrist ， ( cond-mat/0502116)

14. xy yz zx Hopping of a 3d electron via O2p orbital x y z CoO 2 layer

15. xy yz zx xy zx yz The triangular lattice of Co ions is resolved into four Kagomé lattices (green, yellow, red and white) for the electronic states. WK & SM, PRL91, 257003 (’03).

17. I. Terasaki, Y. Sasago, and K. Uchinokura, PRB56, 12685(’97). Y. Wang et al., cond-mat/0305455

18. Hall coefficient a high frequency “residue” R H * Shastry, Shraiman & Singh, PRL70, 2004 (’93); Kumar & Shastry, PRB68, 104508 (’03).

19.  H   t JxJx JyJy These contributions are absent !!

20.  H   t JxJx JyJy Difference of R* H between square and triangular lattices charge carrier High temperature expansion Doubly occupied states are excluded.

21.  H   t JxJx JyJy High temperature expansion

22. a high frequency “residue” R H * JyJy JxJx JyJy  H   t JxJx

23. ….. high frequency “residue” R H *

24. R H * (in units of v/  e) k B T / t triangular lattice WK, Oguri & SM, unpublished. Kagomé lattice t ~ 25K

25. 200 100 0 80 40 0 in-plane resistivity Thermopower  (  cm) Q  (  V/K) 0100200300 Temperature(K) I. Terasaki, Y. Sasago, and K. Uchinokura, PRB56, 12685(’97). Small  Large Thermopower in NaCo 2 O 4 Large Q Spin and Orbital Degrees of Freedom in Co 3+ (3d 6 ) and Co 4+ (3d 5 ) CoO 6 octahedron O Co Basic unit Key of Large Thermopower egeg t2gt2g Orbital degree of freedom 3d orbitals W. Koshibae and S. Maekawa ， PRL87, 236603 (’01).

26. Thermoelectric material heat electricity Thermopower Large Thermopower (Q) & Small Resistivity (  are required.

27. n-SiGe [n] 50010001500       T [K] Figure of Merit Z [K  ] n-Bi 2 Te 3 (n) GeTe 3 -AgSbTe 2 alloy (p) PbTe (n) n-FeSi 2 (n) B 9 C+Mg (p) ZT = 1 NaCo 2 O 4 (p) Figure of Merit Z = Q 2 /   thermal conductivity)

28. Galileo: NASA's Spacecraft Radioisotope Themroelectric Generator SEIKO THERMICCITIZEN ECO-DRIVE THERMO

29. Thermo-electric materials: Heat→Electricity Electricity→Heat Thermo-electric materials ： No vibration (no moving part), Easy to miniaturize, Gentle to environment. Garbage burning plant Heat of car Refrigerator

30. Thermopower at high temperatures: independent of T High temperature particle current energy flux operator chemical potential entropy number of electrons S=k B lng g: total number of the states density matrix Entropy per carrier

31. Spin and Orbital Degrees of Freedom based on the Strong Coulomb Interaction Key of Large Thermopower gege ghgh Thermopower in NaCo 2 O 4 =1=6 gege ghgh Co 3+ Co 4+ Co 3+ egeg t2gt2g Co 4+ Q = 154  V/K x = 0.5 ChargeSpin and Orbital At high temperatures:

32. The degeneracy induced by Spin and Orbital degrees of freedom degeneracy of Co 3+ and Co 4+ Charge Heikes Formula Summary Other Transition Metal Oxides Ti 3+ (3d 1 ), Ti 4+ (3d 0 ) g e / g h 6 / 1  154  V/K  k B /e  ln(g e /g h ) V 3+ (3d 2 ), V 4+ (3d 1 )9 / 6  35  V/K Mn 3+ (3d 4 ), Mn 4+ (3d 3 )10 / 4  79  V/K Cr 3+ (3d 3 ), Cr 4+ (3d 2 )4 / 9 70  V/K Large thermopower is also expected! Rh 3+ (4d 6 ), Rh 4+ (4d 5 )1 / 6   V/K

33. New thermoelectric material - delafossite-type Mg-doped chromium oxides - We have studied high-temperature thermoelectric properties of CuCr 1-x Mg x O 2 (x=0-0.05) between 300 K and 1100 K. CuCr 1-x Mg x O 2 thin film prepared by pulsed laser deposition technique was oriented to c- axis, perpendicular to the sapphire substrate. Experimental Group … 1 (1-x)Cr 3+ + x Cr 4+ 3d23d2 3d33d3 t 2g egeg CrO 2 Cu Crystal structure of CuCrO 2 CrO 2 Cu Y. Ono

34. Y. Okamoto, M. Nohara, F. Sakai and H. Takagi J. Phys. Soc. Jpn. 75, 023704 (’06). Sr 1  x Rh 2 O 4 Rh 3+ (4d 6 ) and Rh 4+ (4d 5 ) Large Thermopower

35. NaCo 2 O 4, x ~ 0.5, t ~  100K Electron dope U =  Hubbard model on the kagomé lattice 154  V/K T [K] Q*Q* Thermopower (Q) at    ( cf. B. Sriram Shastry, PRB73, 085117(’06). )

36. Thermo-electric response tensor at   0, (  t)  0 Nernst coefficient    R H / T 2   1 / T R H is positive and linear in T at high temperature. at high-temperatures,

37. In conclusion; It is of crucial importance to see the electronic lattice hidden in the frustrated crystal lattice.