Cubic-in-magnetization contributions to the magneto-optic Kerr effect investigated for Ni(001) and Ni(111) thin films

The abstract of this article is too long to be included in the arXiv metadata; please see the paper for the full abstract. …In this paper, we introduce the detailed theory of cubic-in-magnetization magneto-optic Kerr effect (CMOKE) by deriving the magneto-optic tensor of third order in magnetization, denoted as $\mathit{H}$, and comparing the strength of CMOKE for different crystal orientations theoretically and experimentally. In crystals with cubic symmetry, the tensor $\mathit{H}$ is described by two independent parameters $H_{123}$ and $H_{125}$. Together with the linear magneto-optic tensor $\mathit{K}$ and quadratic magento-optic tensor $\mathit{G}$, the permittivity tensor is described up to third order in magnetization. We analytically describe equations of the MOKE including the contribution of QMOKE and CMOKE itself for (001)- and (111)-oriented cubic crystal structures. Those are compared to experimental measurements of two samples with an (001)- and (111)-oriented fcc Ni layer, respectively. Further, we use Yeh’s 4$\times$4 transfer matrix calculus to simulate and describe the experimental measurements phenomenologically from the permittivity tensor up to third order in $\mathit{M}$. We find that the MOKE anisotropy that stems from the magneto-optic tensor $\mathit{H}$ described as $\mathrm{\Delta }H=H_{123}-3H_{125}$, is much more pronounced for the (111)-oriented cubic crystal structure, for which it manifests as three-fold in-plane angular dependencies of MOKE with longitudinal and also with transversal magnetization direction, respectively.