Dzyaloshinskii-Moriya Interaction on Surfaces of Topological Insulator

The Topological Hall Effect (THE) is a hallmark of nontrivial spin texture. In this work we theoretically study the THE is realizable in centrosymmetric materials. The only requirement being that local inversion symmetry is broken. To show that the THE can occur we start with the model of surface states of a Topological Insulator (TI) and include magnetization on the top and bottom surfaces of the TI. From here the Spin Susceptibility (SS) tensor is determined numerically and it is shown to have off-diagonal components. These components are then related to the Dzyaloshinskii-Moriya (DM) vector. Demonstration of nonzero DM interaction on the surfaces of the TI reveals nontrivial topology in the real space, along with the nontrivial electronic band structure of the TI in momentum space allows for the possibility of the THE in centrosymmetric materials.