On second-harmonic generation in nonuniformly magnetized media

This paper presents a theoretical study of new effects of double-frequency optical signal generation in magnetic media with a nonuniform magnetization distribution. The study is based on the hydrodynamic approximation of the motion of conduction electrons in the field of an electromagnetic wave and equations for the mean electron spin. Within this approach, the mechanisms of the toroidal moment effect, which was experimentally discovered earlier in a system of magnetic particles with a vertical magnetization distribution as well as in a multilayered magnetic system (which is a collinear nonuniform magnetic system), are demonstrated. A new effect that appears due to the presence of equilibrium spin currents in a nonuniform magnetic system is studied in detail. This effect was predicted from the symmetry and can occur only in noncollinearly magnetized media. It is shown that this effect has a resonance nature with a resonance at a pump frequency equal to the plasma frequency of conduction electrons. Estimates of the susceptibility at the double frequency for the parameters of nickel and the typical scale of variation in the magnetization, which is equal to 10 nm, show that the susceptibility near the frequency of the plasma resonance at the chosen parameters is on the order of 10$^{-9}$ esu, which holds up a hope of the experimental detection of this effect.