Abstract
We theoretically investigate the exchange interaction between magnetic impurities in ultrathin Bi$_2$Se$_3$ topological insulator films by taking into account the low-energy states produced by the impurities. We find that the locally induced impurity resonances strongly influence the exchange interaction between magnetic moments. In particular, we find a non-collinear alignment being more favorable than the collinear ferromagnetic alignment preferred when impurity states are ignored and only the pristine topological insulator band structure is considered. Moreover, we show that by applying of an electric field perpendicular to the ultrathin film, the exchange interaction can be drastically enhanced. This opens for the possibility of highly tunable magnetism by electric field.
Highlights
In the absence of direct coupling, magnetic impurity moments in solids couple indirectly to each other through the electronic band of the host material, with the nature of the coupling mechanism determined by the electronic structure of the host
We here note that the impurity potential terms and effective Hamiltonian of the topological insulator belong to two separate systems
We have investigated effects of impurity resonances on the magnetic exchange coupling between the magnetic moments located on the surface of ultrathin topological insulator films
Summary
In the absence of direct coupling, magnetic impurity moments in solids couple indirectly to each other through the electronic band of the host material, with the nature of the coupling mechanism determined by the electronic structure of the host. Recent work highlighting the effect of the impurities, and only in thick topological insulators, where it is the RKKY interaction mediating the coupling [16] This is in contrary to the fact that recent experiments on ultrathin topological insulator films have indicated that the indirect magnetic coupling depends strongly on the nature of the magnetic impurities [1,2,6,7,8,9]. A noncollinear collective configuration of the magnetic moments becomes favored, with a finite out-of-plane net magnetization This is in sharp contrast to the ferromagnetic ground state previously obtained when only considering the pristine ultrathin topological insulator films [21]. Some detailed part of the calculations can be found in Appendices A–F
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