Theory of nonlinear magneto-optical imaging of magnetic domains and domain walls

A symmetry analysis of nonlinear magneto-optical imaging of magnetic domains and domain walls is presented. We introduce gradient terms giving rise to the magnetization-induced second-harmonic generation (MSHG) via spatial derivatives of the magnetization. The nonvanishing independent elements of the relevant tensors are derived for cubic media. Different contributions to the MSHG image from domains and domain walls are analyzed for thin magnetic films with different symmetry. it is shown that measurements of polarization properties of the MSHG response may yield information about the relative importance of different magnetization-induced contributions and also the type of domain walls.