Transcript No Slide Title

ARPES for f-electrons
Issues and Prospects
J. W. Allen
University of Michigan
International Seminar on Strong Correlations and
Angle-Resolved Photoemission Spectroscopy
Dresden
May 2, 2007
Funding:
U.S. NSF
and Advanced Light Source Doctoral Fellowship Program
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
Z. Fisk
J. Sarrao
A. D. Huxley, J. Flouquet
P. Metcalf
J. Marcus and C. Schlenker
J. He, R. Jin, D. Mandrus2
A. B. Shick
H. Yamagami
D. Vollhardt, G. Keller, V. Eyert
K. Held
V. I Anisimov
J. V. Alvarez
A. Lichtenstein
L. Pourovskii
B. Delley
R. Monnier
University of California, San Diego
University of California, Irvine
Los Alamos National Laboratory
CEA - Grenoble
Purdue University
LEPES, CNRS, Grenoble
Oak Ridge Nat’l Lab and 2University of Tennessee
ASCR – Prague
Kyoto-Sangyo University
University of Augsburg
Max-Planck Institute, Stuttgart
Institute of Metal Physics, Ekaterinburg
University of Michigan
University of Hamburg
Ecole Polytechnique, Paris
Paul-Scherrer Institute
ETH-Zurich
ARPES data acquisition
for three dimensional materials
Fermi Surface Mapping of a 3D metal
“k”-space (repeated zones)
Cu (100) h=83 eV
[001]
[100]
Constant energy
measurement surface
•
•
[110]
Plane wave final state
Surface refraction included
(inner potential = 8.8 eV)
YbBiPt
• 8 maps span full FS along <111> 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
 = 8000 mJ/mol K2
heaviest
Fermions
 ~ 8000 mJ/mol-K
Yb
Bi
Pt
w/ Z. Fisk (UC Irvine)
Kondo resonance in angle integrated Ce 4f spectra:
early experiment and theory
Spectra from
photoemission
CeAl
small EK
and x-ray
inverse
photoemission
(Xerox PARC)
samples:
(Maple, UCSD)
Allen et al
PRB 1983
Fig. from
Allen et al
Adv. in Physics
1985
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
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)
And.
Imp.
hopping t
repulsion U
Hubbard model for
Mott transition
Bath
elec
U/t small
~kTK
f1 f1
f0
f2
quasi-particle peak
growing in gap
as U/t decreases
(“bootstrap Kondo”)
Kondo physics—moment loss &
Suhl-Abrikosov/Kondo resonance
U/t large
EF
Angle integrated bulk sensitive spectra
for Mott transition in (V1-xCrx)2O3
x
Experiment: SPring-8 BL 25SU (S. Suga)
• h = 500-700 eV total E 90 meV
• Cleaved single crystals
from P. Metcalf, Purdue
Mo et al, PRL (2003)
Vollhardt and Kotliar, Physics Today (2004)
McWhan et al
1969
T
Pressure
“Kondo peak”
theory
and
experiment
in M phase
Previous work, 30 years
NO M phase peak
I phase
GAP
Surface layer more
correlated than bulk
Crystal structure and surface layer
surface-layer thickness =
–
(1012) cleavage plane
2.44Å

c = 14.0 Å
side view

a = 4.95 Å
Vanadium
Oxygen
top view
Small spot also essential for large EF peak !
Optical micrograph—J.D. Denlinger
Intensity (arb. unit)
hv=700eV, 100m spot
hv=690eV, >1mm spot
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
E-EF(eV)
= 100 μm spot size
With small spot can select probing
point to avoid steps, edges, strain as
much as possible
EF peak much reduced with
larger spot
Difference for 300 eV to 500 eV
range even larger
Steps, edges have even lower coordination than smooth surface
More surface surface effects: EuB6
Time dependent relaxation of a polar surface
• Covalent bonded B6
• Ionic bonding:
Eu2+ & B6(2-)
time
Eu 4f
 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 = 0 (Cleave)
Statistically 50%
Eu-terminated
t < t*
Clustering of mobile
surface Eu atoms
t > t*
Residual gas
adsorption
w/ Z. Fisk (UC Davis), B. Delley (Paul-Scherrer Institut), R. Monnier (ETH-Zurich)
EuB6 --kill surface effects to see bulk
Surface
FM < 15K
Separating
Bulk
Kill surface with
pburst  1x10-9
torr
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 T<TC
 bulk Ferromagnetism in EuB6 likely from superexchange (like EuO)
w/ Z. Fisk (UC Davis), B. Delley (Paul-Scherrer Institut), R. Monnier (ETH-Zurich)
EuB6 bulk valence band exchange splitting
now observable
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?"
CeMIn5 (M=Co)
Interplay & coexistence
of AFM & SC
M
15 maps
from 90eV to 125eV
Fujimori et al
PRB 2003
CeMIn5 (M=Co)
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)
Ce115, Ce218
Single vs Double Ce layer
92 eV
CeCoIn5
w/ M. B. Maple (UC San Diego), P. Oppeneer (Uppsala, Sweden)
112 eV
• Ce 218: has ~2X more FS
contours than for Ce115 .
Ce2RhIn8
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UGe2
Compare ARPES FS and spectral
function (T= 30K, 92 eV photons)
to LDA+ DMFT
FM + SC
w/ P
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
LaRu2Si2
3D Fermi surface mapping
Full 3D character of FS observed by fine-angle
maps at fixed photon energies & by fine photonenergy-step kZ-dependent slice at fixed angle.
Normal emission photon-dependence
FS slice shows effects of kZbroadening on a 3D big pillowshaped FS topology with fccstacking.
w/ J.L. Sarrao (LANL
Fermi volume change at Kondo temperature:
the f-electron in CeRu2Si2
Luttinger counting theorem

f-electrons counted in Fermi volume
IF magnetic moments quenched
(as in Kondo effect)
paradigm (dHvA) (Tautz et al,1995)
 large Z-point hole FS
f0 LaRu2Si2
 reduced "pillow" hole FS
counts  ½ Ce f- electron
in Kondo CeRu2Si2
--at temperature below TK
Conjecture (Fulde & Zwicknagl, 1988)
f-electrons excluded from FS above
Kondo temperature TK
Difficult to test with low-T dHvA.
LDA
“band 4” hole
Fermi surface
no f- electron
½ extra f-electron
here
( ½ f-electron in other
multiply-connected
complex FS piece)
Same large hole FS for LaRu2Si2 and CeRu2Si2 for
T 120K > 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"
Fermi surface at high T — 4f weight at
low mass , Z points for CeRu2Si2
h = 91 eV
h = 122 eV
LDA
Z

dHvA: m/me = 4, 2.5, 1.6,
Hole sheets (center = Z)
m/me = 120
m/me
=
13,20
Electron sheets (center = )
But ….remnant of f-d mixing in high T CeRu2Si2
LaRu2Si2
CeRu2Si2
curvature near EF
for CeRu2Si2 (f1) but not LaRu2Si2
f-d mixing in
Anderson
Lattice model
URu2Si2
Temperature
& k-dependent
5f weight distribution
T-dependent f-weight
at center of X-pt holepocket
102 eV
108 eV
X-point hole-pocket
Filled by f-weight
Continue..theory issues needing detailed
ARPES data for Fermi surface
Issues involving quantum criticality
T
ARPES lineshapes of heavy fermion
metals showing E/T scaling in
neutron scattering spectra should
also show E/T scaling.
NFL
x
Need clean FS crossing to study.
Quantum Critical Point
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
Summary
Showed ARPES data and comparison to various theories
● V2O3 -- surface effects, need small spot
LDA+DMFT 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
electron removal (and addition) to study
single-particle behavior of many-body system
Spectroscopy of energy and momentum dependence of spectral weight
 (k,) =
(1/) Im [1/ ( – k - (k,)]
of single particle Green’s function
Insert e 
from 
inverse
photoemission
added
electron
with
hole
screening
cloud
sample with
ground state
electron density
remove e  to 
photoemission
added
hole
with electron
screening
cloud
Both processes together give unbound hole/electron pair
the RIGHT WAY TO DEFINE INSULATOR GAP!
Predicted high T broadening
of metal phase EF peak
U=5.0eV, T=1100K
U=5.0eV, T=700K
U=5.0eV, T=300K
U=4.9K, T=300K
Intensity (arb. unit)
T=300 K
(two similar U values)
T = 700 K
T = 1100 K
quasi-particle peak
-3
-2
-1
E-EF(eV)
0
 incoherent
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)
High temperature correlation gap filling
in (V0.972Cr.028)2O3 PI phase: spectra to 800K
negative curvature
near EF, theory and
experiment
due to gap filling
Phase Diagram
DMFT Landau theory
crossover regime (RED)
300 K blue
750K red
experimental paths
0-1-2 and 0'-1'-2'
300K data with
1150 K Lorentizian
broadening
resistivity on paths
(Kuwamoto et al 1980)
300 K to
800K
800 K data
0-1-2
Home lab, helium lamp
scraped surface
0'-1'-2'
crossover
750 K data
More surface sensitive but
surface layer gives
more strongly correlated
Insulator
S.-K. Mo et al, PRL 04
1150 K
PI phase th
LiPB QC – Fig. 1
QC schematic
Mott-Hubbard paradigm: (V1-xMx)2O3 (M=Cr, Ti)
Look for DMFT "Kondo peak"
McWhan, Rice et al.
PRL ’69, PRB ‘73
PI  PM
interpreted
as Mott transition of
1-band
Hubbard model
2e-/ V3+ ion
3 orbitals/ion
4 ions/cell
PI
PM
more
complex
than
1-band
Hubbard
AFI
Importance of realism: Ezhov et al, PRL ’99,
Park et al, PRB ’00
 Motivation for LDA + DMFT calculations (Held et al, PRL ’01)
More work on V2O3
Hubbard gap filling in I phase with T increased to 300 to 800K,
compare to LDA+DMFT, Mo et al, PRL 04
Theory paper on full-orbital LDA+DMFT 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 LDA+DMFT
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
Compare V2O3 PM phase spectrum
to LDA + DMFT (t-orbitals, U=5.0 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
Get photons from synchrotron—
variable photon energy
Sample
light in
e- out
Electron
Analyzer
Detector
screen
Undulator device inserted in
synchrotron electron beam
gives intense light.
Photoemission spectroscopy (and its inverse)
to measure  (p,E) or p-summed  (E)
Sample
Angle variation moves on
spherical p-space surfaces.
light in
<110>
<100>
7
200
6
175
150
Z
Vary photon energy
to change pz
5
pz
kz
e- out
4
125
100
75

3
Full electronic structure
@ fixed photon energy
—3D data set—
Intensity (arb. unit)
Electron
Analyzer
K
E
-12
E
-10
E
-8
-6
-4
-2
E-EF(eV)
q
angles, energies
ff
qAngle integrated
Step
sample or
Parallel
angle
Or k-summed
detector
angle
detection
“Fermi
Surface”
f

p
0




35
2
25
15
-3
-2
-1
pk0x
x
1
2
3