Photoemission and the electronic structure ofmagnetic oxides

Dan DessauUniversity of Colorado, Boulder

Duane F625Dessau@Colorado.edu

Einstein’s Photoelectric effectXPS, UPS, ARPES

sample

analyzer

e

-

h

n

e-

hn

occupied DOS

BE

0D.O.S.

Expt

LDA

LDA

Experiment

Inte

nsity

Valence Bands Copper 2p core levels

remove one

Correlated vs. uncorrelated systems

Static Dynamic

Si, Ge, Cu, etc.Band theory

Works even though 1023

electrons!

Correlated systemsMany-body theories

Dynamic interactions --> Novel and rich physics and materials systems.

Crystal structure of the manganitesCubic perovskite

manganite (ie. La0.6Sr0.4MnO3)

Monolayer perovskiteManganite

(i.e. La0.6Sr1.4Mn2O4)

Bilayer perovskitemanganite

(ie. La1.2Sr1.8Mn2O7)

MnO6octahedra

rock-salt layer

cation(Sr or La)

monolayer

bilayer

ab

c

100 200 300 4000

n=1

n=2

n=∞ cubic

10 2

10 4

10 0

10 -2

10 -4

x=0.4

T c

T c

Temperature (K)

resis

tivity

(W-c

m)

Bilayer manganite - La2-2xSr1+2xMn2O7

cb

a }}

}(La,Sr)MnO3

(La,Sr)O

(La,Sr)MnO3

Cleavage Plane

0.3 0.4 0.5 0.6 0.7

50

100

150

200

250

FM type A-AFI

PI

x

TN/TC (K)

CMR

Doping level x

(x=0.4)

resis

tivity

(W-c

m)

Temperature (K)

Y. M

orito

mo

et a

l.

C.D.

Lin

g e

t al.

Evidence for half-metallicity

• Strong spin polarization in La0.67Sr0.33MnO3 epi-films:

J.H. Park et al., PRL 81, 1953 (1998), Nature 392, 794 (1998).

T = 40K

Double Exchange TheoryKinetic energy gain for ferromagnetic alignment

Susc

eptib

ility

(em

u/m

ol)

ParaFerro

Temperature (K)

Ferromagnetism and Metallicity go together.

H

LaMnO3

La1-xSr xMnO 3 (T<<T c)

La1-xSrxMnO3 (T>T c)

La1-xSrxMnO3 (T>Tc) H°0

eg

t2g

Mn3+ 3d4

large t~

small t~

large t~

Double Exchange TheoryKinetic energy gain for ferromagnetic alignment

Change in conductivity going across Ferro-Para transition: ~ 30%Real materials - many orders of magnitude effect! Why?

Ferro

E FD(E)Para

EJ~0.7 W oW o

Change in t --> change in WCan study with ARPES

q

t = tocos(q/2)~

t2g electrons core-like

S=3/2

eg electron itinerant t = to

~Ferro Para

t ~.707 to~

e-

e-

a1)

a2)

e-

e-

b1)

b2)

Transport without polarons Transport with polarons

To help manganite problem, polaronic effectmust be stronger above Tc than below Tc

Feedback effect necessary - Polaronic effectcooperates with Double-exchange and/or otherphenomena (charge ordering).

Polarons and conductivity

negativemagneto-resistance

Temperature (K)Re

sistiv

ity (o

hm-c

m) H=0T

H=1T

H=3TH=5T

H=7T

H=2T

10-1

100

10-2

1000 200 300

Temperature dependent pseudogaps in CMROxides

Thanks to: X.J. Zhou, P. Bogdanov, Z. Hussain ALS BerkeleyK. Altmann, SRC Madison

Support from the DOE and NSF

Y.D. Chuang et al., Science 292,1509 (2001)

ARPES experimentsYi-De Chuang, Zhe Sun, Adam Gromko, Alexei Fedorov,

Fraser Douglas, Max Bunce, D.S.D.University of Colorado

SamplesT. Kimura, Y. Tokura University of TokyoJohn Mitchell Argonne Nat’l Labs

Questions• How to explain very poor conductivity

– In the “metallic” state of the manganites?– M-I transition into the high T insulating state? (--> CMR)

• Possible mechanisms.•Polarons? Large scattering? Charge/orbital ordering?•Temperature dependent pseudogap (includes some of above).

negativemagneto-resistance

Temperature (K)

Res

istiv

ity (o

hm-c

m) H=0T

H=1T

H=3TH=5T

H=7T

H=2T

10-1

100

10-2

1000 200 300

Very poor metal Insulator

binding energy

emission angle

MDC

EDC

Angle Resolved Photoemission (ARPES)

E vs k relation

EDC: Energy Distribution Curve (ARPESintensity versus binding energy)

MDC: Momentum Distribution Curve(ARPES intensity versus momentum)

e-

hn

occupied DOS

BE

0D.O.S.

EF

Arbi

trary

Uni

t

Binding Energy

Fermi Surface crossing point

k

kF

spectral weight loss due toFermi function cutoff

ARPES on La1.2Sr1.8Mn2O7 (n=2, x=0.4)(Low T Ferromagnetic state)

Integrated spectral weight over (0.2eV,-0.2eV) window

LSDA Fermi surface topology(N. Hamada unpublished)

3d x2-y2 hole pockets

3d 3z2-r2 electron pocket

Y.D. Chuang et al., Science 292, 1509 (2001)

Angle-scanned (unsymmetrized) Fermi Surface bilayer manganite x=0.4 (Low T Ferromagnetic state)

LDA+U dispers

ion relatio

n

ARPES on bilayer x=0.4 samples - Low T (20K) ferro state

Binding energy (eV)

EDCs

Binding energy (eV)

emiss

ion

angl

e (de

gree

)MDCs

-4-2

246

0EF

-0.2eV

Fermi surface topology

Ekx

ky

25

20

15

10

420-2-4

Double Lorentzianfit to MDCs

Binding energy (eV)

emiss

ion

angl

e (d

egre

e)

MDCs

-4-2

246

0EF

-0.2eV

Binding energy (eV)

EDCs

ARPES on bilayer x=0.4 samples - Low T (20K) ferro state

-1.5

-1.0

-0.5

0.0

(0,0) (p,0) (p,p)

bind

ing

ener

gy (e

V )

LDA dispersionMDC centroidEDC centroid

25

20

15

10

420-2-4

Double Lorentzianfit to MDCs

Double Exchange TheoryKinetic energy gain for ferromagnetic alignment

Change in conductivity going across Ferro-Para transition: ~ 30%Real materials - many orders of magnitude effect! Why?

Ferro

E FD(E)Para

EJ~0.7 W oW o

Change in t --> change in WCan study with ARPES

q

t = tocos(q/2)~

t2g electrons core-like

S=3/2

eg electron itinerant t = to

~Ferro Para

t ~.707 to~

hv=22.4 eV 200K spectra taken first

-2 -1.5 -1 -0.5 0

0/0

2/0

4/0

6/0

10/0

14/0

18/0

22/0

(0/0) (p/0)

(p,p)

-2 -1.5 -1 -0.5 0

22/0

22/2

22/4

22/6

22/8

22/10

(0/0) (p/0)

(p,p)

50K Ferro200K Para

Energy Relative to EF (eV)

.06 eV

Temperature dependence of (LaSr)Mn2O7 x=.4 Tc ~ 130K

Bandwidth change : .06 eV/1.5 eV = 4%. Much less than the DE prediction of 30%.==> DE relevant but not key effect.

T. Saitoh et al., PRB (2000)

fitting results

-4

-2

0

2

4

-400 -300 -200 -100 0

1.5

1.0

0.5

0.0

Binding energy (meV)

emission angle (degree)em

issio

n an

gle

(deg

ree)

centroid of peak 1

centroid of peak 2 width

Extraction of the key transport parameters - low T ferrometal state

1)Fermi velocity (from band dispersion near EF) vF ~ 0.038 c

2)Band mass (fitting dispersion with parabola) m ~0.27 me

3)Number of carriers (measurement of the FS volume) n ~ 3.4*1021 holes/cm3

4)Momentum width (HWHM) Dk ~1.2o ~ 0.09 p/a ~ 0.07 A-1 (original)4b)Mean free path (lower limit) l=1/ Dk ~ 14 A ~7 times the Mn-O bond length4c) Mean free time between scattering (lower limit) t=l/vF ~1.24 fs

rARPES = 1/s = m* / n e2t ~ 1.3*10-4 W-cm (Drude)Real value r0 ~ 2*10-3 W-cm (more resistive)

Key ingredient not considered in the Drude calculation: pseudogap. Presence of the pseudogapcan effectively remove carriers from conduction process thus increasing the resistivity

-400 -300 -200 -100 0

weight of peak 10

Wei

ght expected behavior

Binding energy (meV)

Pseudogap

(loss of w

eight)

Temperature dependence of the pseudogap

Pseudogap correlateswith and may drivethe M-I transition.

Temperature (K)

0.4

0.3

0.2

0.1

0.0

1401201008060

60

50

40

30

20

10

0

Tc

wei

ght

Strong pseudogapInsulator

Weak pseudogapPoor metal

weight (-1.7eV,0.3eV)

weight (-0.2eV,0.05eV)

Energy spectra averaged across the entire slice

50

40

30

20

10

0

Ave

rage

-1.5 -1.0 -0.5 0.0

5

4

3

2

1

0

Ave

rage

-.2 -.15 -.1 -.05 0 .05

inte

nsity

inte

nsity

50K 80K100K110K120K130K 150K

Energy (eV)

10

5

0

-5

-10

50-5

Bind

ing

Ener

gy (e

V)

analyzer angle (degrees)

The pseudogap affects all families of the manganites - some very strongly(single layer) and some less so (pseudocubic). Resistivity varies in kind.

Dimensionality dependence of near-EF weight

Optical Conductivity of layered manganite

T. Ishikawa et al., Phys. Rev B 57, R8079 (1998)

• Spectral weight transfer with temperature over large energy scale• Gapped low energy spectral weight (no Drude peak)

Loss of near-EF weight (pseudogap)Simple superposition of metallic and insulating regimes?

-400 -300 -200 -100 0

0

Spec

tral W

eigh

t

Binding energy (meV)

Spec

tral W

eigh

t(d

ensit

y of

sta

tes)

-400 -300 -200 -100 0

metal

0

Binding energy (meV)

insulator Experiment

(Need many many types of regions, all with different size gaps)- May consider fluctuations in space and time to get this.

Also, FS volume matches total # carriers expected by chemical doping(no regions with extra # holes, regions with fewer # holes).

d 3x2 -r

2Mn3+

Mn3+

Mn4+

Mn3+

Mn4+

Mn3+Mn3+

Mn3+Mn3+

FM

AF

Real-space Charge Density Waves (CDW’s) and CDW gaps

2201.75,2.25,0

2.25,1.75,0110

200

020

160K

D.Argyriou et al., Argonne/APS

Extra periodicity induced by CDWobservable in diffraction experiments as

weak superlattice spots at (1/4,1/4,0).

Commensurate/static “CE” ordering

Example: LaSr2Mn2O7 (x=0.5) commensurately doped insulator

G

E(k)k

2∆

G

System gains energy when gap iscentered at EF (commensurate

doping levels).

k-space driven CDW’s and Fermi Surface nesting

Entire measured FS of La1.2Sr1.8Mn2O7 is gapped due to large parallel segments(nearly perfect nesting).

Q

E(k)k

2∆

G

We can guarantee that CDW gap is centered at EF in ak-space driven CDW --> gain extra energy.

If many parts of the Fermi Surface connect (nestingcondition) the instability is greatly enhanced.

char

ge d

ensi

ty

Real space atom position

Charge density wave incommensurate with lattice.Short range in space. Fluctuates in time. Elusive!

Real space picture of the k-space driven CDW fluctuations

• Fermi-Surface-driven CDW cooperates withthe Jahn-Teller effect to distort MnO6octahedra. --> increased energy scale of gap.

• Elastic strain mediates the correlations.• Incommensurability with the lattice --> order

is short ranged in real space

x ~ 6a

ac

Mn La/SrO

O3aO1O2

O3b

B. Campbell et al, (Phys. Rev. B 2001)

From an analysis of the intensity of 108 superlatticereflections (only observed in the high temperature

paramagnetic state)Temperature Dependence

DiffractionI(0.3,0,1)

ARPESWeight at EF

0 50 100 150 200 250 300(K)

Tc

Temperature

Inte

nsity

Weak PseudogapPoor metal

Fluctuating CDW(not observed in diffraction!)

Strong PseudogapInsulator

Semi-static CDW

Sharpness of the energy gap

E k2∆ 2∆

E

DOS

CDW with long range order

E kWith short range order

E

DOS

2∆E

DOS

Including polaronic (Jahn-Teller) energy scale

Looks like lower figure even in low T ferromag state!Polarons and/or charge order at all Temps (with varying strengths).

Temperature dependence of the pseudogap

Pseudogap correlateswith and may drivethe M-I transition.

Temperature (K)

0.4

0.3

0.2

0.1

0.0

1401201008060

60

50

40

30

20

10

0

Tc

wei

ght

Strong pseudogapInsulator

Weak pseudogapPoor metal

weight (-1.7eV,0.3eV)

weight (-0.2eV,0.05eV)

Energy spectra averaged across the entire slice

50

40

30

20

10

0

Ave

rage

-1.5 -1.0 -0.5 0.0

5

4

3

2

1

0

Ave

rage

-.2 -.15 -.1 -.05 0 .05

inte

nsity

inte

nsity

50K 80K100K110K120K130K 150K

Energy (eV)

10

5

0

-5

-10

50-5

Bind

ing

Ener

gy (e

V)

analyzer angle (degrees)

electronic

(0.3,0,1)orbital stripe

(k-space)

Fermi surfacetopology

k-space

charge/orbitalmodulation

Jahn-Teller distortionsof various magnitude

r-space

+CDW (short range)

pseudogap

ARPES

XRD,EXAFS

Double Exchange

CMR effect

lattice

chargeorbital

spin

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