ARPES for f-electrons Issues and Prospects

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ARPES for f-electronsIssues and Prospects
J. W. Allen University of Michigan
International Seminar on Strong Correlations and
Angle-Resolved Photoemission SpectroscopyDresden
May 2, 2007
Funding U.S. NSF
and Advanced Light Source Doctoral
Fellowship Program
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Collaborators

• S.-K Mo and Feng Wang
  University of Michigan
• J.D. Denlinger and G.-H. Gweon
  Advanced Light Source, LBNL
• Kai Rossnagel
  University of Kiel
• S. Suga and A. Sekiyama
  Osaka University
• H.-D Kim, J.-H. Park Pohang
  University, Pohang Synchrotron
• H. Höchst
  Synchrotron Radiation Center, Univ. of Wisconsin
• M. B. Maple
  University of California, San Diego
• Z. Fisk University of California, Irvine
• J. Sarrao
  Los Alamos National Laboratory
• A. D. Huxley, J. Flouquet
  CEA - Grenoble
• P. Metcalf
  Purdue University
• J. Marcus and C. Schlenker
  LEPES, CNRS, Grenoble
• J. He, R. Jin, D. Mandrus2 Oak Ridge
  Natl Lab and 2University of Tennessee
• A. B. Shick
  ASCR Prague
• H. Yamagami
  Kyoto-Sangyo University
• D. Vollhardt, G. Keller, V. Eyert
  University of Augsburg

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ARPES data acquisitionfor three dimensional
materials
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Fermi Surface Mapping of a 3D metal
Cu (100) h?83 eV
k-space (repeated zones)
001
100
110
Constant energy measurement surface

• Plane wave final state
• Surface refraction included (inner potential
  8.8 eV)

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YbBiPt
8 maps span full FS along lt111gt oriented cleave
surface probed bulk very near Yb
3 3-fold symmetry kZ-stacking observed
in Fermi surface First ARPES
Fermi surface map of any Yb-compound Small
photon spot essential to get this data
heaviest Fermions ? 8000 mJ/mol-K
w/ Z. Fisk (UC Irvine)
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Kondo resonance in angle integrated Ce 4f
spectraearly experiment and theory
Fig. from Allen et al Adv. in Physics 1985
Spectra from photoemission and x-ray inverse
photoemission (Xerox PARC) samples (Maple,
UCSD) Allen et al PRB 1983
CeAl small EK
Spectral theory Gunnarsson Schönhammer PRL
1983
CeNi2 large EK
Kondo Volume
Collapse Ce ? phase EK large ? phase
EK small Allen Martin PRL 82 Allen Liu PRB
92
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Mott-Hubbard metal-insulator transition new view
from Dynamic Mean Field Theory(Vollhardt,
Metzner, Kotliar, Georges ? 1990)
DMFT lattice ? a self-consistent Anderson
impurity model (exact in ? dimensions)
U/t small
U/t large
EF
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Angle integrated bulk sensitive spectra for Mott
transition in (V1-xCrx)2O3
x
T
Pressure
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Crystal structure and surface layer
Vanadium
Oxygen
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Small spot also essential for large EF peak !
Optical micrographJ.D. Denlinger
EF peak much reduced with larger
spotDifference for 300 eV to 500 eV
range even larger
With small spot can select probing point to avoid
steps, edges, strain as much as possible
Steps, edges have even lower coordination than
smooth surface
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More surface surface effects EuB6

• Time dependent relaxation of a polar surface

Covalent bonded B6 Ionic bonding Eu2
B6(2-)
Eu 4f
time
? Time-dependent size of X-point electron pocket
Time-dependent surface-shifted Eu 4f state ?
? Surface slab calculation (1) surface state in
bulk gap (2) surface-shifted Eu 4f
(1)
(2)
Time-dependence Model ?
t lt t Clustering of mobile surface Eu atoms
t 0 (Cleave) Statistically 50 Eu-terminated
t gt t Residual gasadsorption
w/ Z. Fisk (UC Davis), B. Delley (Paul-Scherrer
Institut), R. Monnier (ETH-Zurich)
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EuB6 --kill surface effects to see bulk
Surface
Bulk
Kill surface with pburst ? 1x10-9 torr
FM lt 15K

• Separating surface bulk electronic structure

Surface electron-rich Eu-termination ?
X-point electron pockets
higher binding energy-shifted Eu 4f state Bulk
hole-like pockets just touch EF (p-type) ?
observe exchange splitting for TltTC
? bulk Ferromagnetism in EuB6 likely from
superexchange (like EuO)
w/ Z. Fisk (UC Davis), B. Delley (Paul-Scherrer
Institut), R. Monnier (ETH-Zurich)
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EuB6 bulk valence band exchange splittingnow
observable
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Theory issues for non-low D f and d electron
materials needing detailed Fermi surface data
Compare to DMFT LDA for FS and spectral function
"Dual nature" picture for actinide f-electrons,
e.g U 5f3 5f2 1 in FS volume Pu 5f5
5f4 1 in FS volume Zwicknagl and
Fulde (PRB '02 UPt3, UPd2Al2) Wills et
al (J. Elec. Spectros. Rel. Phenom. 04) and
Joyce et al (Physica B 05) for Pu
materials
Distribution of f-weight around Fermi surface
in relation to high mass sheets--
above and below TK
"Two fluid" phenomenology for heavy fermion
metals (S. Nakatsuji, D. Pines and Z.
Fisk, PRL, PRB 04) In transport and NMR, single
ion Kondo part and coherent lattice part, all at
low energy. "Cold spots on FS?"
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CeMIn5 (MCo)
Interplay coexistence of AFM SC
15 maps from 90eV to 125eV
Fujimori et al PRB 2003
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CeMIn5 (MCo)
Three maps (T 26K) span full kz BZ Compare to
2 kz-plane M point quasi 2d sheets
of LDA Fermi surface P. Oppeneer, from PRB 69,
3310 (2004)
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Ce115, Ce218

• Single vs Double Ce layer

Ce2RhIn8
CeCoIn5
92 eV 112 eV
Ce 218 has 2X more FS contours than for
Ce115 .
w/ M. B. Maple (UC San Diego), P. Oppeneer
(Uppsala, Sweden)
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UGe2
FM SC w/ P
Compare ARPES FS and spectral function (T 30K,
92 eV photons) to LDA DMFT
Both agreement and disagreement at detailed level
w/ A. Huxley, J. Flouquet (Grenoble), A. Shick
(Prague), A. Lichenstein
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LDA for LaRu2Si2 and CeRu2Si2 compared
band 4 Z- hole pocket
La
Ce
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LaRu2Si2
3D Fermi surface mapping
Normal emission photon-dependence FS slice shows
effects of kZ-broadening on a 3D big
pillow-shaped FS topology with fcc-stacking.
Full 3D character of FS observed by fine-angle
maps at fixed photon energies by fine
photon-energy-step kZ-dependent slice at fixed
angle.
w/ J.L. Sarrao (LANL
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Fermi volume change at Kondo temperaturethe
f-electron in CeRu2Si2
Luttinger counting theorem ? f-electrons
counted in Fermi volume IF magnetic
moments quenched
(as in Kondo effect)
Conjecture (Fulde Zwicknagl, 1988) f-electrons
excluded from FS above
Kondo temperature TK Difficult to test with
low-T dHvA.
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Same large hole FS for LaRu2Si2 and CeRu2Si2 for
T? 120K gt 6TK ? f-electrons excluded from FS!
XRu2Si2 review J. D. Denlinger et al, JESRP 117,
8 (2001)
samples J. Sarrao LANL
Same conclusion from 2d angular correlation of
positron annihilation studies--
(Monge et al, PRB, 2002) but didn't actually
measure the "pillow"
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Fermi surface at high T 4f weight at low mass
?, Z points for CeRu2Si2
hn 91 eV
hn 122 eV
LDA
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But .remnant of f-d mixing in high T CeRu2Si2
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URu2Si2
Temperature k-dependent 5f weight distribution
T-dependent f-weight at center of X-pt
hole-pocket
102 eV
108 eV
X-point hole-pocket Filled by f-weight
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Continue..theory issues needing detailed ARPES
data for Fermi surfaceIssues involving quantum
criticality
ARPES lineshapes of heavy fermion metals showing
E/T scaling in neutron scattering spectra should
also show E/T scaling. Need clean FS crossing to
study.
Dimensionality problem (Coleman and Pepin,
Physica B '99 and '02 In current theory
universal E/T scaling only below upper
critical dimension 2 but materials are 3D and
show transport power laws consistent with
theory above upper critical D Idea to fix
involves breakup of heavy Kondo quasiparticles in
QC regime-- signature would be f-electron
exclusion from FS
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Summary
Showed ARPES data and comparison to various
theories ? V2O3 -- surface effects, need small
spot LDADMFT comparison,
? EuB6 -- eliminate surface states by dosing,
observe ferromagnetic exchange
splitting ? Li0.0Mo6O17 -- ARPES shows many
Luttinger signatures
must now confront higher
dimensionality ? U, La,CeRu2Si2 --
f-electrons in Fermi surface volume ? New level
of data, FS tomography, for 3D f- electron
materials, Ce 115's, YbBiPt, URu2Si2 ? Compare
LDA DMFT for to ARPES of UGe2
Outlook new capabilities in ARPES and theory
offer Many possibilities for further
experiments and
opportunities for testing theory
and for theory to influence direction of
experiment
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electron removal (and addition) to
studysingle-particle behavior of many-body
system
Spectroscopy of energy and momentum dependence of
spectral weight ?
(k,?) (1/?) Im 1/ (? ?k - ?(k,?) of
single particle Greens function
remove e ? to ? photoemission
sample with ground state electron density
Insert e ? from ? inverse
photoemission
added electron with hole screening cloud
added hole with electron screening cloud
Both processes together give unbound
hole/electron pair the RIGHT WAY TO DEFINE
INSULATOR GAP!
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Predicted high T broadening of metal phase EF
peak
T300 K (two similar U values)
T 700 K
T 1100 K
quasi-particle peak ? incoherent
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Unsuccessful early search for broadening in low
h? photoemission for PM phase of V2O3(no EF peak
to study!)
One low temperature in the AFI phase two
temperatures in the PM phase
S. Shin et al. J. Phys. Soc. Jpn. 64, 1230
(1995)
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High temperature correlation gap filling in
(V0.972Cr.028)2O3 PI phase spectra to 800K
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LiPB QC Fig. 1

• QC schematic

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Mott-Hubbard paradigm (V1-xMx)2O3 (MCr,
Ti)Look for DMFT "Kondo peak"
McWhan, Rice et al. PRL 69, PRB 73
2e-/ V3 ion 3 orbitals/ion 4 ions/cell more
complex than 1-band Hubbard
Importance of realism Ezhov et al, PRL 99,
Park et al, PRB 00 ? Motivation for
LDA DMFT calculations (Held et al, PRL 01)
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More work on V2O3

• Hubbard gap filling in I phase with T increased
  to 300 to 800K,
• compare to LDADMFT, Mo et al,
  PRL 04
• Theory paper on full-orbital LDADMFT with
  comparison to spectra,
• V. I. Anisimov et al, PRB 05.
• Compare to DMFT for spectrum change I to AFI
  phase
• G. Sangiovanni, PRB 06
• PES for all phases and several Cr, Ti dopings,
  systematics of insulating phase gasp, compare to
  LDADMFT
• Mo et al, cond-mat /0608380 and
  PRB in press.

Have tried to FS map by ARPES Hints, but just
not enough beamtime to do systematic job.
517 eV
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Compare V2O3 PM phase spectrumto LDA DMFT
(t-orbitals, U5.0 eV, 300K)
S.-K. Mo et al, PRL 90, 186403 (2003)
Qualitative agreement on presence of prominent
EF peak in spectrum
But experimental peak width larger than theory
width, roughly by factor of 2
And experimental peak weight larger than
theory weight
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Get photons from synchrotronvariable photon
energy
Detectorscreen
Undulator device inserted in synchrotron electron
beam gives intense light.
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Photoemission spectroscopy (and its inverse) to
measure ? (p,E) or p-summed ? (E)
Full electronic structure _at_ fixed photon energy
3D data set
angles, energies ? p