X-ray standing wave method to study magnetism in crystals with site selectivity

We report a new method for studying magnetism at the atomic level with site selectivity. It is based on the combination of the site-selective diffraction-based x-ray standing wave (XSW) technique and x-ray magnetic circular dichroism (XMCD), which provides the magnetic sensitivity. The use of the standing wave resulting from an interference between the incoming and the Bragg reflected electromagnetic waves ensures that the phase information is not lost and thus brings information about the magnetism at a given site directly. In the paper, we provide the theoretical foundations of such a method based on the dynamical theory of x-ray diffraction and time-dependent perturbation theory. By means of computer simulations, the principle of the method is thus presented in a rather accessible way. Finally, we demonstrate the results of a proof-of-principle experiment on single-crystalline yttrium-iron-garnet (YIG, Y$_3$⁢Fe$_5$⁢O$_{12}$). We show data exhibiting a clear variation in the XMCD signal caused by the standing wave. A comparison with theoretical functions illustrates that the established theory reliably describes the phenomena involved and allows to extract useful information about the magnetic moments in YIG.