Quadratic magneto-optical effect in hexagonal non-collinear antiferromagnets

Quadratic magneto-optical (MO) effects can be utilized to investigate the spin order in antiferromagnetic (AFM) materials; however, the previously reported studies were all limited in antiferromagnets with collinear AFM order. Here, we develop a phenomenological theory to investigate the quadratic MO effects in hexagonal non-collinear AFM crystals with triangular spin structures. Based on the permittivity tensor up to the second-order in magnetization, we derive the formula to describe the quadratic MO responses and perform numerical calculations to obtain the MO rotation angle for different AFM spin configurations and sample orientations. For the sample with its spin plane lying perpendicular to the surface plane, we have revealed the emergence of quadratic MO response, which exhibits a strong dependence on the light incident angle. The MO rotation angle shows an approximately sinusoidal variation with a periodicity of 180° when the sample is rotated around its surface normal. The size of the MO response and its deviation from the sinusoidal form are analyzed for different values of the second-order permittivity tensor elements. This study provides important insights into the non-collinear AFM spin-induced quadratic MO effect, which may be used as a guidance for optical detections of the non-collinear AFM order, and, in particular, the ultrafast spin dynamics using the optical pump–probe technique.