Determination of the element-specific magnetic anisotropy in thin films and surfaces

We discuss the various element-specific methods to obtain the magnetocrystalline anisotropy energy (MAE) of thin films, multilayers and surfaces. X-ray magnetic circular dichroism. has recently emerged as a routine method, where the orbital magnetic moment of 3d transition metals can be determined using the sum rule for the L-2,L-3 absorption spectra. The obtained orbital moment can be related to the MAE using Bruno's model, which is only valid under the assumption that the majority-spin subband is completely filled. This limitation can be avoided by employing x-ray magnetic linear dichroism (XMLD). The XMLD branching ratio is proportional to the anisotropy in the spin-orbit interaction, which, in second-order perturbation, can be related to the MAE. We present an expression for the angular dependence of the sum rules, which can be used to determine the magnetic anisotropy from the linear dichroism. for a system with arbitrary point-group symmetry.