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. 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 dynamics 4. Interplay between double-exchange interaction, charge ordering, and orbital ordering
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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 - PowerPoint PPT Presentation
Transcript of C. D. Hu Department of physics National Taiwan University
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
Double-exchange interaction
La1-xDxMnO3 D: divalent elements 3-d
Lan(1-x)Sr1+nxMnnO3n+1 n = # of layers. 2-d
Phase diagram
OOI
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.
atom
Crystal
field
eg
t2g
Jahn-Teller
distortion
x2-y2
3z2-r2
xy
xz, yz
Mn
YT
Mn OMn Mn OMn
10, eVtJJcctHji i
ijiDE
iσS
Zener, Anderson, Hasegawa: Double-Exchange interaction
Mean field picture
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
fBBAAfStH
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
fAccAfkENipHiF
dttFFeimne
fBBAAfStH
,
)(,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
f
ff
f
f
f
ff f
Charge ordering
• Many compounds• cuperates• manganites• magnetites
Nd doped La2-xSrxCuO4 (Niemoller et. al.)
ac-plane, Stripe in b-directuion
Charge-ordered stripes seen in La0.33Ca0.67MnO3 by Uehara, Mori, Chen and Cheong, Nature399, 560 (1999).
DV2O4 D: divalent elements
New J. Phys. 7, 53. Radaelli
PRL 93 157206. Tchernyshyov
cubic to monoclinic
Miles, et. al.Rev. Mod. Phys. 29, 279
Orbital ordering Fe3O4 Verway transition
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
Orbital ordering
Manganite, Spinel (AB2X4, MgTi2O4, FeSc2S4), R1-xAxTiO3, TiOX (X=Cl,BR),
V2O3, LiNiO2, NaTiO2, Ca3Ru2O7, KCuF3, Fe3O4,
Fe3O4
PRL 93, 156403. Jen, Guo, Huang
PRB 66, 214422. Wright, Attfield, Radaelli
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
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.
PRL. 88 167204Kim et. al.
PRL. 81, 1517x=0.3
Feathures:Drude peak and broad peak
polaron?
small polaron large polaron
orbital?
PRB. 58, 11841Kilian and Khaliulin
J. Phys. Soc. Jpn. Shiba et. al.
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.
