  In most studies utilizing the magneto-optic Kerr effect (MOKE), the detected
change of polarized light upon reflection from a magnetized sample is supposed
to be proportional to the magnetization $\boldsymbol{M}$. However, MOKE
signatures quadratic in $\boldsymbol{M}$ have also been identified and
utilized, e.g., to sense the structural order in Heusler compounds, to detect
spin-orbit torques or to image antiferromagnetic domains. In our study, we
observe a strong anisotropic MOKE contribution of third order in
$\boldsymbol{M}$ in Ni(111) thin films, attributed to a cubic magneto-optic
tensor $\propto $ $\boldsymbol{M}^3$. We further show that the angular
dependence of cubic MOKE (CMOKE) is affected by the amount of structural domain
twinning in the sample. Our detailed study on CMOKE for two selected photon
energies will open up new opportunities for CMOKE applications with sensitivity
to twinning properties of thin films, e.g. CMOKE spectroscopy and microscopy or
time-resolved CMOKE.
