Analysis of the linear relationship between asymmetry and magnetic moment at the M edge of 3d transition metals

The magneto-optical response of Fe and Ni during ultrafast demagnetization is studied experimentally and theoretically. We have performed pump-probe experiments in the transverse magneto-optical Kerr effect (T-MOKE) geometry using photon energies that cover the M absorption edges of Fe and Ni between 40 and 72 eV. The magnetic asymmetry was obtained by forming the difference of reflected intensities obtained for two opposite orientations of the sample magnetization. Density functional theory (DFT) was used to calculate the magneto-optical response of different magnetic configurations, representing different types of excitations: long wavelength magnons, short wavelength magnons, and Stoner excitations. In the case of Fe, we find that the calculated asymmetry is strongly dependent on the specific type of magnetic excitation. Our modeling also reveals that during remagnetization Fe is, to a reasonable approximation, described by magnons, even though small nonlinear contributions could indicate some degree of Stoner excitations as well. In contrast, we find that the calculated asymmetry in Ni is rather insensitive to the type of magnetic excitations. However, there is a weak nonlinearity in the relation between asymmetry and the off-diagonal component of the dielectric tensor, which does not originate from the modifications of the electronic structure. Our experimental and theoretical results thus emphasize the need to consider a coupling between asymmetry and magnetization that may be more complex than a simple linear relationship. This insight is crucial for the microscopic interpretation of ultrafast magnetization experiments.