C. D. Hu Department of physics National Taiwan University
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Transcript of C. D. Hu Department of physics National Taiwan University
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Some interesting physics in transition metal oxides: charge ordering, orbital ordering and spin-charge separation
C. D. HuDepartment 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
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Double-exchange interaction
La1-xDxMnO3 D: divalent elements 3-d
Lan(1-x)Sr1+nxMnnO3n+1 n = # of layers. 2-d
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Phase diagram
OOI
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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.
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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.
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atom
Crystal
field
eg
t2g
Jahn-Teller
distortion
x2-y2
3z2-r2
xy
xz, yz
Mn
YT
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Mn OMn Mn OMn
10, eVtJJcctHji i
ijiDE
iσS
Zener, Anderson, Hasegawa: Double-Exchange interaction
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Mean field picture
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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>
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Slave fermion
., iiiiii fcfc
Schwinger bosons
.,|2/1,2/1|
,,|2/1,2/1|
mSmSmSB
mSmSmSA
SffBBAA
fBBAAfStH
iiiiii
jijjijiiDE
2
)(12
Finally
combine α or β with the localized spin.
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'. . . .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
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pkpkkppkikiDEi
ti
jijjijiiDE
fAccAfkENipHiF
dttFFeimne
fBBAAfStH
,
)(,11
)(12
2
22 )/(10 TKcm
Similar to one-magnon process.
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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
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f
ff
f
f
f
ff f
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Charge ordering
• Many compounds• cuperates• manganites• magnetites
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Nd doped La2-xSrxCuO4 (Niemoller et. al.)
ac-plane, Stripe in b-directuion
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Charge-ordered stripes seen in La0.33Ca0.67MnO3 by Uehara, Mori, Chen and Cheong, Nature399, 560 (1999).
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DV2O4 D: divalent elements
New J. Phys. 7, 53. Radaelli
PRL 93 157206. Tchernyshyov
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cubic to monoclinic
Miles, et. al.Rev. Mod. Phys. 29, 279
Orbital ordering Fe3O4 Verway transition
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Fe3O4 Verway transition
O O-2
O A-type: 1/3 Fe+2
O B-type: 1/3 Fe+2 O B-type: 1/3 Fe+3
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Orbital ordering
Manganite, Spinel (AB2X4, MgTi2O4, FeSc2S4), R1-xAxTiO3, TiOX (X=Cl,BR),
V2O3, LiNiO2, NaTiO2, Ca3Ru2O7, KCuF3, Fe3O4,
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Fe3O4
PRL 93, 156403. Jen, Guo, Huang
PRB 66, 214422. Wright, Attfield, Radaelli
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z-directiontz
x, y-directiontx(y)
0 0'
0 1t
3 34 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 ) 'cosx 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
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La0.5Ca0.5MnO3
La0.5Sr1.5MnO4
PR 100, 545. Wollen, Koehler PR 100, 564. Goodenough
: Mn4+, : spin,
lobes: orbitals of Mn3+
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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.
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PRL. 88 167204Kim et. al.
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PRL. 81, 1517x=0.3
Feathures:Drude peak and broad peak
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polaron?
small polaron large polaron
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orbital?
PRB. 58, 11841Kilian and Khaliulin
J. Phys. Soc. Jpn. Shiba et. al.
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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.
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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.