Differential destructive interference of the circular polarization eigenmodes of scattered soft x rays at the grazing incidence in magnetic thin films

Recently, the authors found that an additional magneto-optical effect that linearly polarized soft x rays incident on a single magnetic layer on a nonmagnetic substrate can be converted to any states among the linearly s- and p- and circularly left- and right-handed polarizations by changing the grazing angle of incidence in specular reflection geometry. In this article, the authors report that the physical origin of such an effect is the differential interference of the circular polarization eigenmodes of scattered soft x rays at the grazing incidence. Totally destructive interference takes place selectively for one helicity but not for the other one at a certain grazing angle and in a specific energy region just below the absorption edges, thus leading to differential circular reflectivity. Numerical calculations using an iterative method of transmission, reflection, and propagation matrices allow us not only to verify the underlying mechanism but also to find the necessary specific conditions of photon energy and incidence angle where such a phenomenon can occur.