Spin-orbit coupling in {Mo$_3$S$_7$(dmit)$_3$}

Abstract

Spin-orbit coupling in crystals is known to lead to unusual direction dependent exchange interactions, however understanding of the consequeces of such effects in molecular crystals is incomplete. Here we perform four component relativistic density functional theory computations on the multi-nuclear molecular crystal {Mo$_3$S$_7$(dmit)$_3$} and show that both intra- and inter-molecular spin-orbit coupling are significant. We determine a long-range relativistic single electron Hamiltonian from first principles by constructing Wannier spin-orbitals. We analyse the various contributions through the lens of group theory. Intermolecular spin-orbit couplings like those found here are known to lead to quantum spin-Hall and topological insulator phases on the 2D lattice formed by the tight-binding model predicted for a single layer of {Mo$_3$S$_7$(dmit)$_3$}.