S. Maekawa (IMR, Tohoku University) Spin, Charge and Orbital and their Excitations in Transition...
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Transcript of S. Maekawa (IMR, Tohoku University) Spin, Charge and Orbital and their Excitations in Transition...
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)
Internal degrees of freedom of electron
Spin Magnet
Charge Electric Current
z
xy
Oxygen
d(3z2r2)d(x2y2)
d(xy) d(yz) d(zx)
Orbital (Shape of wave function: Shape of electron)
Hong Kong Conference
December 18, 2006
Anomalous Electronic Latticesin Cobaltates
S. Maekawa, W. Koshibae and N. Bulut(IMR, Tohoku University, Sendai)
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
x Co3+ (3d6) and (1 x) Co4+ (3d5) in CoO6 units
CoO6
octahedron
•Crystal Structure
CoO2 layer
edge-shared CoO6 units
Na layer
CoO2 layer
Na layer
CoO2 layer
In NaxCoO2,
K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R.A. Dilanian, T. Sasaki, Nature 422, 53 (2003).
Superconductivity in water-intercalated NaxCoO2·yH2O
Na layer
CoO2 layer
H2O
In cubic CoO6 units,
Co3+eg
t2g
Co4+
Co3+ (3d6)S = 0
Co4+ (3d5)S = 1/2
z
x
y
d(3z2r2)d(x2y2)
d(xy) d(yz) d(zx)
5 - 3d orbitals
eg
t2g
NaxCoO2:
Anomalous physical properties in CoO2 layer:
i. Giant Hall effect at T R.T. NaxCoO2
(Y. Wang, et al., cond-mat/0305455)ii. Ferromagnetism
[Bi2xPbxSr2O4]yCoO2, Tc 3.2 K(I. Tsukada et al., J. Phys. Soc. Jpn. 70, 834 (’01).)
iii. Giant thermopower at T R.T.NaxCoO2
(I. Terasaki, Y. Sasago, and K. Uchinokura, PRB56, 12685(’97).)[Bi2xPbxSr2O4]yCoO2
(T. Yamamoto et al., Jpn. J. Appl. Phys. 39, L747 (’00).) Ca3Co4O9
(A. C. Masset et al., PRB62, 166 (’00).)iv. Superconductivity
NaxCoO2·yH2O(K. Takada et al., Nature 422, 53 (’03).)
v. Charge ordering NaxCoO2
(Foo et al., cond-mat/0312174)vi. Antiferromagnetism
Na0.5CoO2
(T. Uemura et al.)
Novel physics in CoO2 layer with triangular structure
1. Kagomé lattice hidden in CoO2 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). )
t2g orbital degeneracy in edge-shared CoO6 units
CoO2 layer
Edge shared octahedra
90 degrees
O
Co
Co
x y
z
2px
d(xy)
d(zx)
+
+
+
2px
d(xy)+
d(xy)
OK to GO ! OK to GO !
NO
GO
!
OK
to GO
!
•Kagomé in triangular lattice
xyyz zx
•Hopping of a 3d electron via O2p orbital
x y
z
xy yz zx
xy t
yz
zx t
xy yz zx
xy t
yz t
zx
xy yz zx
xy
yz t
zx t
CoO2 layer
xyyz zxxyzx 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).
0
is the zero-frequency magnetic correlation function between two nearest-neighbor sites and
on the triangular or the kagome lattices,
Here, is shown for the kagome and
, .z zi jC d m r
i
r
j
C
m
C
the triangular lattices at =1.15 for 8 | | and 4 | | .
The results for the kagome lattice were obtained for 6 6 (filled points) and 4 4 (empty points) unit cells.
The results for the triangular
lattic
n U t t
e were obtained for 12 12 (filled points) and 8 8 (empty points) lattices.
0
limH HR R
•Hall coefficient
a high frequency “residue” RH*
*2 20
,lim lim .
x yH H
Bxx
J JiVR R
Be
0
xyH
xx yy xy yx B
RB
2
2 2
2
2
*
1, , , ,
1, ,
1
xy x y x y
xx xx x x
HH
H
ieJ J J H H J
V
ieJ H J
V
RR
Shastry, Shraiman & Singh, PRL70, 2004 (’93); Kumar & Shastry, PRB68, 104508 (’03).
2 3
,
1 1 1Tr 1 ,
2! 3!
x y
x y
J J
H H H J JZ
H t
JxJy
These contributions are absent !!
, ,x y xxB B
t tJ J t
k T k T * B
Hk T
Rt
*2 20
,lim lim .
x yH H
Bxx
J JiVR R
Be
H t
Jx
Jy
H
t
Difference of R*H between square and triangular lattices
charge carrier
* .HR const
*2 20
,lim lim .
x yH H
Bxx
J JiVR R
Be
xxB
tt
k T
High temperature expansion
2 31 1 1, Tr 1 ,
2! 3!x y x yJ J H H H J JZ
† . .jiij
H t c c h c
Doubly occupied states are excluded.
* BH
k TR
t
H t
JxJy
*2 20
,lim lim .
x yH H
Bxx
J JiVR R
Be
High temperature expansion
2 31 1 1, Tr 1 ,
2! 3!x y x yJ J H H H J JZ
xxB
tt
k T
a high frequency “residue” RH*
3
* 02 20
,lim lim .
x yH H
Bxx
J Jia NR R
Be
2 3
,
1 1 1Tr 1 ,
2! 3!
x y
x y
J J
H H H J JZ
Jy
Jx
Jy
H t
H t
Jx
H t
H tH t
0.0 0.5 1.0 1.50.0
0.1
0.2
0.3
0.4R
H*
(in
unit
s of
v/
e)
kBT / t
triangular lattice
WK, Oguri & SM, unpublished.
Kagomé lattice
t ~ 25K* BH
k TR
t
200
100
0
80
40
0
in-plane resistivity
Thermopower
(
cm
)Q
(V
/K)
0 100 200 300Temperature(K)
I. Terasaki, Y. Sasago, and K. Uchinokura, PRB56, 12685(’97).
Small
Large Thermopower in NaCo2O4
Large Q
Spin and Orbital Degrees of Freedom
in Co3+(3d6 ) and Co4+(3d5 )
CoO6
octahedron
OCo
Basic unit
•Key of Large Thermopower
eg
t2g
Orbital degree of freedom
3d orbitals
W. Koshibae and S. Maekawa , PRL87, 236603 (’01).
•Thermoelectric material
heat
electricity
Th
erm
opow
er
Large Thermopower (Q) & Small Resistivity (are required.
n-SiGe [n]
500 1000 1500
T [K]
Fig
ure
of M
erit
Z [
K
] n-Bi2Te3 (n)
GeTe3-AgSbTe2 alloy (p)
PbTe (n)
n-FeSi2 (n)B9C+Mg (p)
ZT = 1
NaCo2O4 (p)
•Figure of Merit Z = Q2/ thermal conductivity)
•Galileo: NASA's Spacecraft
Radioisotope Themroelectric Generator
•SEIKO THERMIC •CITIZEN ECO-DRIVE THERMO
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
Thermopower at high temperatures:
QM M
eT eT
12 11/
M T dt d j t i j110 1 100
zz
tr ( )k p
independent of T
High temperature
particle currentenergy flux operator
eT
T
SN E V
FH IK,
chemical potentialentropy
FH IK1e
SN E V
,
number of electrons
FH IKke
gN E V
B ln
,
S=kBlngg: total number
of the states
M T dt d j t i j120 2 100
zz
tr ( )k p
density matrix
Entropy per carrier
Spin and Orbital Degrees of Freedom based on the Strong Coulomb Interaction
Key of Large Thermopower
Qke
gN
ke
gke
gke
xxE V
e h FH IK
B B B Bln
ln ln ln( ), 1
ge gh
•Thermopower in NaCo2O4
=1 =6ge gh
Co3+ Co4+
Co3+eg
t2g
Co4+
Q = 154 V/K
x = 0.5
ChargeSpin and Orbital
At high temperatures:
The degeneracy induced by Spin and Orbital degrees of freedom
degeneracy of
Co3+ and Co4+
Charge
ke
g
ge
h
B lnQ
ke
xx
B ln( )1
Heikes Formula
•Summary
•Other Transition Metal Oxides
Ti3+(3d1), Ti4+(3d0)
ge / gh
6 / 1 154 V/K
kB/eln(ge/gh)
V3+(3d2), V4+(3d1) 9 / 6 35 V/K
Mn3+(3d4), Mn4+(3d3) 10 / 4 79 V/KCr3+(3d3), Cr4+(3d2) 4 / 9 70 V/K
Large thermopower is also expected!Rh3+(4d6), Rh4+(4d5) 1 / 6 V/K
New thermoelectric material - delafossite-type Mg-doped chromium oxides -
• We have studied high-temperature thermoelectric properties of CuCr1-xMgxO2
(x=0-0.05) 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.
Experimental Group … 1
(1-x)Cr3+ + x Cr4+ 3d23d3
t2g
eg
CrO2
Cu
Crystal structure of CuCrO2
CrO2
CrO2
Cu
Cu
Cu
Y. Ono
Y. Okamoto, M. Nohara, F. Sakai and H. TakagiJ. Phys. Soc. Jpn. 75, 023704 (’06).
Sr1xRh2O4
Rh3+ (4d6) and Rh4+ (4d5)
Large Thermopower
2 21* ln 6
1 4Bk x x
Q t O te x
NaCo2O4, x ~ 0.5, t ~ 100K
Electron dope U = Hubbard model on the kagomé lattice
1* 154[ V/K]
4B
B
k t xQ
e k T
0 100 200 3000
50
100
150 154 V/K
T [K]
Q*
Thermopower (Q) at (cf. B. Sriram Shastry, PRB73, 085117(’06).)
•Thermo-electric response tensor at 0, (t) 0
1 122 20
2
2
lim 1 1
/
/
H
H
H
H
R Be eM
R BeT eTT T
Q e R T B
e R T B Q
Q NB
NB Q
((((
Nernst coefficient RH / T2 1 / T
RH is positive and linear in T at high temperature.
at high-temperatures, 12 12the tensor diagonal, M M 1
(((
In conclusion;
It is of crucial importance to see the electronic lattice hidden in the frustrated crystal lattice.