Quadratic magneto-optic Kerr effect spectroscopy of Fe epitaxial films on MgO(001) substrates

Abstract

The magneto-optic Kerr effect (MOKE) is a well known and handy tool to characterize ferro-, ferri-, and antiferromagnetic materials. Many of the MOKE techniques employ effects solely linear in magnetization $\mathbit{M}$. Nevertheless, a higher-order term being proportional to ${\mathbit{M}}^{2}$ and called quadratic MOKE (QMOKE) can additionally contribute to the experimental data. Here, we present detailed QMOKE spectroscopy measurements in the range of 0.8--5.5 eV based on a modified eight-directional method applied on ferromagnetic bcc Fe thin films grown on MgO substrates. From the measured QMOKE spectra, two further complex spectra of the QMOKE parameters ${G}_{s}$ and $2{G}_{44}$ are yielded. The difference between those two parameters, known as $\mathrm{\ensuremath{\Delta}}G$, denotes the strength of the QMOKE anisotropy. Those QMOKE parameters give rise to the QMOKE tensor $\mathbit{G}$, fully describing the perturbation of the permittivity tensor in the second order in $\mathbit{M}$ for cubic crystal structures. We further present experimental measurements of ellipsometry and linear MOKE spectra, wherefrom permittivity in the zeroth and the first order in $\mathbit{M}$ are obtained, respectively. Finally, all those spectra are described by ab initio calculations.