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S. Maekawa ( IMR, Tohoku University )

S. Maekawa ( IMR, Tohoku University ). Spin, Charge and Orbital and their Excitations in Transition Metal Oxides. (Hong Kong, Dec. 18, 2006) . Contents : i) Spin-charge separation in one-dimensional cuprates, ii) Non-linear optical response due to spin-charge separation,

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S. Maekawa ( IMR, Tohoku University )

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  1. S. Maekawa (IMR, Tohoku University) Spin, Charge and Orbital and their Excitations in Transition Metal Oxides (Hong Kong, Dec. 18, 2006) 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,

  2. z Oxygen y d(x2y2) x d(3z2r2) d(xy) d(yz) d(zx) Internal degrees of freedom of electron Spin Magnet Charge Electric Current 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 (NaxCoO2 and NaxCoO2・yH2O) i) Review of Unconventional properties ii) Orbital degeneracy in the frustrated lattice crystal lattice vs. electron lattice unconventional properties

  5. Crystal Structure CoO6 octahedron CoO2 layer edge-shared CoO6 units In NaxCoO2, x Co3+ (3d6) and (1 - x) Co4+ (3d5) in CoO6 units CoO2 layer Na layer CoO2 layer Na layer

  6. Superconductivity in water-intercalated NaxCoO2·yH2O H2O Na layer K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R.A. Dilanian, T. Sasaki, Nature 422, 53 (2003). CoO2 layer

  7. In cubic CoO6 units, Co3+ Co4+ eg NaxCoO2: t2g Co3+ (3d6) S = 0 Co4+ (3d5) S = 1/2 5 - 3d orbitals z eg y d(x2y2) x d(3z2r2) t2g d(xy) d(yz) d(zx)

  8. Anomalous physical properties in CoO2 layer: • Giant Hall effect at T R.T. NaxCoO2 (Y. Wang, et al., cond-mat/0305455) • Ferromagnetism [Bi2-xPbxSr2O4]yCoO2, Tc~ 3.2 K (I. Tsukada et al., J. Phys. Soc. Jpn. 70, 834 (’01).) • Giant thermopower at T R.T. NaxCoO2 (I. Terasaki, Y. Sasago, and K. Uchinokura, PRB56, 12685(’97).) [Bi2-xPbxSr2O4]yCoO2 (T. Yamamoto et al., Jpn. J. Appl. Phys. 39, L747 (’00).) Ca3Co4O9(A. C. Masset et al., PRB62, 166 (’00).) • Superconductivity NaxCoO2·yH2O (K. Takada et al., Nature 422, 53 (’03).) • Charge orderingNaxCoO2 (Foo et al., cond-mat/0312174) • Antiferromagnetism • Na0.5CoO2 • (T. Uemura et al.)

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

  10. Novel physics in CoO2 layer with triangular structure • Kagomé lattice hidden in CoO2 layer(WK and SM: PRL 91, 257003 (’03), NB, WK and SM: PRL 95, 037001 (05)) • 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). ) t2g orbital degeneracy in edge-shared CoO6 units

  11. Kagomé in triangular lattice CoO2 layer Co O z 90 degrees y x Co Edge shared octahedra OK to GO ! OK to GO ! 2px 2px + - + - - - + - + + - + d(xy) d(xy) NO GO ! OK to GO ! - + + - - + + - d(xy) d(zx)

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

  13. Hopping of a 3d electron via O2p orbital xy yz zx z y x CoO2 layer

  14. xy xy yz zx 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).

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

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

  17. Jy Jx bH  bt These contributions are absent !!

  18. High temperature expansion bH  bt bH  bt Jy Doubly occupied states are excluded. Jx Difference of R*H between square and triangular lattices charge carrier

  19. Jy Jx bH  bt High temperature expansion

  20. a high frequency “residue” RH* Jx Jy bH  bt bH  bt Jx Jy bH  bt bH  bt bH  bt

  21. high frequency “residue” RH* ….. …..

  22. Kagomé lattice RH* (in units of v/de) triangular lattice kBT / t WK, Oguri & SM, unpublished. t ~ 25K

  23. 200 in-plane resistivity r (mWcm) 100 0 Thermopower 80 Q(mV/K) 40 0 0 100 200 300 Temperature(K) Large Thermopower in NaCo2O4 I. Terasaki, Y. Sasago, and K. Uchinokura, PRB56, 12685(’97). • Key of Large Thermopower Spin and Orbital Degrees of Freedom in Co3+(3d6 )and Co4+(3d5 ) Small r Basic unit Co Large Q O CoO6 octahedron 3d orbitals eg t2g Orbital degree of freedom W. Koshibae and S. Maekawa，PRL87, 236603 (’01).

  24. Thermoelectric material electricity Thermopower Large Thermopower (Q) & Small Resistivity (r) are required. heat

  25. 10-2 Figure of Merit Z [K-1] 10-3 10-4 500 1000 1500 T [K] • Figure of Merit Z = Q2/rk (k:thermal conductivity) n-Bi2Te3(n) GeTe3-AgSbTe2 alloy (p) PbTe (n) ZT = 1 NaCo2O4 (p) n-SiGe [n] n-FeSi2(n) B9C+Mg (p)

  26. Galileo: NASA's Spacecraft Radioisotope Themroelectric Generator • SEIKO THERMIC • CITIZEN ECO-DRIVE THERMO

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

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

  29. At high temperatures: Spin and Orbital Degrees of Freedom based on the Strong Coulomb Interaction Key of Large Thermopower Spin and Orbital Charge • Thermopower in NaCo2O4 x = 0.5 Co3+ Co4+ eg Co3+ Co4+ ge gh t2g =1 =6 ge gh Q = 154 mV/K

  30. Summary The degeneracy induced by Spin and Orbital degrees of freedom degeneracy of Co3+and Co4+ Charge Heikes Formula • Other Transition Metal Oxides ge/ gh -(kB/e)ln(ge/gh) Ti3+(3d1), Ti4+(3d0) 6 / 1 -154 mV/K V3+(3d2), V4+(3d1) 9 / 6 -35 mV/K Cr3+(3d3), Cr4+(3d2) 4 / 9 70 mV/K Mn3+(3d4), Mn4+(3d3) 10 / 4 -79 mV/K Rh3+(4d6), Rh4+(4d5) 1 / 6 154mV/K Large thermopower is also expected!

  31. Experimental Group … 1 Cu CrO2 New thermoelectric material - delafossite-type Mg-doped chromium oxides - eg Cu CrO2 t2g Cu CrO2 Cu Crystal structure of CuCrO2 (1-x)Cr3+ + x Cr4+ 3d3 3d2 Y. Ono • We have studied high-temperature thermoelectric properties of CuCr1-xMgxO2(x=0-0.05) between 300 K and 1100 K. • CuCr1-xMgxO2thin film prepared by pulsed laser deposition technique was oriented to c-axis, perpendicular to the sapphire substrate.

  32. Sr1-xRh2O4 Rh3+ (4d6) and Rh4+ (4d5) LargeThermopower Y. Okamoto, M. Nohara, F. Sakai and H. Takagi J. Phys. Soc. Jpn. 75, 023704 (’06).

  33. Thermopower (Q) at w  (cf. B. Sriram Shastry, PRB73, 085117(’06).) Electron dope U =  Hubbard model on the kagomé lattice NaCo2O4, x ~ 0.5, t ~ +100K 154 mV/K Q* T [K]

  34. at high-temperatures, • Thermo-electric response tensor at w 0, (bt)  0 Nernst coefficient N -RH / T2 -1/ T RH is positive and linear inT at high temperature.

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

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