Since the discovery of the quantum anomalous Hall (QAH) effect in the magnetically doped topological insulators (MTI) Cr:(Bi,Sb)₂Te₃ and V:(Bi,Sb)₂Te₃, 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)₂Te₃. 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.

由于在磁掺杂拓扑绝缘体（MTI）Cr：（Bi，Sb）₂ Te ₃和V：（Bi，Sb）₂ Te _3中发现了量子异常霍尔（QAH）效应，因此寻找了磁耦合机理铁磁性发作的潜在基础已经成为一个中心问题，并且提出了各种不同的方案。通过结合共振光发射，X射线磁性圆二色性和密度泛函理论，我们确定了（Bi，Sb）₂ Te ₃中V和Cr杂质的局部电子和磁性构型。最新的第一性原理计算发现其3 d的明显差异状态和显示的密度这些杂质态如何介导特性短程p d交换相互作用，其强度敏感地与3的位置而变化d指出相对于费米能级。在具有不同主体化学计量比的薄膜上进行的测量支持了这一趋势。我们的结果以统一的方式解释了所观察到的磁性的起源，并确立了杂质态介导的交换相互作用在MTI磁性中的重要作用。