An essential property of synchrotron radiation: linear and circular polarization for X-ray absorption spectroscopy

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An essential property of synchrotron radiation: linear and circular polarization for X-ray absorption

spectroscopy

E. Dartyge, A. Fontaine, F. Baudelet, C. Giorgetti, S. Pizzini, H. Tolentino

To cite this version:

E. Dartyge, A. Fontaine, F. Baudelet, C. Giorgetti, S. Pizzini, et al.. An essential property of syn-

chrotron radiation: linear and circular polarization for X-ray absorption spectroscopy. Journal de

Physique I, EDP Sciences, 1992, 2 (6), pp.1233-1255. �10.1051/jp1:1992206�. �jpa-00246598�

Classificafion

Physics

Abstracts

78.20L 74.70V 78.70D

75.508 75.25

An essential property ^of synchrotron radiation

_:

linear and

circular polarization for X-ray absorption spectroscopy

E.

Dartyge,

A.

Fontaine,

F.

Baudelet,

C.

Giorgetti,

S. Pizzini and H. Tolentino

LURE (CNRS-CEA-MENJS), Bit. 209D, F91405

Orsay,

France

(Received J3

February

J992, accepted in

final form 2April

J992)

Abstract. It is _now well-documented that

linearly

polarized

X-rays,

available from synchrotron radiation _sources,

yield

_a fundamental tool _to determine the

anisotropy

of local atomic _or electronic structure.

Recently

_{a new area} of science

emerged

in direct connection with the

helicity

of

X-ray photons. X-ray spectroscopists

_{are very} keen _users of this property ^and now, inseltion

devices are

specifically

tailored to fulfil

polarization requirements.

I. Introduction.

« ESRF

[I]

is _a low emittance

ring primarily

based _on insertion devices and offers _uS the

unique opportunity

to carry out that

X-ray Absorption Spectroscopy (XAS)

which

requires

:

high

brilliance in the

X-ray region (1-30 kev)

well defined linear _or circular

polarization.

ESRF iS the first machine to

keep

the natural characteristics of the

Synchrotron

emission

non

Spoiled by

the emittance of the machine _».

These comments were

heading

the report ^{of the XAS} group of the first users'

meeting [2]

held in March 89. It iS very

significant

that the

polarization

of the _Source was

recognized

aS an

essential

quality

which makes way to new routes of

investigation.

The

forthcoming availability

of the ESRF _Sources

by

the end of 1992 makes these iSSueS _more

appealing right

_now.

Thanks to the

existing

_Storage

rings,

it iS _now well documented that the linear

polarization

of

X-rays

iS

truly important

_to determine the

anisotropy

^of local atomic _or electronic Structure. This

capability

is

currently

used for Surfaces

[3], Superlattices [4],

or

anisotropic single crystals

of the _new

superconductors [5],

for instance. Successful attempts to look at linear

magnetic

dichroism _were first carried _out in 1986

during

^the

operation

of ACO

[6].

A _{new area} of Science

recently emerged directly

connected with the

helicity

of

X-ray photons,

The

prediction

of Strekine and Stem and the

pioneering

work of Shiitz et al.

[7]

have

Stimulated, throughout

the

world,

numerous circular XAS

[8]

_or

photoemission [9]

_programs

dedicated to various aspects ^of

magnetism.

This _was

unpredictable just

5 years ago.

Since _no tractable

theory

iS

really

available _to

quantitatively

describe the interaction of

circular

polarized X-ray photons

and

magnetic-

or more

generally

^chiral- condensed

matter, it is

actually

_a new

piece

of science which has _to be created. Whatever _our present

enthusiasm,

_we have to

keep

in mind that it took _a

long

time

(one century)

to merge the

discovery

^of

magnetic

dichroism

by

Pieter Zeeman

(1886) [10]

in the

discovery

of the _« X- Strahlen _»

by

Wilhelm Conrad

R6ntgen (1895) [11, 12].

Nevertheless the emergence of circular

magnetic

dichroism in 1987 allow _us to dream

already

about

applications

for bit Storage with a very

high density taking advantage

^of the circular

X-ray magnetic dichroism,

and the increased

spatial

resolution due _to the smallness of the

wavelength.

The aim of section 2 is _to recall the essential features of the

light

emitted

by

_a relativistic

charged particle.

Section 3 illustrates the

possibility

of linear

polarized X-rays

to carry out

symmetry-dependent

XAS

investigation

of

anisotropic single crystals.

The subtle understand-

ing requires

the control of the symmetry ^{of the emitted}

photoelectron

made

possible by

the linear

polarization

of the

impinging photon.

^Section 4 tums to the helical

X-ray-based approach

of

magnetism

^which is still in its

infancy

but nevertheless full of

promises.

However let _us

emphasize

_once

again

that _a

fairly large

_progress ^{of the}

theory

is

required

to reach _a full

understanding

of the

experimental

data.

2.

Properties

of

synchrotron

radiation.

The main _source of

X-rays

has been for _more than 75 _years the fluorescent emission of cooled

metallic anodes shot

by energetic

electrons accelerated up ^to 30 KeV _{or more.} The

decay following

the _core level excitation goes

mainly through

two channels, The radiative _one

involves the emission of

element-specific

lines. Since this

property

^is atomic-like and the

decay

channel is

independent

of the process of excitation of the _core

level,

there is _no way ^to get

polarized X-rays

out of it. The fluorescence lines are known _to be

unpolarized,

I,e.

natural.

This is also _true for the

bremsstrahlung which,

in _some respect, ^{is similar} to

synchrotron

radiation since it _comes from the

change

of _momentum with

time,

of the

impinging

electrons

travelling

in the target. ^However once

again

there is _{no reason} to get a

polarized

_source out of it since electron acceleration has _no

preferential

direction.

Conversely,

in _a storage

ring,

electron

(or positron)

revolves

along

a closed

loop

with

quasi circularly

bent parts. ^{Therefore the} acceleration is well-defined and radial.

Originally

the bent parts ^{of the}

trajectory

were within the

poles

of

bending

_magnets, whereas the

straight

sections

were

totally

dedicated _to electron

optics,

r,f,

cavity,

or elements needed for the

injection.

It is well known that accelerated

charges

emit

electromagnetic

radiation. It _occurs when the

point charge

travels in the gap of the

bending

magnets or in the

straight

sections of the

vacuum chamber if insertion devices- which _are

periodic magnetic

structures- _are

implemented.

The radiation

intensity

and

polarization,

the

angular

distribution and the

frequency spectrum

are

directly

related to the

properties

of the

charge's trajectory

and motion. For relativistic motion _a number of

interesting

effects determine the

exceptional properties

of

synchrotron radiation,

I,e, the white Spectrum ^{and its critical} energy, the

collimation, the

polarization. Everyone working

in this field has been directed to Jackson's

book, Chapter14 [13].

Here _we

just

want to summarize the aspects ^of

synchrotron

radiation

which _are essential to

polarization-dependent

measurements.

2,I EMISSION _{OF A} RELATIVISTIC POINT CHARGE lN A CIRCULAR MOTION. For _an

accelerated

charge

ⁱⁿ nonrelativistic motion the

angular

distribution of power radiated per unit solid

angle

shows _a

simple

sin 2 8 behavior

given by

~

= eo

~ Q ^~

sin~

_8.

da

~

iv

is the acceleration and 8 is the

angle

between the acceleration

p

and _n, the unit vector which

points

towards the observer from the

charge

itself. This contains also the well-known fact that the Brewster

angle

^{iS 45° for}

X-rays

whose index is close to

unity.

In

general

^{the fields} E and B _can be written

explicitly

_aS a function of the

charge velocity

and acceleration _:

B

"

l~

_X

Elret

e

n_p

e

Inx ^((n-@)xj)

~~~~

_~~

4 "~0

y~(i _{p n)~ R~}

ret

~ 4 "EOC

(i p n)~

R

ret

where

=

d@/dt

^{is the}

ordinary

acceleration divided

by

_c, and _y iS

given by

the energy of the

particle

E

= ymc ~.

Fields _are divided into

velocity

field and acceleration field which

depends linearly

_on

acceleration. The

velocity

field is _a static field

essentially

and falls off _as R~~, whereas the acceleration field is _a radiation

field,

E and B

being

_transverse

(perpendicular

to the radius

vector

n)

and

decreasing

_as

^R~'

For relativistic motion the acceleration field

depends

_on both

velocity

and acceleration.

Consequently

the

angular

distribution is _more

complicated.

If _one looks at the radial component ^of

Poynting's

_vector,

[S.n]~~= o~~~~

~~ ~~~

~~~~~

^~

~ R^~

(l fl n)~

ret

It is easy ^to find out two

types

^of relativistic effect. The detailed

angular

distribution of the

intensity

and the

polarization

_comes from the

specific relationship

between acceleration and

velocity.

The cubic _term in the denominator arises from the Lorentz transformation from the

coinciding

rest frame of the

particle

to the observer's frame. For p close _{to one} it is

obviously

this _term which «collimates _» the emission

along

the radius vector n and enhances the

intensity dramatically.

If _one

proceeds

with the necessary

integration,

_one

gets

^the _power ^radiated per unit of solid

angle. If,

in

addition,

_we consider _a

point charge

in

instantaneously

circular

motion,

its acceleration iS

perpendicular

to its

velocity p,

and the power

density

tums out to be _:

dP

(t,)

~

e2 iv

_j~

~ sin2

_e

cos2 _#

dn ^°

c3(1 p

_cos

e)3 y2(1 _p

_cos

_&)2

~ll'~

_Eo

^~i~

_Y^~

~i

' le~~~

Ii ~~i~+~lis~t

where the

angles

8 et # are defined

according

to the classical scheme

(Fig. 1)

:

2, I, I The collimation. This power

density

is

proportional

to the inverse of

(I p

cos

8)~.

which _means that the emission is

essentially

^{collimated within} _a cone whose

opening

is _as small _{as :}

8

= y with _y

larger

than 500 for _a low energy machine such _as

SuperAco

_at LURE and I1 740 _at ESRF. The

frequency dependence

of the

opening angle

^of the _cone of emission goes with the

following approximation

for the standard deviation

[14a]

_:

«~ = 0.57 y~

'(wjw

_)°.~~ with 0.2 _<

wjw

<100 where w~ is defined below.

1 _turn

~ -

#

U3 z

o u

$

~

~

Time

)

^~

2~

,

""~

z

Fig.

I. Schematic definition of the

geometrical

_parameters of the

synchrotron

radiation emission.

2,1.2 The

spectral

distribution. This collimation _comes from the relativistic motion of the

point charge.

It has _a direct

counterpart

^{in the}

spectral

distribution. The

observer,

who Sits in the

laboratory

far from the

moving point charge,

_Sees the emission

only

when the

charge

travels

along

_{a very}

Specific portion

of the circular

trajectory,

the extension of which iS limited to 2 y~ ~. In other words the observer receives

light during

Short

pulses,

At

=

T(2

y~ ~/2

ir) Separated by

the

period

T of the full revolution. The Fourier transform of the delta-like

function in the time Space iS _a broad band in the

frequency

_Space :

Synchrotron

radiation iS _a

« white

light

_».

2,1.3 The _cut

off frequency

_w~. The

length

^difference between the _arc of circle

(2

_{p y~ ~)} from which the

charged particle

emits _to the observer and the linear

trajectory

followed

by

the

photons (2

_p sin

y~') _generates

a

phase

shift which remains small if the

frequency

of

light

is smaller than the critical

frequency

_w~. The

length

difference between the two

trips

is

just proportional

to the cubic _term of the sine

development

since the

angle

is subtracted. Therefore the

photon

critical

wavelength

^is

proportional

to

(p

y~

~).

^{It is} easy to tum it into

photon

_energy. The numeric coefficient _comes from the additional

argument

^of

equality

between the power emitted below w~ and the power emitted above w~

3c

y~

~°~~4ir

p

2.1.4 The total emitted power.

Integrating

_over the full solid

angle

leads _to the well-known

y~ dependence

of the total emitted power

[15]

_:

~°

~2

6ireo ~~~~'~

Obviously only

electrons _or

positrons

_are suited to

produce synchrotron

radiation. For _a

given

_energy, the power

produced by

protons of

equal

_energy is

by (M/m~)~,

^i.e.

1,13 _x

lli~

_{lower than the power}

produced by

electrons. Once

again

the relativistic motion enhances the

photon production tremendously.

An infinite radius of curvature reduces the emission to zero since there is _{no more} acceleration.

Let _us compare the

storage rings

of

LURE, namely

DCI and

Super ACO,

to ESRF which will be in

operation

_very soon.

Table 1.

w~ A~ ^{he E} p

(Kev> (A)

mrad

(w

=

w~) (GeV) (m)

SuperAco

0.65 19 0.83 0.8 1.8

DCI 3.4 3.5 0.37 1.8 3.7

ESRF 19.2 0.65 0. I 6.0 25.0

he is the FWHM of the vertical

opening angle

for the total energy

flux,

I,e.

he

=

1.3 y~

If _one looks

only

at the

light polarized

in the

plane

of the orbit the FWHM is smaller

by

_a

factor

0.87,

I,e.

A,

⁸ ₌ ^1,13 y~ ~. The lobes of the emission of the

photons perpendicular

to the

plane

of the orbit

point

at 0.6

y~~

with _zero emission

just right

in the

plane

of the

orbit

[14a].

2.2 POLARIzATIONS.-

Coming

back to the transverse electric field

generated by

the

relativistic

moving charge,

E~~(x, t)

₌ ^{~ ~ ~}

~~~ ~ ~~ ~~

4 free c

(I n)

R

r~t

one can add _more comments for the _case of the circular

trajectory,

_n is

roughly

_a

difference between two almost colinear unit vectors, ^{therefore it is}

orthogonal

to _n.

The vectorial double _cross

product gives

_a vector with two

components,

one

along

the

(n @)

direction and the other

along

the acceleration _:

nx

j(n-p>x>j

=

(n-p>(n.>)->(n.(n-p))

=

(n- p>(n.»- j(I _-n.p>.

Since the acceleration is the derivative of the

velocity,

_one of the

components

^{of the electric} field is

phase

shifted

by ir/2

with

respect

to the other. This is at the

origin

of the circular

polarized light.

Fourier

transforming

the electric field and

assuming

the observer _to be

right

above the axis of emission

(giving ir/2

to

4),

substantiate the

previous

result _:

~~~~ ~~o

cR

~c

~~~

~

~c

~~~

~~ ~

~~

~_~~

~~~~ ~~ 2i~o

cR

~c

~~~

~~ ~c

~~~

~~ ~

~~ ~~~

with A~ ^and A~'

being

the

Airy

functions

A

(x

-

i II

_{CDS + xt} dt

A

~'(x

=

j~

^{t sin ~~} + xt dt

=

~ ~~

ir ~ 3 dx

E~

^{contains the}

imaginary

number _« I _» which allows this

component

to be

ir/2 phase-shifted

with

respect

to

E~

and creates the circular

polarized photon

_{as soon as} the beam is not collected _on the axis.

Crossing

the

plane

of the orbit

changes

the

helicity

of the

photons

from

left-handed to

right-handed (or

the

reverse)

and therefore _at

=

0,

the

photons

_are

produced strictly linearly polarized.

It is rather intuitive to

appreciate

that

S,

the total power,

integrated

_over the

angles,

emitted with _{a «}

polarization (along

the

acceleration)

should be much

larger

than

S~

emitted with _{a ir}

polarization.

Therefore the flux of circular

polarized photons

is

always

a

small fraction of the total flux. Nevertheless

slitting

at a reasonable

angle

below _or above the

plane

of the orbit

(y~

_{~) can} lead _{to a} circular

polarization

rate of 80 fb with _a flux about 2.5 times smaller than that

right

at the

maximum,

I,e, in the orbit

plane.

The intrinsic

properties

of the

synchrotron

radiation emission tell _us that

bending

magnets

cannot be the best _sources of

circularly polarized light

since the _rate falls off

rapidly

for

w ~ w~, and it is _never

large

at lower energy.

Table II.

w = w~

S,

=

7/8(S,

₊

S~) S~

=

1/8(S,

+

S~)

w « w~

S,

=

3/4(S,

₊

S~) S~

=

I/4(S,

+

S~)

Up

_{to now we} discussed the emission of _one

charged particle following

the ideal orbit.

Taking

into account _a real

storage ring

and the existence of _a

large

bunch of

charges requires

to introduce the

concept

^{of emittance and}

optical

functions which control the _source size. The

divergence

_can be limited, either

by

the intrinsic

properties

of

synchrotron

^{radiation like} at

ESRF,

_or controlled

by

the

optical

functions of the storage

ring

like in almost all the

existing

low energy machines.

However,

to a

large

extent, all the characteristics of the

synchrotron

emission _are still valid _as summarized above.

2.3 INSERTION _{DEvicEs FOR CIRCULAR POLARIzED PHOTONS.-} As _{soon as}

synchrotron

radiation ceased _to be _a

parasitic subproduct

^of

high

_energy

physics experiments,

and

provided

a

powerful probe

for other

scientists,

the

design

of tailored _source became _an

exciting challenge.

The search for _{new sources} of

synchrotron

radiation has

always

been _one of the

goals

of national laboratories. As it is

currently repeated,

the

newly designed

S.R.

facilities _are insertion device-based. This statement

just points

out that insertion devices

(I.D.),

undulators and

wigglers,

_{are more}

powerful

sources and their characteristics _are tunable.

The basic idea of _a conventional I.D, is _to

supply

a

quasi sine-dependent

vertical

magnetic

field

along

the

trajectory

in order to create many bends in the

point charge trajectory.

Consequently

the

intensity

of the emission which _occurs from every curved part ^{of the}

trajectory

is

strongly

enhanced.

One has _to

distinguish

between

wigglers

and undulators.

For

wigglers

the

trajectory

followed

by

the

charge particle

is

long

with

respect

to the

photon trajectory.

The intensities created

by

each

bump just

add up.

Conversely

if the

magnetic

field is _{not too} strong ^the

phase lag

taken

by

the

charged particle

with

respect

to its _own

light

is

small

enough

and interference _can take

place. Amplitudes

themselves add up,

leading

to constructive and destructive interferences

according

to the

wavelength

of

light.

With in the limit of low

magnetic

field

(K~ 0), right

_on the

axis,

the fundamental

wavelength

is

by y~

shorter than half of the

magnetic period

of the ID since the Lorentz contraction has to be

applied twice,

_once because the

charged particle

flies

through

the

periodic magnetic

structure, and _once because the observer _{« runs} at the

speed

of

light

_» into the _wave

planes

A~~~~~~ ⁼

~

~~~l'

1

+

§~

^{+ y~}

j

with K

= 0.934 A

~~~_

[cm Bo ~resla

2 _y

K _measures the maximum

angle

of deflection of the sine

trajectory

of the

charged particle,

with y~ as

angle

unit. K is

large

for _a

wiggler (a

few

units)

and small for _an undulator

(K

~

l

).

A conventional I.D, does not generate ^circular

polarized light.

On

axis,

I,e, _on the

plane orbit,

the

light

is

linearly polarized

as it is for _a

bending

_magnet.

Away

from this

plane, right-

handed

(left-handed)

circular

polarization

is created

by

the

charged particle

in the half

period

where the field is

positive (negative).

Since _an I.D, is

essentially

_an altemation of

positive

and

negative magnetic fields,

the _net result is _a linear

polarization right

on

axis, plus

_an

increasing

part ^{of natural}

light

with

increasing

off-axis observation. Therefore the

generation

of linear

polarization

with insertion devices is

straightforward.

It is _more subtle to

generate high

flux of

circularly polarized X-rays.

Three main I.D, concepts ^{have been}

produced

to

generate

^{intense circular}

polarized light.

A well-documented review has been

recently

written

by

Elleaume

[14b].

Let _us go

through

_a

rapid presentation

to underline the

flexibility

of the I.D.

design.

2.3. I The helical undulator.

Historically

the very first helical undulator _was conceived with

a

superconductive

^{helical field for} the free electron laser

[16].

At Novosibirsk _{a room} temperature helical undulator has been installed in the

early

80s'. In 1986 Onuki

[17]

proposed

to combine _two

planar

undulators with

exactly

the _same

period,

_one with _a vertical

magnetic field,

and the other with _a horizontal

magnetic

field. The three parameters to tune the I.D, _are the two

magnitudes

of the

magnetic

_gap and the

phasing

of _one undulator with

respect

^{to the other which} can be

changed by

_{a mere}

longitudinal

translation _{over a} distance of _one

period.

If the _two fields _are

equal,

and the undulators _out of

phase by qr/2,

helical

photons

_are

produced

_on axis in the fundamental. An additional

phase

shift of half _a

period

restores a helical

polarization

but with _a

sign opposite

to the initial _one. In the intermediate

position

the

light

is

polarized

at 45

degrees.

2.3.2 The

asymmetric wig gler.

Other schemes have been

proposed

to have _{access to}

higher photon energies

based _on

wiggler

radiation

[18].

The

asymmetric wiggler

is

designed

to

produce

_an

asymmetric trajectory,

still

periodic.

But _one half of the

trajectory

is made of _a

small radius of _curvature

(p)

and the other half of _a

large

radius of curvature

(p ).

The emission of this

wiggler

is _{a mere}

overlap

of the emission of two kinds of

magnetic dipole,

_one with

large

critical energy w~

(large

curvature and let _us say

positive)

and the other with low critical energy

w] (for

low but

negative curvature).

In _a range of

energies higher

than

w]

_one

only

collects radiation from the first set of

bumps

which _are all of the _same nature. The circular

polarization

which _was present ^{in the}

bending

_magnet and cancelled in the

symmetric

wiggler

is restored. The selection of the circular

polarization

is achieved _as for

bending

magnets

by moving

the slits up and down. A

prototype

^{of such} an I.D, is

currently

at work at

SuperAco [19].

2.3.3 The

planar

helical undulator. -Elleaume

[20] proposed

in 1988 to build _an exotic undulator

capable

to deliver very brilliant

radiations,

with

fully

variable

polarization,

in _an

intermediate range

(0.5-10 kev).

The

concept

^{of this undulator}

assigns

_a function _to the lower

jaw (namely

the

generation

of the usual

periodic

vertical

magnetic field),

different from the role

given

to the upper

jaw

which creates a horizontal undulator field of identical

spatial period.

The

adequate longitudinal phasing

allows

polarization

to be tuned fkom

right-handed

to linear _at 45

degrees,

then

left-handed,

then linear at 135

degrees.

The

independent

variation of the

height

of the two

jaws

allows the variation of

ellipticity

within the _extremes of almost total horizontal

polarization (upper jaw

far

off-working position)

or almost total vertical

polarization (lower jaw

far

off-working position).

Besides very

important advantages

in the mechanical

aspect,

^the

optical performances

_are

attractive. A very

high

rate of

polarization (~

95

fb)

_can be achieved for any one of the three pure

polarized

states of the Stokes

decomposition.

This device is under construction to be

installed _on BL#6 _at ESRF which is dedicated _{to «}

Spectroscopies

with variable

polarization

in the 1-5 kev

spectral

_{range »}

[21].

Besides the

production

of

photons

of _a

given helicity,

the

experimentalist

has to face two other serious

problems

which _are first the

polarization

transfer of the

optics and,

second the

experimental

evaluation of the circular

polarization

rate. These

points

_are

certainly

relevant to the

physics

of the

polarized photon

and its interaction with matter, but it has been

subject

to careful attention for years,

long

before the

generalization

of the _use of

synchrotron

radiation

[22].

3.

Anisotropy

of the _core hole relaxation in XAS _a8

probed

in square

planar cuprates.

3, I FUNDAMENTALS.

Zaanen, Sawatzky

and Allen

[23] suggested

that U~~ ^is

larger

than A for the late divalent transition metal

oxides,

in

particular

for insulators such _as CUO _or

undoped

_cuprates

(e.g. La2Cu04

and

Nd2Cu04)

which contain the

nearly

_square

planar (Cu02)-chess

board-like atomic arrangement. U~~ ^{is the Coulomb} interaction between _two d electrons in the _same 3d band and A the

ligand

to metal

charge-transfer

_energy.

The first excitation in these

cuprates

^with n d-electrons

(d~)

is _a

charge-transfer

from the

ligand

to the transition metal

(d~

- d~ +

L,

where L

represents

a hole in the anion valence

band).

To describe the

ground

state of this system one has _to take into account the

02p-Cu3d hybridization

_energy

(T ),

which is

responsible

for the

partial covalency. Therefore,

the gap is

controlled

by (A~+ _4T~)~'~

The Cu local

point

_{group symmetry}

(D~~) yields

the main

features of the electonic structure of these

insulators,

the

02p-Cu3d hybridization being large specially

^for

in-plane (x,

_y

symmetry)

^orbitals.

In the cluster

approach,

the

ground

state of square

planar

_cuprates is well described

by

the admixture of

configurations

ao(3d~)

₊

po[3d~°L)

,

with

a(

+

pi

=

I and

al

~

pi,

_{because of the so-called divalent character} of the Cu ion. A

more

explicit

_way of

writing

the admixture of

configurations

would be

ao(Cu. ^ls~ 3d~,

O

ls~. 2p~)

+

po(Cu. ^ls~ 3d~°,

O

ls~. 2p~)

but _we will _use the _more

compact

^and

widespread terminology given

before.

The d-hole has

x~- y~

symmetry

(d~2_~2).

^{In the} one-electron band

picture,

the

charge-

transfer _gap

separates

^{the full valence band}

having

dominant

02p

character from the conduction band

having

dominant Cu 3d character. In other

words,

the lowest excitation of CUO and the

non-doped

cuprates ^consists

primarily

in

transferring

the hole with Cu

3d~z_~2

^{dominant character into the O}

2p-like

valence band, ^which is otherwise full.

The nickelates

Ln2NiO~ (Ln: lanthanide) crystallize

in the _same T structure

[24]

_as

La2Cu04. Similarly,

the

ground

state is

mainly given by

^{the admixture} _ao

3d~)

₊

_po 3d~L),

with

a(+ film

I. In this _case the two d-holes of

Ni(II)

ions have

x~-y~

_and 3

z~-r~

symmetries _{(d~2_~2}

and

d~

_{=2_~2).}

Nevertheless,

the

in-plane (x,

_y

symmetry) hybridization

is _a

little stronger ^{than the}

out-of-plane hybridization,

because of the distorsion of the

octahedron. As

predicted by crystal

field

theory,

this distortion is found _to be

large

in cuprates ^and to

persist

with _a much smaller

magnitude

in the nickelates.

This paper focuses _on the elements

entering

the relaxation process due _to the _core hole and to the

photoelectron

present ^{in the final} state of the

X-ray absorption spectroscopies (XAS).

We report on Cu and Ni

K-edge

XAS

experiments

and

give

evidence of the

importance

of the

symmetry

^the

photoelectron

itself in the _core hole relaxation process.

3.2 DEscRiPTioN _{OF HIGH ENERGY} sPEcTRoscoPiEs. The

description

of these spectros-

copies

will be

given

_at three levels.

I)

The _one electron

picture

of

high

_energy

spectroscopies

^is the

approximation

taken _at the level _zero. This

description might

be sufficient in

spectroscopies

where _narrow bands _are filled up and the

photoelectron

_goes into _a very broad final state, such _as the O

K-edge XAS,

where

band structure dominates.

ii)

In order _to understand

high

_energy

spectroscopies

of transition

metals,

_or, more

generally, partially

filled _narrow band systems, ^{it is} necessary to take into _account the presence of the _core hole in the final state and _to let the system ^{relax in order} to screen the

perturbation.

The

gain

in Coulomb energy

(U~~),

^due to the interaction between the _core hole and the

quasi-localized d-electrons,

_puts the

3dl~l _(n

< lo

) poorly-screened configuration

at

energies higher

than the

3dl~+ IL

well-screened _one and

changes

their admixture. In the final state, the

configurations [fi)

and

[f~)

_:

fi)

" +

ai(c. 3dl~~ e~)

+

pi(c 3dl~

+ ~l L.

e;)

[f2) =-flf(c. 3dl~~ e~)+ai(c. ^3d~~+~lL, _e~)

with

al

₊

pi

=

I

(e~

_represents the

photoelectron

with _{a wavevector}

k)

_; are

separated

in

energy

by [(U~~ A)~

₊ 4 T~]~'~

fi)

is at

energies

lower than

f~)

and has dominant

3dl~

+ l L character

pi

~ a

/).

In Cu

2pXPS

one observes two

lines,

_a Lorentzian-like main line

fj)

and _a satellite

)f~) (the

core hole is _a

2p

state and _n

=

9), separated by approximately 9eV,

which

corresponds roughly

to

[(U~~

^A)~ + 4

T~]~'~

It is difficult to get this

separation accurately by

XPS since the satellite has _a broad

multiplet

structure. U~~ ^{has been found to have values}

between 8 _to 10eV

[25, 26]

but the value of U~~ ^{should be different if the} core hole

c is _on

2p

orbitals or on ls

orbitals,

since the

overlap

between the wavefunctions

(c

and

3d,

to

simplify) bracketting

^the Coulomb interaction are different. This two-

configuration concept

was first used

by

Bair and Goddard

[27]

in the

analysis

of

CUK-edge

XAS to

explain systematic

double

features, split by

_an almost constant value of 7

eV, always

found in copper divalent

compounds [28, 31].

In

XPS,

the

photoelectron

_goes to the _vacuum, with _a

large

kinetic energy. In

XAS,

it stays in the

probed

material with _a low kinetic energy when the

photon

_energy ^is

just

above the threshold.

Formally,

_{one can} think about the

CUK-edge

XAS

signal

_{as a} convolution of the

two lines found in

XPS,

times the Cu

partial density

of states

(XPS

8

Cump-DOS

: m =

4, 5, ...).

The convolution with the

4p

states, the lowest

lying

_ones,

gives

rise _to the

resolved double features mentioned above. The transitions to mp

(m~4)

_appear as a

continuum.

The relaxation due _to the _core hole

potential

has been essential in the

analysis

of

high

energy

spectroscopies

of copper

compounds [28, 34],

but this

approach

still leaves the

photoelectron

^itself as a spectator ^{in the}

screening

_process. This is correct for _a

photoelectron

with _a

large

^kinetic energy, as in XPS. However, ^if the

photoelectron

is excited in the

neighborhood

of the Fermi level with _a very small kinetic energy, as near the threshold in

XAS,

it may ^not have

just

a

passive

role.

iii)

In this paper, we report on

experimental

evidence for the need to go a step ^further

(«level

two _» in the

approximation)

and _to take into account the role of the slow

photoelectron

in the many

body problem.

This appears

qualitatively

via the

anisotropy

of the

relaxation _process. In the final _state admixture of

configurations

in

XAS,

a~(c.. ^3d~, e~)

+

pf(c. ^3d~°L., e~),

_e~ has _to be

specified perpendicular (k~)

or

parallel

_(kjj

)

to the square

planar unit, according

to the direction of the

polarization

of the incident

photon

;

k~

^and _kjj leads to

(af

and

fit ₎

and

(a(

_and

p(), respectively. Indeed,

the

major

difference between XPS and XAS deals with the _status of the

photoelectron

e~.

3.3 ANISOTROPY OF THE RELAXATION. The

charge-transfer

_process leads _to the

filling

of

a d hole _: for the electron transfer O

2p

_~ Cu 3d in

cuprates only

_one channel

(x~ y~

in-

plane symmetry)

is

available,

whereas in nickelates two

quasi equivalent

channels

(x~- y~ in-plane

and 3

z~- r~ out-of-plane)

_are

opened

with _an almost

equal probability.

According

to the symmetry ^{of the}

photoelectron,

which _can be excited either

in-plane (x,

_y

symmetry)

_or

out-of-plane (z symmetry),

_one should

expect

a different behavior in the final state for cuprates ^and nickelates. Thanks _{to two sets} of

angle-resolved CUK-edge

and Ni K-

edge

XAS

experiments

_on

single crystals

of

La~Cu04

and

Pr~Ni04 respectively,

_we show that the admixture of

configurations

in the final state of the XAS

spectroscopy

^is

anisotropic

for

cuprates (af

_#

al

_and

_fit

_#

p()

_{but show}

no

anisotropy

for nickelates. The

novelty

of this

study

^{consists in}

providing

evidence for the

anisotropic

role of the

photoelectron,

which

interferes with the _core hole-induced

charge-transfer

^of the final state,

leading

_to

(PI

_)~ ~

(p))~

_{for cuprates.}

The XAS measurements _were carried _{out at}

LURE-Orsay taking advantage

of the linear

polarized synchrotron

radiation from DCI storage

ring running

at 1.85 GeV. The

X-rays

_were

monochromatized

by

_a

Si(331)

channel _cut

crystal giving

a resolution better than I eV _at the Cu and Ni

K-edges.

The incident beam _was measured

by

an ion chamber and the XAS spectra

were obtained

by

total electron

yield using

_a detector

designed

at LURE

[35].

Before

describing

the results of the

experiments,

_we

schematically

illustrate the

picture

of the

anisotropy.

The square

planar (CUO~)~~

unit with _a

photoelectron just

near threshold is shown in

figure

3. The

02p~,~

orbitals

hybridize strongly

with

Cu3d~2_~2

^{orbitals and with Cu}

4p~,

~ ones, As

long

_as the

polarization

of the

photon

is set

along

the _z

axis,

the

photoelectron

(e~)

is put ^into

p-states orthogonal

to that of the

02p~,~ electron,

which fills the

d~2_~2

^hole as a result of the relaxation.

Therefore,

the Coulomb interaction between the

photoelectron (e~

and the electron

coming

from the

charge-transfer

O

2p

_~ Cu 3d is very limited because of the lack of

overlap

between their wavefunctions. This interaction should be of

prime importance

when the

polarization

of the

photon

is _set within the

plane.

The

photoelectron (e[)

_is

_put

_{into states which}

_overlap

_with the O

2p~,~

states. The

repulsive

i 6

Phousimri.i _ii

4 E+12

Bending

Magnet

Energy

₌ 6 GeV

1_2 B

= OAT

= loo mA

i Vert. ₌ 7 E.10

p ~ Poi. Rate Bet» ₌ 27 _m

o_8

°' ~~~

Photon ₌ 10 kev dist = 30 _m

o_6 Slit heiaht

= .8 mm

0 4 Watt/mr

°10

0.2 Vertical Slit

Rate Pa~tion (mm)

O

2 3 4 5 6 7 8 9

Fig.

2. Figure shown with the courtesy of Elleaume, ESRF. Flux and

polarisation

rates of the 10 kev radiation generated

by

a 0.4 tesla

bending

magnet ^{of the 6 GeV} storage

ring

of ESRF

operated

at

100 mA _current. The observation is made at 30 _m from the _source

using

a slit 0.8

mm-high,

moved

vertically.

The residual

unpolarised

contribution is due to the _{non zero}

angular spread

^{and the slit width.}

Off-axis, the radiation is essentially circular

polarized.

The power

density

_per unit of horizontal

angle passing

through the slit and

integrated

all

photon energies

is also

plotted.

ecu

~

Co

~ _II

~

e

Fig.

3. Schematical view for the

origin

of the

anisotropy

of the relaxation in the final state of _square

planar Cu02.

The

photoelectron deposited

with low kinetic energy in orbitals

perpendicular

to the

square

plane (e,g.

4p~*)

weakly

interfere with the

charge-transfer

_process taking

place

in the

planes,

contrary to the

photoelectron

put into

in-plane

orbitals (e.g.

4pi~,).

interaction between the

photoelectron e(

and the O

2p~,

~

electron,

which is

going

to fill up the

d-band, yields

_a reduction of the

spectroscopically-induced charge

transfer O

2p

_~ Cu 3d.

Therefore,

the final _state admixture of

configurations

with the

polarization

in the

plane

differs from that with the

polarization perpendicular

to the

plane. Following

this

view,

in XAS the

photoelectron e(

does

participate

in the

screening

_{as an actor,} whereas the

photoelectron et

remains _a spectator, ^{almost like in XPS.}

Moreover,

it is

straightforward

to

speculate

that _a

very

energetic e( photoelectron

_no

longer

interacts with the O

2p~,

~ one involved in the many

body

relaxation. In other

words,

the

anisotropy

of the relaxation has _to be

energy-dependent.

This

anisotropy

is

specific

to the square

planar geometry

^of

Cu(II),

since it is _a

property

^due

to the existence of _a

unique non-degenerated

channel available for the

02p~Cu3d

transfer.

Obviously,

this

anisotropy

should not exist in

analogue

nickelates. When _one channel of the relaxation is attenuated

by

the

photoelectron e(

_or

et,

_the other _one is free to

get ^the _{oxygen 2 p~} or 2

p~,~

^electron transferred.

3.4 EXPERIA4ENTAL _{RESULTS AND} DiscussioN. -These

conjectures

_are

supported by

the

experimental

results shown in

figures

4 and 5. The Cu and Ni _near

K-edge

XAS spectra are

shown for different orientations of the

single crystals La~Cu04

and

Pr~Ni04.

Labels

B and C in

figure

4

identify

the Is

~ 4 p~*

weakly antibonding

transitions

(hereafter

called s*

transitions).

The

spectra

are measured with the

sample

at _a small

glancing angle

(@m10°)

in order to

put

^the z axis almost

aligned

with the electric

field;

labels M and N

identify

the

ls~4p/~ antibonding

transitions

(«* transitions)

obtained with

polarization

in the _x,

y-plane.

The Cu _near

K-edge

XAS spectrum ^of

Nd2Cu04 Powder,

which

crystallizes

in the T' structure different from the T structure

[2]

of the other _two

samples,

is shown in

figure 4,

with the

Cu20

_spectrum. The

Nd2Cu04

T' structure has _no

capping

_oxygen.

Therefore,

_even in the

powder spectrum,

^{the ls} ~ 4 p~*

non-bonding

transitions

(ir* transitions)

_are

clearly

identified because

they

_appear well below

(B

at 4.6 eV and C _at 12

eV)

those due to the ls

~4pf~ antibonding

transitions

(«* transitions) (M

at 16.3 eV and N at 22.5

eV).

The

LaICU04 _{»PC CrYWU} ^° w

N

z 8=6f

I

6 =50°

...,~, ""'",

~

_{~_~p}

...[..'"",

.,

6=30°

", "'"~'("...

u1 ~_~p c ....,

".,_[T

# '/,

"..."

a LJ

~

i

~

j.

i

~

j,'

.:~.'

./

0 5 IQ 15 20 25 30

E E

o

jevl

Fig.

4.

Angle-resolved CUK-edge

XAS spectra ^of

La2CuC4 single crystal.

0 ₌ 0

corresponds

to the electric field in the

plane. Apalt

from an energy

re-scaling

to account for differences in next

neighbor

distances, the

anisotropy

of the relative

intensity

of the

3d~$

(B and M) and 3d~ (C and Aj transitions is induced

by

the symmetry of the

photoelectron

wavevector k relative to the O2p~,

~

ligand

electron. The dashed curve (0 ₌ 40°) is close _to that of the

powder

spectrum.

M B Fr2Nioas1I1g~czysui

~

N

$

⁶⁼⁸⁰ '_

~

6=@p ^'-

#

6*30° ^~' _{'_} '-,__

#

6*0° "_

g~ '._

C """'

#

$

~

f§~

Z

5 10 is lo 25 lo

E E

o

(eV)

Fig.

5.

Angle-resolved

Ni

K-edge

XAS spectra of Pr2Ni04. A part ^from a contraction of the energy scale due _to

slightly

different distances

along

_{x, y} and _z directions, _{one can} observe that the dominant

configuration

is the

fully

relaxed _one (B and M) for both orientations, different from what

happens

in cuprates.

CU~O

spectrum, where the Cu ion has _a full 3d

band,

is recalled for

comparison.

The linear

coordination of copper in the

3d1° configuration yields

two

ls~4p

ir*

non-bonding

transitions,

at the

origin

of the

peak

located _at 2.6 eV.

These transitions _are

assigned using

Natoli's rule

[36]

which correlates the energy

position

of the ls _~ 4 p

antibonding

_« * transition of _a

given

final state

configuration

to the

neighbour

distances.

(E~ Eo) RI

=

(E, ^Eo) RI

= constant, ^{for the} same

pair

of atoms within _a range of distances R~ ^between

approximately

1.8

A

_{and 3.5}

A _[37]. Eo

is _{a sort} of

origin

of the kinetic energy, which _can be found

experimentally by

the

position

of the ls

~4p~* non-bonding

transition observed in

Nd2Cu04,

where there is _no

apical ligand.

In

figure

4 _{one can} observe that in addition to the strong well-screened

ls~ 3d~°L _4p [

_e * transition

(B ),

its twin

poorly-screened ^ls~ 3d~ 4p (

e ^* transition

(C )

^is there but is

relatively

weak.

Clearly

with the

perpendicular polarization,

the system ^is

close to

being fully

relaxed

(3d~°L)

in the final _state, I.e.

PI

_»

jut _(.

As

long

as the

polarized photoelectron

is emitted in the _x,

y-plane,

this is _no

longer

true : the

weight

of the

ls~ 3d~

_4pj(

configuration

is far from weak. The _{two «} * transitions

(M

and

N)

_are more

balanced

((p)( al _),

even

though

it is

quite

difficult _to

give

_more than _a

qualitative

conclusion since the continuum _cannot be evaluated with confidence. These

La~Cu04 single crystal

data _are identical _to those

published by Oyanagi

et al.

[38]

but differ _on the

assignment

of the _e * transitions.