Quadratic-in-magnetization permittivity and conductivity tensor in cubic crystals

We present diagonal and off-diagonal elements of the permittivity and conductivity tensor up to the second order in magnetization for cubic crystals. We express all tensor elements as a function of a general sample orientation, for arbitrary magnetization direction and for (001), (011) and (111) surface orientations. Finally, we discuss, how to extract values of quadratic elements G of the second order permittivity tensors for different sample surface orientations from both experiment and ab-initio calculations.