Band structure analysis of the magneto-optical effect in bcc Fe

Abstract

Magneto-optical effects are among the basic tools for characterization of magnetic materials. Although these effects are routinely calculated by the ab initio codes, there is very little knowledge about their origin in the electronic structure. Here, we analyze the magneto-optical effect in bcc Fe and show that it originates in avoided band-crossings due to the spin-orbit interaction. Therefore, only limited number of bands and k-points in the Brillouin zone contribute to the effect. Furthermore, these contributions always come in pairs with opposite sign but they do not cancel out due to different band curvatures providing different number of contributing reciprocal points. The magneto-optical transitions are classified by the dimensionality of the manifold that is formed by the hybridization of the generating bands as one- or two-dimensional, and by the position relative to the magnetization direction as parallel and perpendicular. The strongest magneto-optical signal is provided by two-dimensional parallel transitions.

The 2022 magneto-optics roadmap

“…Although it has been demonstrated that linear response theory (Kubo formula) well describes spectra of quadratic MO effects, their detailed origin and understanding within electronic band structure is elusive nowadays, as it is already complicated to detail the origin of linear MOKE in simple FM material [61]. It is a challenge to establish understanding of the origin of higher-order MO effects within electronic structure, key prerequisite to tune, optimize and finally better employ the effect (see section 2).…”