Linear and quadratic magnetooptic spectroscopy of bcc Fe

The magnetooptic Kerr effect (MOKE) is a widely used tool for both basic research and applications. Despite well-known linear MOKE (LinMOKE) being linear in magnetization, there is also a MOKE being quadratic in magnetization... [ view full abstract ]

The magnetooptic Kerr effect (MOKE) is a widely used tool for both basic research and applications. Despite well-known linear MOKE (LinMOKE) being linear in magnetization, there is also a MOKE being quadratic in magnetization (QMOKE). Both LinMOKE and QMOKE are described by change of permittivity tensor upon magnetization direction. In case of cubic crystal owning point symmetry, linear combination of four spectra (so called principal spectra) are enough to describe permittivity tensor for any magnetization orientation. Namely, those spectra consists of one optical spectra ε, one spectra linear in magnetization K and two quadratic spectra, Gs=G11-G12 and G44. Here, we will present both experimental and ab-initio technique to determine all four principal spectra in bcc Fe. This approach is applied to thin films of Fe(5-30nm)/MgO(001). The absorption part of all principal spectra of bcc Fe is shown in Figure (a-d).

In general, optic and magneto-optic properties of crystals are determined by the well-known Kubo formula for direct inter-band transitions. It states that the absorption of a photon followed by the excitation of electron in solids is governed by electric dipole element , where |i>, |f> are initial and final electron states and p is the momentum operator. In order to understand in detail the electric dipole elements, we visualize them in the reciprocal space by two different means: on surfaces of constant energy difference between initial and final states and by joint spaghetti diagram (Figure (e), (f) for ε and K, respectively). It allows us to identify hot-spots contributing to the magneto-optic response, and conditions of those hot-spots in topology of the band structure.

The work was supported by Czech Science Foundations (grant no. 13-30397S).