Magneto-optical spin Hall effect of light in topological insulators

•The Brewster angle’s position and SHEL shifts are decided by the dissipative and reactive components.•The SHEL shifts are insensitive to external magnetic field and Fermi energy in case of high frequency.•The potential applications of determination the external magnetic field and the Fermi energy of TIs is proposed. We examine a tunable spin Hall effect of light (SHEL) on the surface of topological insulators (TIs) under the influence of an external magnetic field, to the best of our knowledge, which can be regarded as the magneto-optical SHEL. It is revealed that the position of the Brewster angle and the value of the SHEL shifts are decided by the dissipative and reactive components of TIs optical conductivity, respectively. Specifically, the SHEL shifts are insensitive to the external magnetic field and the Fermi energy in the case of high frequency while it is sensitive to them in the case of low frequency. The potential applications of determination the external magnetic field and the Fermi energy of TIs by probing the SHEL shifts is proposed. Moreover, we can select high frequencies so that the measured SHEL shifts are not affected by the external magnetic field. These results can be extensively extended to other TIs. By incorporating the weak measurement techniques, the magneto-optical SHEL may provide application references in the fabrications of TIs parameter sensors or other topological photoelectric devices.