S. Maekawa

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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,
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Internal degrees of freedom of electron
Spin
Magnet
Charge
Electric Current
Orbital (Shape of wave function Shape of
electron)
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Hong Kong Conference December 18, 2006


Anomalous Electronic Lattices in Cobaltates
S. Maekawa, W. Koshibae and N. Bulut (IMR, Tohoku
University, Sendai)
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Co - Oxides in triangular lattice (NaxCoO2 and
NaxCoO2yH2O)
i) Review of Unconventional properties ii)
Orbital degeneracy in the frustrated lattice
crystal lattice vs. electron lattice unconvention
al properties
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• Crystal Structure

In NaxCoO2,
x Co3 (3d6) and (1 - x) Co4 (3d5) in CoO6 units
CoO2 layer
Na layer
CoO2 layer
Na layer
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Superconductivity in water-intercalated
NaxCoO2yH2O
H2O
Na layer
K. Takada, H. Sakurai, E. Takayama-Muromachi, F.
Izumi, R.A. Dilanian, T. Sasaki, Nature 422, 53
(2003).
CoO2 layer
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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)
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• Anomalous physical properties in CoO2 layer

• Giant Hall effect at T ? R.T. NaxCoO2 (Y.
  Wang, et al., cond-mat/0305455)
• Ferromagnetism Bi2-xPbxSr2O4yCoO2, 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-xPbxSr2O4yCoO2 (T.
  Yamamoto et al., Jpn. J. Appl. Phys. 39, L747
  (00).) Ca3Co4O9 (A. C. Masset et al., PRB62,
  166 (00).)
• Superconductivity NaxCoO2yH2O (K. Takada et
  al., Nature 422, 53 (03).)
• Charge ordering NaxCoO2 (Foo et al.,
  cond-mat/0312174)
• Antiferromagnetism
• Na0.5CoO2
• (T. Uemura et al.)

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I. Terasaki, Y. Sasago, and K. Uchinokura,
PRB56, 12685(97).
Y. Wang et al., cond-mat/0305455
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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
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• Kagomé in triangular lattice

CoO2 layer
O
Co
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)
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Martin Indergand, Yasufumi Yamashita, Hiroaki
Kusunose, Manfred Sigrist,
( cond-mat/0502116)
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• Hopping of a 3d electron via O2p orbital

z
y
x
CoO2 layer
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I. Terasaki, Y. Sasago, and K. Uchinokura,
PRB56, 12685(97).
Y. Wang et al., cond-mat/0305455
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• Hall coefficient

a high frequency residue RH
Shastry, Shraiman Singh, PRL70, 2004 (93)
Kumar Shastry, PRB68, 104508 (03).
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Jx
Jy
bH ? bt
These contributions are absent !!
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Difference of RH between square and triangular
lattices
charge carrier
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High temperature expansion
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a high frequency residue RH
Jx
Jy
bH ? bt
bH ? bt
Jx
Jy
bH ? bt
bH ? bt
bH ? bt
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..
..
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Kagomé lattice
RH (in units of v/de)
triangular lattice
kBT / t
WK, Oguri SM, unpublished.
t 25K
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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).
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• Thermoelectric material

electricity
Thermopower
Large Thermopower (Q) Small Resistivity (r) are
required.
heat
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• 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)
B9CMg (p)
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• CITIZEN ECO-DRIVE THERMO

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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.
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Thermopower at high temperatures
density matrix
particle current
energy flux operator
High temperature
independent of T
Entropy per carrier
chemical potential
entropy
SkBlng
g total number of the states
number of electrons
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At high temperatures
Spin and Orbital Degrees of Freedom based on the
Strong Coulomb Interaction
Key of Large Thermopower
Charge
Spin and Orbital

• Thermopower in NaCo2O4

x 0.5
Co3
Co4
eg
Co3
Co4
ge
gh
t2g
1
6
ge
gh
Q 154 mV/K
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• 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
154 mV/K
Large thermopower is also expected!
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Experimental Group 1
Y. Ono
We have studied high-temperature thermoelectric
properties of CuCr1-xMgxO2 (x0-0.05) between
300 K and 1100 K.
CuCr1-xMgxO2 thin film prepared by pulsed laser
deposition technique was oriented to c-axis,
perpendicular to the sapphire substrate.
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Sr1-xRh2O4
Rh3 (4d6) and Rh4 (4d5)
Large Thermopower
Y. Okamoto, M. Nohara, F. Sakai and H. Takagi J.
Phys. Soc. Jpn. 75, 023704 (06).
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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
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• Thermo-electric response tensor at w ? 0, (bt) ?
  0

Nernst coefficient N ? -RH / T2 ? -1 / T
RH is positive and linear in T at high
temperature.
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In conclusionIt is of crucial importance to
see the electronic lattice hidden in the
frustrated crystal lattice.
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