Abstract
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.
Highlights
Detection and control of spin order in magnetic materials is the main principle enabling magnetic information to be read and stored
The MO rotation angle shows an approximately sinusoidal variation with a periodicity of 180○ when the sample is rotated around its surface normal
For the out-of-plane triangular spin configuration, the MO effect is emergent with a strong dependence on the light incidence angle and its overall amplitude is mainly determined by the combined MO tensor element ΔGhex = Gxxxx + Gxxyy − 2Gxxzz
Summary
Detection and control of spin order in magnetic materials is the main principle enabling magnetic information to be read and stored. For Voigt or Cotton–Mouton effects, Ferré and Gehring reported a simplified calculation in the near-normal-incidence approximation, and Saidl et al. verified the angular dependence of the Voigt effect complying with sin 2(θ − ε), where θ and ε denote the orientation of the Néel vector and light polarization, respectively. Despite this recent progress, the understanding of the quadratic MO effects is still limited in FM materials via QMOKE and collinear AFM materials via Voigt or Cotton–Mouton effects. Deviation from the sinusoidal form becomes significant only in the case of large second-order tensor elements or large difference of nonmagnetic diagonal elements, which is beyond the descriptions of the analytical formula of the MO effect (i.e., strict sinusoidal form) used for the collinear AFM cubic crystal
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