PowerPoint-Pr

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Testing modern theories for correlated systems
Hao Tjeng
II. Physikalisches Institut University of
Cologne, Germany tjeng_at_ph2.uni-koeln.de

• systems LaTiO3, YTiO3, La1-xSrxTiO3d, VO2,
  Ti2O3, V2O3, Ca2-xSrxRuO4
• theories LDA, LDAU, LDADMFT, LDACDMFT
• spectral weight transfer, metal-insulator
  transitions
• orbital occupations and spin-spin correlations
• dimers, H2-model

2
How does the spectral weight distribution change
in a Mott-Hubbard system as a function of U / W
??
Motivation
3
Bandwidth control W vs. U 3d1 perovkites
4

• Ca -- Sr
• same valence
• no doping
• different bond-angles
• different band widths

Interesting proposition spectral weight
transfer near a Mott transition by band width
control
Remark both systems are on the metal side of
the MIT.
5
Bulk-sensitive PES
LDADMFT
There should be differences ! But too bad that
the differences are too small !
6
How about LaTiO3 versus YTiO3 ?!

• both are correlated systems
• La Y same valence
• different Ti-O-Ti bond-angles
• different band widths
• consequences for spectral weight distributions
  ?!

• Remark
• both systems are on the insulating side of the
  MIT
• the band gaps are different but both are small

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Phase diagram YTiO3 - LaTiO3 with Ca, Sr, and O
doping
8
Existing experimental data

• However
• LaTiO3 and YTiO3 have very similar Ti-3d
  spectral weight !!
• O-2p spectrum does not agree with O-2p from LDA
  !!

• Something wrong with the data from literature
  ????

9

NOT TRUE!! very different lineshapes !!

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OUR EXPERIMENTS samples made by Holger Roth
Single Crystals LaTiO3 and YTiO3 Ø 6 mm 10-50
mm length
LaTiO3 TN 148 K YTiO3 TC
29 K
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OUR EXPERIMENTS bulk-sensitive
photoemission high photon energy normal
emission on cleaved single crystal surfaces
Samples are of good quality measurements are
reliable !!
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Close-up of the Ti-3d band region
LaTiO3 and YTiO3 have different band widths
indeed !!
13
The Ti-3d band region comparison experiment
with theories
GGA band structure calculations much too narrow
bands !!
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The Ti-3d band region comparison experiment
with theories
GGAU band structure calculations even worse !!
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The Ti-3d band region comparison experiment
with theories
LDADMFT seems to work well !! Surprising ?!?
16
The Ti-3d band region comparison experiment
with theories
Full GGA t2g band width works even better !!
Very surprising ?!
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How does the spectral weight distribution change
in a Mott-Hubbard system as a function of U / W
??
non-correlated metal
which scenario ?
DMFT
B-R
Hubbard
Mott-insulator

• LaTiO3/YTiO3 t-J type of Mott-insulators ?!
  
• no dubbel occupation
• total effective band width given by total
  1-electron band width

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Phase diagram YTiO3 - LaTiO3 with Ca, Sr, and O
doping
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Doping dependence
excess oxygen d1-2d
Sr doping d1-x
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Doping dependence
excess oxygen d1-2d
Sr doping d1-x

• very rapid increase of metallic peak with
  doping
• more rapid with Sr than with oxygen excess

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Doping dependence
excess oxygen d1-2d
Sr doping d1-x

• very rapid increase of metallic peak with
  doping
• more rapid with Sr than with oxygen excess

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Calculating electronic structure and spectral
weights of correlated systems
Dynamical Mean Field Theory See review G.
Kotliar and D. Vollhardt, Physics Today, March
2004, page 53-59.

• Realistic LDADMFT calculations
• good results for
• a-g transition in Cerium
• d-phase Plutonium

• Summary LaTiO3, YTiO3, La1-xSrxTiO3d -
  perovskite d1 systems
• LDA, LDAU fail completely
• LDADMFT good results for photoemission !
• inverse photoemission
  untested !!

24
Metal insulator transitions 3d1 system VO2
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Metal insulator transition in VO2 at 340 K.
T gt 340K metal, rutile
M. Marezio et. al., Phys. Rev. B 5, 2541 (1972)
T lt 340K insulator, monoclinic, dimerized
zig-zag chain
log-scale
linear scale
P. B. Allen et. al., Phys. Rev. B 48, 4359 (1993)
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p. 3389
p. 3042
27
rutile metallic phase
monoclinic insulating phase
Band theory allways produces a metal
No agreement with UPS spectrum of Goering et al.,
Phys. Rev. B 55, 4225 (1997)
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cond-mat/0310216v1 9 Oct 2003
LDADMFT
UPSVO2 thin film
No agreement with UPS of K. Okazaki et al.,
Phys. Rev. B 69, 165104 (2004)
LDADMFT produces a metal for both rutile and
monoclinic structure, using "realistic" values
for U ( 4 eV).
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Unfortunately also no agreement between
experiments
Sawatzky and Post, PRB 20, 1546 (1979)
hn 1486 eV
Shin et al., PRB 41, 4993 (1990)
hn 21.2 eV
Okazaki et al., PRB 69, 165104 (2004)
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Our experiment bulk sensitive photoemission on
VO2 single crystals
monoclinic, insulating
rutile, metallic
"prominent" quasi-particle peak
V-3d
O-2p
hn 700 eV ESRF-ID08, DE0.15 eV cleaved
single crystal, flat surface, normal emission
max. probing depth
"incoherent" peak
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Comparison I
Band theory
monoclinic insulating phase
Experiment
bulk sensitive photoemission
V-3d
O-2p
rutile metallic phase
No gap between 1.0 and 2.0 eV region
Eyert, Ann. Phys. 11, 650 (2002)
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Comparison II
LDADMFT
Liebsch et al., PRB 71, 085109
V-3d
O-2p

• LDADMFT is too metallic
• U 4 eV is too small ?!
• position of insulating peak is okay

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Comparison III
LDA cluster DMFT
rutilemetallic
U 4 eV !!
monoclinic insulating !!!
V-3d
O-2p
LDA cluster DMFT S. Biermann, A. Poteryaev, A.
Lichtenstein, A. Georges, Phys. Rev. Lett. 94,
026404 (2005)
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Valence Band
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What is the underlying physics?? ? Orbitals in
VO2 3d1 - (t2g)1
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Soft-X-Ray Absorption Spectroscopy powerful
in combination with theory

• use of core levels local transitions
• element and site specific
• involves most relevant orbitals
• 2p-3d (TM), 3d-4f (RE), 1s-2p (O,N,C)
• dipole allowed very strong intensities
• dipole selection rules multiplet structure
• give extreme sensitivity to symmetry of
• initial state charge, spin and orbital

EFermi
O 2p
V 3d
hn 510 eV
hn 530 eV
V 2p3/2
2p1/2
theory TM 2p-3d Cluster calculations with
full atomic multiplet theory O 1s-2p
LDAU calculations
O 1s
Spectrum (hn) Sf½ái½e.r½fñ½² d(hn - Ef
Ei) ½iñ initial state, ½fñ final state e.r
dipole transition

• Technique developed in late 1980s
• Fink, Sawatzky, Fuggle
• Thole, van der Laan
• Chen, Sette

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Exp
Exp
Theory
Theory
All multiplet structures can be reproduced !!
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holes are in-plane
Normalized Fluorescence Yield
Photon energy (eV)
39
polarization dependence in VO2 experiment and
best fits
40
Orbital occupation in VO2 insulating and
metallic phase
XAS
XAS
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Calculating electronic structure and spectral
weights of correlated systems
LDA cluster DMFT S. Biermann, A. Poteryaev, A.
Lichtenstein, A. Georges, Phys. Rev. Lett. 94,
026404 (2005)
Switching of orbital occupation XAS Haverkort
et al., Phys. Rev. Lett. 95, 196404 (2005)
Spectral weight transfer Photoemission Koethe
et al., Phys. Rev. Lett. 97, 116402 (2006)

• Summary Metal-insulator transition in d1
  system VO2
• LDA fail completely
• LDAU ???
• LDADMFT not good enough !
• LDACDMFT good results, also for photoemission
  !
• inverse photoemission
  untested !!

42
Dimers have great impact in VO2

• from XAS
• from LDACDMFT
• - but not so from PES

• How about Ti2O3 and V2O3 ?
• dimers important ?
• can we observe them with PES ?

43
Role of dimers in V2O3 and Ti2O3?

• Corundum structure
• MIT in V2O3 and Ti2O3
• V-V and Ti-Ti pairs in c-direction

V2O3
Wei Bao et al., Phys. Rev. Lett. 78, 507 (1997)
44
Classic Ansatz for V2O3

• V3 3d2, S1
• V3-V3 pairs a1g molecular singlet formation ?
  effectively S1/2
• low T AF 1.2µB/V R. M. Moon, PRL 25, 527
  (1970) ? taken as evidence for S1/2!

45
same Ansatz for Ti2O3

• Ti3 3d1, S1/2
• Ti3-Ti3 pairs a1g molecular singlet formation
  ? effectively S0

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Comparison Experiment vs. Theory
Orbital occupation in Ti2O3 from XAS
At insulating state
dimers are formed in Ti2O3!
Insulating state Ti3-Ti3 c-axis dimers are
electronically formed
orbital occupation a1ga1g !
47
Comparison Experiment vs. Theory
Orbital occupation in Ti2O3 from XAS
At insulating state
dimers are formed in Ti2O3!
Insulating state Ti3-Ti3 c-axis dimers are
electronically formed
orbital occupation a1ga1g !
48
Temperature dependence
Orbital occupation in Ti2O3 temperature-dependen
ce
49
Orbital occupation in Ti2O3 temperature-dependen
ce
dimer
isotropic

• MIT in Ti2O3
• gradual transition
• 101 change in ?

LDA n(a1g)n(egp) 0.96 0.04 in metallic phase
L. F. Mattheiss, 1996
LDADMFT n(egp)0.09 insulating phase 0.15
metallic phase

n(a1g) n(egp) LDA (Mattheis 1996) (M)
0.96 0.04 DMFT (Poteryaev 2005) (I)
0.90 0.10
(M) 0.85 0.15 Cluster (Tanaka
2004) (I) 0.90 0.10
(M) 0.61 0.39
A. I. Poteryaev et al., 2004
Three-band Hubbard model
n(a1g)n(egp) 0.90 0.1 at 10K
n(a1g)n(egp) 0.61 0.39 at 800K
A. Tanaka,2004
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Bulk sensitive photoemission on Ti2O3 single
crystals
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Bulk sensitive photoemission on Ti2O3 single
crystals
U/t 0
U/t 1
U/t 5
anti- bonding
bonding
U/t 10
U/t 100
Two-peak structure like in a H2 molecule model
? (relative weights according to quantum
mechanical interference effect)
52
H2 molecule model
M
S
S
M
bonding
anti-bonding
bonding
anti-bonding
EF
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Comparison experiment vs. theory
Poteryaev, Lichtenstein, Kotliar., Phys. Rev.
Lett. 93, 086401 (2004).
Chang, Koethe et al. (Cologne)
too low intensity of anti-bonding peak ?!
55
Classic Ansatz for V2O3

• V3 3d2, S1
• V3-V3 pairs a1g molecular singlet formation ?
  effectively S1/2
• low T AF 1.2µB/V R. M. Moon, PRL 25, 527
  (1970) ? taken as evidence for S1/2!

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p. 11506
J.-H. Park, L.H. Tjeng, A. Tanaka, J.W. Allen,
C.T. Chen, P. Metcalf, J.M. Honig, F.M.F. de
Groot, G.A. Sawatzky

• Experiment
• S 1!
• rejects the existence of the claimed molecular
  orbital singlet formation ( the dimer)

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I. S. Elfimov, T. Saha-Dasgupta, and M. A. Korotin
no electronic sign for a dimer
t2
t4
t3
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Where to find and not to find the dimers?
c-axis pair bond length c-axis pair bond length c-axis pair bond length
below TMIT above TMIT
Ti2O3 2.579 Å (300K) 2.725 Å (780K)
V2O3 2.761 Å (15K) 2.709 Å (300K)
Cr2O3 2.650 Å (300K) 2.650 Å (300K)
c-axis dimers are present structurally in
corundum structures but exist electronically only
in Ti2O3 and Cr2O3.
59
Metal insulator transitions 3d2 system V2O3
k-dependence of the self-energy
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metal-insulator transitions (MIT) in V2O3
Phys. Rev. B 22, 2626 (1980)
Phys. Rev. B 7, 1920 (1973)
classical example for a Mott-transition, i.e.
beyond band structure effects
(note big resistivity jumps by themself do not
make the MIT special)
61
p. 105
TMIT 140 K
metallic V2O3
insulating V2O3
Egap 0.66 eV

• metal-insulator transitions (MIT) in V2O3
• enormous transfer of spectral weight
• kBTMIT ltlt Egap

extreme case best test case for new theories
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Enormous transfer of spectral weight across MIT
in V2O3
J.-H. Park, thesis, Univ. of Michigan, 1994
AFI
PI
AFI
PM
photoemission
Photoemission AFI very different from PM, but
AFI very similar to PI (neutrons AFI very
different from PM and PI, but PM similar to PI)
63

• In contrast to weak coupling, e.g. BCS
• 2D / kBTc 3.5

• Why ??
• Which entropy drives the transition ??

Our hypothesis at the MIT, not only gap closes
but also spin and orbital structures change with
consequences for the band width.
Are there new theoretical developments to address
these issues? Maybe ! But must be beyond
single-site approaches ?!
64
How good is single-site DMFT with spectral
weights across MIT ??
J.-H. Park, thesis Univ. of Michigan, 1994
Phys. Rev. Lett. 86, 5345 (2001)
AFI
PM
photoemission
PI
AFI

• Single-site DMFT fast transfer of spectral
  weight, but not enough!
• AFI to PM one-electron band width changes with
  10
• needed larger change in effective band
  width 30 or more

65
p. 11506
J.-H. Park, L.H. Tjeng, A. Tanaka, J.W. Allen,
C.T. Chen, P. Metcalf, J.M. Honig, F.M.F. de
Groot, G.A. Sawatzky

• Experiment
• orbital occupation changes in
• going from AFI to PM to PI

66
Experimental observations
V2O3 orbital occupation of the V 3d2 ions
significantly changes across the AFI-PM, AFI-PI,
and PM-PI transitions J.-H Park et al., Phys.
Rev. B 61, 11506 (2000)
V2O3 dramatic switching of magnetic short-range
exhange interactions across the AFI-PM and
AFI-PI transitions W. Bao et al., Phys. Rev.
Lett. 78, 507 (1997)
? k-dependence of the self-energy ?!!
inter-site spin and/or orbital
correlations
67

• changes in orbital occupation changes in S(w,k)

• changes in orbital occupation changes in
  exchange interactions
• - short range, nearest neighbor
• - Goodenough-Kanamori-Anderson rules

• changes in exchange interactions changes in
  S(w,k)

Optical transitions excitonic
ferromagnetic-cluster
antiferromagnetic-cluster
hn
hn
hn U0 2 JH
hn U0
Note JH 0.7 eV hardly screened from atomic
values, Antonides et al., PRB 15, 1669 (1977)
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• changes in orbital occupation changes in S(w,k)

• changes in orbital occupation changes in
  exchange interactions
• - short range, nearest neighbor
• - Goodenough-Kanamori-Anderson rules

• changes in exchange interactions changes in
  S(w,k)

Optical transitions excitonic
ferromagnetic-cluster
antiferromagnetic-cluster
hn
hn
hn U0 2 JH
hn U0
Note JH 0.7 eV hardly screened from atomic
values, Antonides et al., PRB 15, 1669 (1977)
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Photoemission, Inverse Photoemission,
Conductivity gap
hn
ferromagnetic-cluster
ferromagnetic-cluster
far left
far right
PES
IPES
t
t
Egap U0-2JH-2t
WN-1 t
WN1 t
hn
antiferromagnetic-cluster
antiferromagnetic-cluster
far left
far right
PES
IPES
t
t
Egap U0-2JH-0.9t
WN-1 t2/JH
WN1 t2/JH
70
Photoemission, Inverse Photoemission,
Conductivity gap
hn
ferromagnetic-cluster
ferromagnetic-cluster
far left
far right
PES
IPES
t
t
Egap U0-2JH-2t
WN-1 t
WN1 t
hn
antiferromagnetic-cluster
antiferromagnetic-cluster
far left
far right
PES
IPES
t
t
Egap U0-2JH-0.9t
WN-1 t2/JH
WN1 t2/JH
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Influence of intersite spin correlations on
electronic structure

• J.-H-Park, L.H. Tjeng et al., Phys. Rev. B 61,
  11506 (2000)
• Spin and orbital occupation and phase
  transitions in V2O3
• with example of ferro/antiferro-cluster
• A. Tanaka, J. Phys. Soc. Jpn. 73, 152 (2004)
• On the metal-insulator transition in VO2 and
  Ti2O3 from a unified viewpoint
• L.N. Bulaevvskii and D.I. Khomskii, Sov. Phys.-
  Solid State 9, 2422 (1968)
• Insulator-metal transitions in antiferromagnets

For intersite spin correlations to have strong
impact on band width, it is required that the
correlations on a short range scale are
changed --- Orbital occupation changes will
trigger this in a natural manner

• k-dependence of the self-energy
• crucial part of MIT in dn systems (degeneracy ?
  JH)
• important for inverse photoemission on d1
  systems (degeneracy ? JH)

Photoemission / inverse photoemission the
technique for measuring short-range exchange
correlations