First and second order in magnetization effects in optical second-harmonic generation from a trilayer magnetic structure

Abstract

Linear and nonlinear optical properties of a thin planar CoFe/Al2O3/CoFe structure for different angles of incidence of the fundamental radiation are studied by means of the magneto-optical Kerr effect and magnetization-induced second-harmonic generation (SHG). The composition of this multilayered structure supports the appearance of the antiferromagnetic state, which leads to nonreciprocal optical effects and is discussed in terms of the magnetic toroid moment. We show that in accordance with the phenomenological description, SHG magnetic hysteresis loops for a linearly polarized pump beam are determined by linear in magnetization M components of the SHG polarization, while for a circularly polarized pump such a description necessarily involves both linear and quadratic in M components of the nonlinear polarization. Symmetry analysis of the magnetization-induced SHG supports the differences between the cases of linear and circular polarization of the incident radiation observed in the experiment, as well as a partial suppression of first in magnetization SHG contributions. Relative values of the linear and quadratic in magnetization components of the SHG polarization are estimated for the trilayer structure and for a reference homogeneous ferromagnetic film.