Influence of a static electric field on magnetic materials monitored by X-ray magnetic circular dichroism

The magnetic circular X-ray dichroism (XMCD) in X-ray absorption spectroscopy (XAS) is extensively used to monitor the response of a magnetic system to an external perturbation. Application of a static external electric field to control its magnetic properties may just lead to a charge rearrangement or to a steady electric current dependent on the geometry. As it is demonstrated, the first situation can be handled with minor modifications of the standard well established schemes to calculate XAS and XMCD spectra. For the second case, however, more advanced schemes have to be used that account for the steady-state out-of-equilibrium situation. It is shown, that this can indeed be achieved by making use of the Keldysh non-equilibrium Green function formalism that allows in particular to express the X-ray absorption coefficient in terms of the corresponding greater Green function $G^{>}\left(E\right)$. As an alternative approach, a bi-linear response formalism is presented that can be used to calculate the modification of the XMCD spectra due to the electric field directly.