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

• Published in: Journal of magnetism and magnetic materials 2012-01, Vol.324 (2), p.105-112
• Main Authors: Elzo, M., Jal, E., Bunau, O., Grenier, S., Joly, Y., Ramos, A.Y., Tolentino, H.C.N., Tonnerre, J.M., Jaouen, N.
• Format: Article
• Language: English
• Subjects: Condensed Matter; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Density; Exact sciences and technology; Formalism; Iron; Magnetic materials; Magnetic moment; Magnetic properties and materials; Magnetic properties of monolayers and thin films; Magnetic properties of surface, thin films and multilayers; Materials Science; Physics; Reflectivity; Roughness; Spin arrangements in magnetically ordered materials (including neutron and spin-polarized electron studies, synchrotron-source x-ray scattering, etc.); Studies of specific magnetic materials; Thin film; X-ray resonant magnetic scattering; X-rays
• ISSN: 0304-8853; 1873-4766
• DOI: 10.1016/j.jmmm.2011.07.019

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. ► Magnetism at interfaces and in thin films is increasingly studied. ► X-ray resonant magnetic reflectivity yields the in depth magnetization profile in thin films. ► We present a formalism and methodology to study the data. ► We illustrate the technique with an example.