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 dynamics4. Interplay between double-exchange interaction, charge ordering, and orbital ordering
Double-exchange interaction
La1-xDxMnO3 D: divalent elements 3-d
Lan(1-x)Sr1+nxMnnO3n+1 n = # of layers. 2-d
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.
Manganites Structure
LaMnO3 La+3 Mn+3 O-23
Mn+3 3d4 xy, yz, zx orbitals form t2g band, localized spin 3/2 x2-y2, 3z2-r2 form eg band, mobile spin 1/2 S=3/2+1/2 -------doping-----
La1-xCaxMnO3 La+3 Ca+2 Mn+4 O+23
Mn+3 3d4 xy, yz, zx orbitals form t2g band, localized spin 3/2 S=3/2.
Recent Development (PRB 64,054406(2001))
From the point of view of the total spin on a site.
2 2(2 1)
total localized conduction
total
S S s
S
|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>
Slave fermion
., iiiiii fcfc
Schwinger bosons
.,|2/1,2/1|
,,|2/1,2/1|
mSmSmSB
mSmSmSA
SffBBAA
fBBAAfS
tH
iiiiii
jijjijiiDE
2
)(12
Finally
combine α or β with the localized spin.
'. . . .i iH K E U n n J S s J T
1
( )2 1
. .
2
i i j i j ji j
i i
i i i i i i i i
H t f A A B B fS
U n n J T
A A B B f f f f S
pkpkkppkikiDEi
ti
jijjijiiDE
fAccAfkEN
ipHiF
dttFFeimne
fBBAAfS
tH
,
)(,11
)(12
2
22 )/(10 TKcm
Similar to one-magnon process.
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
Charge-ordered stripes seen in La0.33Ca0.67MnO3 by Uehara, Mori, Chen and Cheong, Nature399, 560 (1999).
Orbital ordering
Manganite, Spinel (AB2X4, MgTi2O4, FeSc2S4), R1-xAxTiO3, TiOX (X=Cl,BR),
V2O3, LiNiO2, NaTiO2, Ca3Ru2O7, KCuF3, Fe3O4,
z-directiontz
x, y-directiontx(y)
0 0'
0 1t
3 3
4 3 1
t
(PR. 93, 1498. Slater, Koster)
† † †. . ( )z x yi a j i a j i a jK E t c c t c c t c c
2 (cos cos ) 2 / 3(cos cos ). .
2 / 3(cos cos ) 2 / 3(cos cos ) 'cos
x y x y
x y x y z
t k a k a t k a k aK E
t k a k a t k a k a t k
simple cubic lattice
Interplay between DE and OO
La0.5Ca0.5MnO3
La0.5Sr1.5MnO4
PR 100, 545. Wollen, Koehler PR 100, 564. Goodenough
: Mn4+, : spin,
lobes: orbitals of Mn3+
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.
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.
La0.5Sr1.5MnO4 1s4p (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 Mn3+ and Mn4+ are different.3. Intensity varies with the direction of polarization due to the Aj coupling.4. Incident photon: polarization. z-axis: b direction. orbitals: y2-z2 and x2-z2.
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