Emergence of magnetic topological states in topological insulators doped with magnetic impurities

Abstract

Emergence of the topological invariant and the magnetic moment in topological insulators doped with magnetic impurities is studied based on a mutual cooperation between the spin-orbit coupling of electrons and the spin exchange of these electrons with magnetic impurity moments. The mutual cooperation is realized based on the Kane-Mele model in the presence of magnetic impurities. The topological invariants and the spontaneous magnetization are self-consistently determined within the dynamical mean-field theory. We find different magnetic topological phase transitions, depending on the electron filling. At half filling an antiferromagnetic topological insulator, which exhibits the quantum spin Hall effect, exists in the phase region between the paramagnetic topological insulator and the trivially topological antiferromagnetic insulator. At quarter and three-quarter fillings, a ferromagnetic topological insulator, which exhibits the quantum anomalous Hall effect, occurs in the strong spin-exchange regime.