Polarization Dependence in X-ray Spectroscopy and Scattering. S P Collins et al Diamond Light Source UK

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1 Polarization Dependence in X-ray Spectroscopy and Scattering S P Collins et al Diamond Light Source UK

2 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

3 X-ray interactions with matter: Key techniques Absorption/transmission Elastic scattering Inelastic scattering (resonant, non-resonant) Photoelectron spectroscopy

4 Max von Laue 1914 Nobel Laureate in Physics for his discovery of the diffraction of X-rays by crystals. 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

5 X-ray Diffraction and Crystallography ( and why we need synchrotrons)

6 Polarization by scattering x ( ε ε ˆ ˆ ) 1 E E ( ε ε ˆ ˆ ) 1 y ( ε ε ˆ ˆ ) 0 2 ( εˆ εˆ ) cos2 z ( ε ε ˆ ˆ ) 1

7 Polarization of Synchrotron Radiation Intense beams of linearly polarized x-rays

8 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.

9 Absorption/transmission Is polarization important in absorption?

10 Polarizing glasses are very cool Linear dichroism and birefringence gives information about internal polarization of materials. Does it work with x-rays?

11 Relative transmittance b=-45 o a=90 o a= b=+45 o m(cm -1 ) HN Polarizer angle a (degrees) Energy (kev)

12 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

13 Fluorescence Strontium titanate SrTiO 3 A B C C A B

14 Sir William Henry Bragg ( ) Sir William Lawrence Bragg ( ) 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 1915 Nobel prize for physics "for their services in the analysis of crystal structure by means of X- rays".

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27 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

28 Magnetic forces on electron: Magnetic scattering Electromagnetic wave E Electron S H There are several other magnetic terms, each having different polarization dependence. They are all very weak. Forces: electric magnetic (Zeeman) f f = -ee = -2 ( S H) mb Ratio of Zeeman force to electric force: I I f f Z e mag charge 1 2 ~ 10 2 m c 6 e ~ 10 2 or less!

29 FeBO 3 : A weak ferromagnet studied by x-ray diffraction (Diamond I16)

30 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 N S S N N S

31 A circular dichroism measurement Magnet poles I=I e -( m m) t o Ferromagnetic sample Circularly polarized beam Magnetizing field I=I o

32 X-ray absorption and orbital polarization

33 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.

34 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.

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36 Diamond Beamline I16

37 Tellurium results from I16: 001 and 002 forbidden reflections

38 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

39 X-ray birefringence imaging - Dynamical Diffraction Transmission image through diamond - horizontal polarization Vertical polarization

40 Polarization of Synchrotron Radiation Intense beams of linearly polarized x-rays Quarter-wave phase plate

41 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 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.

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