X-ray birefringence and dichroism obtained from magnetic materials

In the past decade, synchrotron radiation has triggered a surge in studies of the polarization dependence of X-ray beams passing through non-isotropic materials. A vast range of experimental results concerning polarization-dependent absorption (dichroism) and dispersion (birefringence, for example) are available from materials which are either magnetic or exhibit preferred directions due to the local atomic environment. This article aims to bring together the diversity of modern experiments in this field with established methods of optical calculus, in a way that highlights the simplicity of the underlying physics. A useful framework is formed when observable quantities, in the X-ray case, are related to atomic variables of the sample material. Atomic descriptions of absorption spectra with various levels of complexity are considered, and some well documented sum-rules are encountered. The framework is the most general allowed within the electric dipole approximation. By way of illustration, dichroic X-ray absorption by two materials with highly anisotropic properties and magnetic ions with different valence shells are considered; namely, a 3d-transition ion in ferrous niobate, and a lanthanide ion in dysprosium borocarbide. Both materials display interesting magnetic properties that are challenging to interpret at an atomic level of detail, and it is shown how absorption experiments can contribute to resolving some issues.