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

A formalism for the reflectivity of electromagnetic waves by magnetic materials is presented with an application. It is applied 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 case-by-case, from the optical light regime up to soft and hard X-rays. Eigenwaves are used throughout the whole formalism. In order to illustrate the methodology, we present an application to a W/Fe/W trilayer performed at the Fe L-edge, in the soft X-ray regime. (c) 2011 Elsevier B.V. All rights reserved.