Non-local effect of impurity states on the exchange coupling mechanism in magnetic topological insulators

Since the discovery of the quantum anomalous Hall (QAH) effect in the magnetically doped topological insulators (MTI) Cr:(Bi,Sb)Te and V:(Bi,Sb)Te, the search for the magnetic coupling mechanisms underlying the onset of ferromagnetism has been a central issue, and a variety of different scenarios have been put forward. By combining resonant photoemission, X-ray magnetic circular dichroism and density functional theory, we determine the local electronic and magnetic configurations of V and Cr impurities in (Bi,Sb)Te. State-of-the-art first-principles calculations find pronounced differences in their 3d densities of states, and show how these impurity states mediate characteristic short-range pd exchange interactions, whose strength sensitively varies with the position of the 3d states relative to the Fermi level. Measurements on films with varying host stoichiometry support this trend. Our results explain, in an unified picture, the origins of the observed magnetic properties, and establish the essential role of impurity-state-mediated exchange interactions in the magnetism of MTI.