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Spin-spin interaction in the bulk of topological insulators
We apply mean-field theory and Hirsch-Fye quantum Monte Carlo method to study
the spin-spin interaction in the bulk of three-dimensional topological
insulators. We find that the spin-spin interaction has three different
components: the longitudinal, the transverse and the transverse
Dzyaloshinskii-Moriya-like terms. When the Fermi energy is located in the bulk
gap of topological insulators, the spin-spin interaction decays exponentially
due to Bloembergen-Rowland interaction. The longitudinal correlation is
antiferromagnetic and the transverse correlations are ferromagnetic. When the
chemical potential is in the conduction or valence band, the spin-spin
interaction follows power law decay, and isotropic ferromagnetic interaction
dominates in short separation limit.Comment: 9 pages, 10 figure
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