Probing interface ferromagnetism of EuS/Bi$_{2}$Se$_{3}$ heterostructures with magnetic second harmonic generation

Ferromagnet / topological insulator interfaces are novel heterostructures that can host various interesting physical phenomena, such as massive Dirac fermions, the quantum anomalous hall effect, and the topological magnetoelectric effect. By using magnetic second harmonic generation (MSHG), we separately measure the in-plane and the out-of-plane magnetization at the interface between a ferromagnetic insulator EuS and Bi$_{2}$Se$_{3}$. In contrast to bulk-sensitive linear magneto-optics, such as the Faraday and Kerr effects, MSHG allows a selective measurement of ferromagnetism and crystal symmetry of the interface, at which inversion symmetry is broken. Our technique can thus be used to study magnetism and crystal structure of such ``buried'' interfaces to which other conventional probes do not have direct access.