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

TL;DR

This paper develops a detailed third-order magneto-optic Kerr effect theory for Ni thin films, comparing theoretical predictions with experimental measurements for different crystal orientations, revealing orientation-dependent anisotropies.

Contribution

It introduces the cubic-in-magnetization magneto-optic Kerr effect tensor and compares its strength across crystal orientations both theoretically and experimentally.

Findings

CMOKE tensor parameters differ between (001) and (111) orientations.

MOKE anisotropy is more pronounced in (111)-oriented crystals.

Three-fold in-plane angular dependencies observed in (111) orientation.

Abstract

*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 $\bm{H}$, and comparing the strength of CMOKE for different crystal orientations theoretically and experimentally. In crystals with cubic symmetry, the tensor $\bm{H}$ is described by two independent parameters $H_{123}$ and $H_{125}$. Together with the linear magneto-optic tensor $\bm{K}$ and quadratic magento-optic tensor $\bm{G}$, 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 $\bm{M}$. We find that the MOKE anisotropy that stems from the magneto-optic tensor $\bm{H}$ described as $\Delta H = H_{123}-3H_{125}$, 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.