Superexchange dominates in magnetic topological insulators

TL;DR

This paper demonstrates that superexchange interactions, rather than Van Vleck or RKKY mechanisms, primarily govern magnetism in topological insulators doped with magnetic impurities, with the sign depending on impurity environment.

Contribution

The study clarifies the dominant magnetic interaction in topological insulators, showing superexchange prevails over other mechanisms in the absence of band carriers.

Findings

Superexchange dominates in magnetic topological insulators without band carriers.

The sign of superexchange depends on impurity coordination and charge state.

Interband RKKY-like interactions are negligible in these systems.

Abstract

It has been suggested that the enlarged spin susceptibility in topological insulators, described by Van Vleck's formalism, accounts for the ferromagnetism of bismuth-antimony topological chalcogenides doped with transition metal impurities. In contrast, earlier studies of HgTe and related topological systems pointed out that the interband analog of the Ruderman-Kittel-Kasuya-Yosida interaction (the Bloembergen-Rowland mechanism) leads to antiferromagnetic coupling between pairs of localized spins. Here, we critically revisit these two approaches, show their shortcomings, and elucidate why the magnitude of the interband contribution is small even in topological systems. From the proposed theoretical approach and our computational studies of magnetism in Mn-doped HgTe and CdTe, we conclude that, in the absence of band carriers, the superexchange dominates, and its sign depends on the coordination and charge state of magnetic impurities rather than on the topological class of the host material.