Polarization Dependence in

X-ray Spectroscopy and

Scattering

S P Collins et al

Diamond Light Source

UK

Overview of talk

1. Experimental techniques at Diamond: why we

care about x-ray polarization

2. How polarized x-rays are generated

3. Future directions

Photoelectron spectroscopy

Inelastic scattering

(resonant, non-resonant)

Elastic scattering

X-ray interactions with matter: Key techniques

Absorption/transmission

1914 Nobel Laureate in Physics

for his discovery of the

diffraction of X-rays by crystals.

Max von Laue

Laue predicted that if x-rays were a form

of short-wavelength electromagnetic

radiation then they should produce

diffraction effects as they pass through

crystals

This idea was put to the test by Friedrich…

The field of X-ray diffraction and

crystallography was born

X-ray Diffraction

and

Crystallography

(…and why we

need

synchrotrons)

x

E

E’

z

y

Polarization by scattering

1)ˆˆ( εε

1)ˆˆ( εε

1)ˆˆ( εε

2cos)ˆˆ( εε0)ˆˆ( εε

2

Polarization of Synchrotron Radiation

Intense beams of linearly

polarized x-rays

X-ray Diffraction & Scattering: Why do we care

about polarization?

Because the scattering depends strongly on linear

polarization; scattering can become very weak in the

horizontal plane; data must be ‘corrected’ for

polarization.

But the polarization dependence tells us nothing about

the sample, it just reminds us that light is a transverse

wave.

Bragg scattering can be used as a polarization analyser.

Absorption/transmission

Is polarization important in absorption?

Polarizing glasses are very

cool…

Linear dichroism and

birefringence gives information

about internal polarization of

materials.

Does it work with x-rays?

0.40

0.42

0.44

0.46

0.48

0.50

0.52

0.54

0.56

33.10 33.15 33.20 33.25 33.30 33.35

Energy (keV)

m(c

m-1

)

a=90o

a=0

HN22

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

0 30 60 90 120 150 180 210 240 270 300 330 360

Polarizer angle a (degrees)

Re

lati

ve

tra

ns

mit

tan

ce

b=-45o

b=+45o

X-ray Absorption: Why do we care about

polarization?

Because absorption from anisotropic systems depends

on linear polarization.

This effect can give rise to x-ray dichroism and

birefringence at particular photon energies

One could construct polarizing devices or study, for

example, orientations of chemical bonds.

And going beyond the electric dipole approximation

one can observe more exotic high-order atomic

‘multipoles’ such as hexadecapoles in cubic systems…

A B

C Flu

ore

scen

ce

A B

C

Strontium titanate SrTiO3

Sir William

Lawrence Bragg

(1890-1971)

Sir William

Henry Bragg

(1862-1942)

1915 Nobel prize for physics "for

their services in the analysis of

crystal structure by means of X-

rays".

So what was left for the Bragg’s to

do?

• The father and son team carried out

their own experiments and, in analogy

with optical diffraction, worked out a

formula for the wavelength of the

diffracted wave: the famous Bragg’s

Law

Resonant ‘forbidden’ scattering: Why do we care

about polarization?

Because the polarization breaks the symmetry that

normally causes an exact cancellation of the scattering

at these positions

The residual scattering is extremely interesting as it

provides direct information about very weak processes

that are normally hidden, e.g. exotic electronic

polarization effects, magnetism…

E

H

SElectromagneticwave

Electron

Forces:electric

magnetic

= -e

= -2 ( )

f E

f S H mB

Magnetic forces on electron: Magnetic scattering

There are several other

magnetic terms, each

having different

polarization dependence.

They are all very weak.

Ratio of Zeeman force to

electric force:

or less!

6

charge

mag

2

2

10~

10~2

1

I

I

cmf

f

ee

Z

(Zeeman)

FeBO3: A weak ferromagnet

studied by x-ray diffraction

(Diamond I16)

Magnetic x-ray scattering: Why do we care about

polarization?

Because the magnetic x-ray scattering has a very

different polarization dependence from change

scattering

This enables it to be identified as magnetic

It also allows us uniquely to obtain information about

the distribution of spin and orbital magnetic moments

in the material

S

N

N

S

N

S

Magnetpoles

Circularlypolarizedbeam

I=Io

I=I eo

- t( )mm

Ferromagneticsample

Magnetizingfield

A circular dichroism measurement

X-ray absorption and orbital polarization

Beamline I06 - Nanoscience

A polarised soft x-ray beamline for microscopy and spectroscopy

PEEM images recorded using X-Ray Magnetic Circular Dichroism (left) and X-ray Magnetic Linear Dichroism (right) showing ferromagnetic and antiferromagnetic domains, respectively, in Co thin films grown on NiO.

Magnetic Circular Dichroism: Why do we care

about polarization?

Because the angular momentum of the photon circular

polarization couples directly to the angular momentum

of electronic states to give a huge sensitivity to

magnetism.

Synchrotron radiation is now one of the major tools for

studying magnetic materials

This process also forms the basis of novel microscopy

techniques allowing magnetic domains and dynamics

to be studied 10 nm resolution

There are similar effects in resonant scattering.

Diamond

Beamline

I16

Tellurium results from I16: 001

and 002 forbidden reflections

Studies of Chiral Systems: Why do we care about

polarization?

Because circular polarization breaks the mirrors

symmetry of the photon beam, allowing studies of

chiral samples

These are of fundamental importance to chemistry and

biology (nature is chiral)

These effects play an important role in contemporary

condensed matter physics, i.e. the magnetoelectric

effect, chiral magnetic structures

X-ray birefringence imaging - Dynamical Diffraction

Transmission

image through

diamond -

horizontal

polarization

Vertical

polarization

Polarization of Synchrotron Radiation

Intense beams of linearly

polarized x-rays

Quarter-wave

phase plate

The Future:

Production of linear and circular beams: already very efficient,

especially linear polarization

Reversible circular polarizers to pick out very small changes that

couple to photon helicity: still challenging. The state-of-the-art is

sensitivity at 10-5 level but this if very difficult. 10-3 is more

typical; 10-7 would certainly provide new techniques such as x-

ray natural circular dichroism in chiral liquids.

Polarization analysers and polarization sensitive detector: very

challenging. The efficiency and complexity of current devices is

perhaps the main limiting factor is synchrotron techniques such

as magnetic scattering.