Soft X ray Absorption and Resonant...

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Soft X‐ray Absorption and Resonant S tt iScattering

Di‐Jing Huang

Nat’l Synchrotron Radiation Research Center, TaiwanDept of Physics Nat’l Tsing Hua University Taiwan

[email protected]

Dept. of Physics, Nat’l Tsing Hua University, Taiwan

Cheiron 2009, SPring‐8, Japan

Oct. 31

Soft X‐ray Absorption and Resonant Scattering

1.Soft X‐ray AbsorptionBasicExperimental Setup

Applications‐ Chemical analysis‐ Orbital polarization‐Magnetic Circular Dichroism

2.Resonant Soft X‐ray Scattering Introduction

Basic of resonant X‐ray scatteringExamples:

Magnetic Transition of a Quantum Multiferroic LiCu2O2

2

2

Soft x‐ray: 250 eV a few keV3

Interaction of photons with matter:

SynchrotronRadiation

photoemissionReflected Photons

FluorescencePhotoelectric effect

Transmission(absorption)

Inelastic Scattering

Crystal

Bragg Diffraction

Photoabsorption

Scattering/diffraction

l i f

4

• lattice structure: arrangement of atoms

• electronic states

•magnetic order

• excitations (electronic states or phonons)

3

Continuum

Absorption

Atom

EV

core levelPhoton energy

A

Continuum

Solid

EF nBand resonance + atomic multiplet

5core level

F

Photon energy

Absorptio atomic multiplet

atomicbackground

2

f if i

dE E h

d

PAPhoto‐absorption

Dipole approximation: 1 1ie i k r k r( )i t i te e k rA ε ε=

If k r << 1,

polarization of x-ray

2

f i

df i E E h

d

Pε

ˆ[ , ]

( )

ε

ε εf i

imf i f H i

imE E f i im f i

ε P r

r r

ˆ[ , ] , if [ ( ), ] 0H V ri m

P

r r 2

f if i E E h ε r

6

ˆijM f i ε r

Absorption probability:

)(2 2

ifij EEMW

4

ˆijM f i ε r)(

2 2

ifij EEMW

Dipole transition

Absorption probability:

cos,sinsin,cossinr̂

sin cos sin sin cr̂ osx y ze e e ε

),(cos 0,134 Y ),(sin 1,13

8

Ye i

41,1 1, 1 1,2 03 2

r̂ ( )xx y yi

z

iY Y Y

ε', ' 1, 1 , 0 l m l mY

1 m m m

1 l l l

when

5 1 62 3 2 3n nd d

Dipole allowed transition 2p 3d:

7

1l l l5 1 62 3 2 3n nijM p d p d ε r

L. circularly polarized: ml = +1 (∵ Y1,1)

R. circularly polarized: ml = - 1 (∵ Y1,-1)

1s np K‐edge XAS can be accurately

described with single‐particle

methods

Dipole allowed transitions :

methods.

2 3p d L‐edge XAS: the single‐particle

approximation breaks down and

the pre‐edge structure is affected

by the core hole wave function. The 1s

2s

3s

K

L1

M2,3

L2

L3

2p1/2

2p3/2

3p1/2, 3/2

M1

8

multiplet effect exists.1sK

5

L3

Fe

•Two absorption “peaks” from 2p 3d:

L3

d

L2

L2

3 22 /p

1 22 /p

•Absorption cross section is proportional to numbers of d holes and density of states in the core level.

9

• L‐edge XAS provides information on the chemical state, orbital symmetry, and spin state of materials.

Fe

2 64 3s d

2 74 3s d2 84 3s d

CoNi

Cu

84 3s d 1 104 3s d

10

Each element has specific absorption energies. “finger print” element specific spectroscopy

6

• soft x‐ray absorption & scattering:

In transition‐metal oxides

scattering:TM: 2p 3dO: 1s 2p

• direct, element‐specific probing of electronicprobing of electronic structure of TMO

TM 2p

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Soft X-ray Absorption and Resonant Scattering

1. Soft X-ray AbsorptionBasicExperimental SetupA li iApplications- Chemical analysis- Orbital polarization- Magnetic Circular Dichroism

2. Resonant Soft X-ray Scattering IntroductionBasic of resonant X-ray scatteringExamples:Examples:Magnetic Transition of a Quantum Multiferroic LiCu2O2

12

7

incident light

Measurement of Soft X‐ray Absorption

I0incident light

transmitted light

mesh

electrometer

detector

13

Photoelectric absorption

3d

Photoexcitation and Relaxation

3d

Fluorescent x‐ray emission

3d

Auger electron emission

2p1/2

2p3/2

3p1/2

3p3/2

3d

2s

3s

L1

M

L2

L3

3d

L1

M

L2

L3

3d

L1

M

L2

L3

1s

2s

K

14

K K

8

Auger electrons

hn

Photoabsorption

Auger electrons

secondary electrons

M1

L2

L32p

d

3s

og)

secondary electrons

15Kinetic energy

Intensity (l

PhotoelectronsAuger electrons

Incident light

Measurement of Soft X-ray Absorption

I0

total electrons(40 ~ 50 Å)

0

electrometer

Fluorescence(1000 Å)

transmitted light

16

(1000 Å)

Auger electrons(20 Å)

9

L edge XAS provides information on theL‐edge XAS provides information on the

chemical state, orbital symmetry, and spin

state of materials.

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18

10

Polarization of Synchrotron Radiation

Left handedLinearly polarized

Left‐handed circularly polarized

Right‐handed circularly polarized

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3d

For 2p3/23d

Soft X‐Ray Magnetic Circular Dichroism in Absorption

Right‐handed circularly polarized light

L33dFor spin up,

3dp gpreferentially excites spin‐down electrons.

Left‐handed circularly polarized light preferentially excites

left‐handed

right‐handed= 5/3

For spin down

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spin‐up electrons. left‐handed

right‐handed= 3/5

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3d

Right‐handed circularly polarized light

For 2p3/23d


3dp gpreferentially excites spin‐down electrons.

Left‐handed circularly polarized light preferentially excites

orbital moment (A‐B)Spin moment (A+2B)

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spin‐up electrons.

MCD is defined as the difference in absorption intensity of magnetic systems excited by left‐ and right‐handed circularly polarized light.

MCD


Soft X‐ray MCD in absorption provides a unique means to probe:

element‐specific magnetic hysteresis orbital and spin momentsmagnetic coupling.

There are two ways to obtain a MCD spectrum:1) Fixing M, measure XAS with left and right 1)

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) g gcircular lights.

)

2) Fixing the helicity of light, measure XAS with two opposite directions of M.

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Chen et al., PRB 48, 642 (1993)

23

Nature 416, 301 (2001)

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13

25




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Spin, Charge, and orbital ordering of correlated electron systems

La0.5Sr1.5MnO4La1/3Ca2/3MnO3

Sternlieb et al. (1996)

Moritomo et al. (1995)

Murakami et al.(1998)

C. H. Chen et al. (1998)

La1.6‐xNd0.4SrxCuO4

modulation vector k

27J. Tranquda et al. (1995)

modulation vector k

Small valencedisproportionation !

Q/Qtotal << 1

Elastic x-ray scattering

k

'k

2

q

q k' k

momentum transfer

2 sinq k 'k2r

-k r

r'k

' kk

2 sin

4sin

q k

k

q 'k

2

3d scattering form factor

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A volume element at will contribute an amount to the scattering field with a phase factor .

r3d r

reiq jrj(r )eiq

qj

f

Fourier transform of charge distribution.

2

qfd

d

15

0( , ) ( ) '( ) ''( )q q sf f f i f

Resonant scattering

As the photon energy approaches the binding energy of one of the core-level electrons,

dispersion corrections

2222

222

)()(

)('

s

ssf

2

''

f

'f

''f

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2222 )()(''

s

sf

0

f

Photon energy

Absorption 4Im( )f

k

Advantage of Resonant Soft X-ray Scattering

0

3 3 2

32 23'

~( )

dik r ik r

resd d

p pd

p

re ref

E E i

0, k

, 'k

2 p

3d

'q k k momentum transfer

modulation vector

TM

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• With =E3d E2p, fres is enhanced dramatically and ordering of d is focused.

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Resonant X-ray magnetic scattering

1m

F1,1 F1,-1

1m

scattering amplitudes

1

electric dipole transitions

)(ˆ)εε(8

31,11,10

* FFzif res

mag

Hannon et al., PRL(1988)

1 lm

0ε ε

1 lm 1 lm

'kε

001

010

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As a result of spin-orbit and exchange interactions,magnetic ordering manifests itself in resonant scattering.

kq 0ε 100

Resonant soft x‐ray magnetic scattering:

•Cross section comparable to that of neutron iscattering.

•Good q resolution (q < 0.0005 Å‐1)

•Spectroscopic information.

•Limited to a small k space, less bulk sensitive.

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1.5 GeVNSRRC, Taiwan

Setup of Soft X-ray Scattering

UHV two-circlediffractometer

EPU 33




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Magnetism: ordering of spins

Magnetization can be induced by H field

Ferroelectricity: polar arrangement of charges

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Electric polarization can be induced by E field

Induction of magnetization by an electric field; induction of polarization by a magnetic field.

Magnetoelectric effect

‐ first presumed to exist by Pierre Curie in 1894on the basis of symmetry considerations

Multiferroics: materials exhibiting ME couplingCr O

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Cr2O3

BiMnO3

BiFeO3

…..

However, the effects are typically too small to be useful in applications!

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Two contrasting order parameters

Magnetization: time‐reversal symmetry broken

:

t t M M

P P

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Polarization: inversion symmetry broken

: ,

r P MP Mr P qr

Recently discovery in the coexistence and gigantic coupling of antiferromagnetism and ferroelectricityin frustrated spin systems such RMnO3 and RMn2O5

(R=Tb, Ho , …) TbMnO3: Kimura et al., Nature 426, 55, (2003)

TbMn2O5: Hur et al., Nature 429, 392 (2004)

revived interest in “multiferroicity”

Magnetism and ferroelectricity coexist in materials called “multiferroics.”

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• TC < TN• Ferroelectricity is induced magnetism.

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2 5

3 0

3 5

(a )

0 T 1 T 3 T 5 T 7 T 9 T

E //b , H //a (F C )1 k H z

w a rm in g

TbMn2O5 Nature, 429, 392 (2004)

2 0

2 0

4 0

(b ) E

p o le//+ b

H //a (Z F C )

m2 )

• 3 transitions on cooling.

•Magnetic field induces a sign reversalof the electric polarization.

2 5

0 1 0 2 0 3 0 4 0

-4 0

-2 0

0

0

P1

P2

T

P

0

40

-80

40

P1

P2

T

P

0

40

-80

40

P (n

C/c

m

T (K )

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Quantum multiferroic magnet LiCu2O2

O2‐

Cu2+ orthorhombic, Pnmaa=5 734 Å

Cu1+

Li1+

a=5.734 Å, b=2.856 Å, c=12.415 Å

Qausi‐1D spin ½ chain:Qausi 1D spin ½ chain: •Characterization of the ground state?•Multiferroicity(Park et al. PRL98, 057601; Seki et al., PRL (2008); cond‐mat 0810.2533

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(1/ 2, ,0)q

a

b

J1

J2

94°

Masuda et al., PRL (2004)

1( )n ne S SP

along the a axis ?

(1/ 2, ,0)q

in units of 2 2 2( , , )a b c

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ol K

)C (J/mo

Two transitions ?


42Seki et al., PRL (2008)

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LiCu2O2 (100) single crystal

5

930 eV

3dCu2+

Resonant soft x‐ray magnetic scattering

5 mm

2p3/2

930 eV

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Correlation length = 1/HWHM

T = 10K: a = 690 Å b = 2100 Å

(1/ 2, ,0)q

qa (2p/a)

qb (2p/b)

non‐zero scattering intensity above TN

qb ( p/ )

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23

t iti t t

intensity

( ,1)abq q

onset of the long‐range spin ordering and induced P

21.5 K

23.5 Ktransition temperature of the precursor phase

ab: in‐planecorrelation length

cleaved LiCu2O2(001) 5 mmc: correlation length

along the c‐axis

SW Huang et al., PRL (2008)

46

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,( ,1)a bq qq1

q

•There is an in‐plane short‐range AFM ordering above TNq2

g N

•extension of the zero‐temperature AFM ordering

•spin coupling

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spin coupling along the c axis is essential for inducing P.

2 /( ) e S Bk TT

Above TN, in‐plane correlation

2D renormalized

averageJ ~ 4.25 meV

2D renormalized classical behavior

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•The ground state of LiCu2O2 exhibits a long range AFM ordering.

•The spin coupling along the c axis is essential for inducing P.

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Thank you!

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Appendix: Basic of Magnetic Circular Dichroism in X-ray Absorption

Considering L-edge 2p3/2 3d absorption, and ignoring the spin-orbit interaction in the 3d bands,

3d2

2ˆ, r ,l jl m j m ε

m l = 2 1 0 -1 -2 For left-handed circular light

2p3/2

2

21,1( )

2,lm j

x yiR r Y Y j m

1 1/3 1/18

m j = 3/2 1/2 -1/2 -3/2

L3 Left-handed circularly polarized light preferentially excites spin-up electrons.

radial part1/6 1/3 1/3

2For light-handed circular light

=25/185/6

1/3 1/3 1/6

m j = 3/2 1/2 -1/2 -3/2L3

m l = 2 1 0 -1 -2

=5/6 1/18 1/3 1

25/18

2

21, 1( )

2,x y

lm jR r Y Y j mi

Right-handed circularly polarized light preferentially excites spin-down electrons.

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26

33 Y 33 Y


cos,sinsin,cossinr̂

),(cos 0,134 Y ),(sin 1,13

8

Ye i

r̂ sin cos sin sin cosx y ze e e ε

1/3 1/3 1/6

1/18 1/3 1

m j = 3/2 1/2 -1/2 -3/2

j=3/2

L3

m l = 2 1 0 -1 -2

1,123

23 , Y

1,131

0,132

21

23 , YY

0,132

1,131

21

23 , YY

1,123

23 , Y

2

21, 1( ) ,

2x y

lm j

iR r Y Y j m

2

3 1 12,2 1,1 2 2 3,

2x y

j

iY Y j m

41,1 1, 1 1,03 2 2

r̂ ( )x y x yi i

zY Y Y

ε

)|( YYmlmlmlY Clesbsch-Gordan coefficients

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1,11,12,231

21

23

1,12,2 , YYYmjYY j

21

21

2211)|( 2211

ll

llllmmlml YlmmlmlYY

2211

21

),|( 2211 mlmlmm

lm YYmlmlmlY

2

3 1 12,0 1, 1 2 2 18,

2x y

j

iY Y j m

.....0,261

1,11,1 YYY181

1,11,10,231

21

23

1,10,2 , YYYmjYY j2,21,11,1 YYY 51

33 Y 33 Y

2

21, 1( ) ,

2x y

lm j

iR r Y Y j m


41,1 1, 1 1,03 2 2

r̂ ( )x y x yi i

zY Y Y

ε

1/3 1/3 1/6

1/18 1/3 1

m j = 3/2 1/2 -1/2 -3/2

j=3/2

L3

m l = 2 1 0 -1 -2

1,123

23 , Y

1,131

0,132

21

23 , YY

0,132

1,131

21

23 , YY

1,123

23 , Y

2

3 1 12,1 1,1 2 2 3,

2x y

j

iY Y j m

3 1 2 12,1 1,1 2,1 1,1 1,02 2 3 3, jY Y j m Y Y Y

.....1,221

0,11,1 YYY

21

21

2211)|( 2211

ll

llllmmlml YlmmlmlYY

2211

21

),|( 2211 mlmlmm

lm YYmlmlmlY

Clesbsch-Gordan coefficients2

3 1 12, 1 1, 1 2 2 3,

2x y

j

iY Y j m

3 1 2 12, 1 1, 1 2, 1 1, 1 1,02 2 3 3, jY Y j m Y Y Y

.....1,221

0,11,1 YYY52

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33 Y 33 Y

2

21,1( ) ,

2x y

lm j

iR r Y Y j m

1 1/3 1/18

m j = 3/2 1/2 -1/2 -3/2

j=3/2

L3

m l = 2 1 0 -1 -2

1/3 1/3 1/6

m j = 3/2 1/2 -1/2 -3/2

j=3/2

L3

m l = 2 1 0 -1 -2

1,123

23 , Y

1,131

0,132

21

23 , YY

0,132

1,131

21

23 , YY

1,123

23 , Y

,2

j

2

3 1 12,1 1,1 2 2 3,

2x y

j

iY Y j m

3 1 2 12,1 1,1 2,1 1,1 1,02 2 3 3, jY Y j m Y Y Y

)|( YYmlmlmlY Clesbsch-Gordan coefficients

2

3 32,2 1,1 2 2, 1

2x y

j

iY Y j m

3 32,2 1,1 2,1 1,1 1,12 2, 1jY Y j m Y Y Y

21

21

2211)|( 2211

ll

llllmmlml YlmmlmlYY

2211

21

),|( 2211 mlmlmm

lm YYmlmlmlY

.....0,261

1,11,1 YYY

3 1 1 12,0 1,1 2,0 1,1 1, 12 2 3 18, jY Y j m Y Y Y

2,21,11,1 YYY

.....1,221

0,11,1 YYY2

3 1 12,0 1,1 2 2 18,

2x y

j

iY Y j m

11,1 1, 1 2,06 .....Y Y Y 53

X-ray magnetic scattering

kinetic energy m.B SO

2 2

2 2 2int2

2 ( )2 2( ) ( )

e e

j jmc me e

j jmc mcj

cjj j

AA r sH P s

tA AA

Non‐resonant

Blume, J. Appl. Phys. (1985)2

222 2

2

int

2

2

2 2 ' '

jj iq rj

j

iq r

j

f ec e

V m

f H i

mi e i

cf s

ci

f

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Resonant

int int

22

( )

n ii

nf

f H n

EE

n HE

i

E

mag 32

charge

~ ~ 10f

f mc

6

e

mag 10~

for ~ 600 eV

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