X-ray resonant magnetic reflectivity of stratified magnetic structures: Eigenwave formalism and application to a W/Fe/W trilayer

International audience; A formalism to simulate the reflectivity of electromagnetic waves by magnetic materials is presented with an application. The formalism is applicable to retrieve the magnetic moment density along the depth of magnetic materials with arbitrary magnetic moment direction using matricial algebra, including roughness between layers. The reflectivity is derived following a classical description with Maxwell equations and a permittivity built from the quantum scattering amplitude. Approximations on the relative power of the Thomson scattering and the magnetic terms are trackable in order to evaluate the validity of the formalism on a case-by-case basis, from the optical light regime up to soft and hard x-rays. The originality of the present formalism lies in the use of eigen-waves throughout the treatment. An application to a Fe thin film illustrates the methodology.