Quadratic magneto-optical Kerr effect spectroscopy: Polarization variation method for investigation of magnetic and magneto-optical anisotropies

We present a method for a precise determination of magnetic anisotropy and anisotropy of quadratic magneto-optical response of thin films of ferromagnetic and ferrimagnetic materials. The method is based on measurements of a magneto-optical response for light close to the normal incidence on the sample with a fixed position. The measurement is performed for a set of orientations of an external magnetic field and a series of incident light linear polarizations beyond the standard s and p orientations. Based on the symmetry of the signal, we are able to separate the part of magneto-optical response that is even with respect to magnetization and, in turn, to exclude all non-magnetic contributions which come from imperfections of the experimental setup or from the sample itself. It is, therefore, possible to study the sample placed inside a cryostat: the polarization changes due to cryostat windows and possible strain-induced optical anisotropy of the sample are removed by the applied data processing. Thanks to this, we can perform measurements on low or elevated temperatures (from 15 to 800 K in our case), making it possible to study the behavior of magnetic materials in different magnetic phases and/or close to phase transitions. The applicability of this experimental technique was tested by measuring the low-temperature response of two samples of ferromagnetic semiconductor (Ga,Mn)As with a different Mn content at several wavelengths, which enabled us to deduce the magnetic and quadratic magneto-optical anisotropies in this material. In particular, we observed that the anisotropy of quadratic magneto-optical coefficients in (Ga,Mn)As is much weaker than that reported previously for other magnetic material systems.