We perform semilocal and hybrid density-functional theory (DFT) studies of the $\mathrm{Sn}/\mathrm{Ge}(111)$ surface to identify the origin of the observed insulating $\sqrt{3}\times \sqrt{3}$ phase below $\sim 30\mathrm{K}$. In contrast with the semilocal DFT calculation predicting a metallic $3\times 3$ ground state, the hybrid DFT calculation including van der Waals interactions shows that the insulating ferrimagnetic structure with a $\sqrt{3}\times \sqrt{3}$ structural symmetry is energetically favored over the metallic $3\times 3$ structure. It is revealed that the correction of the self-interaction error with a hybrid exchange-correlation functional gives rise to a band gap opening induced by a ferrimagnetic order. The results show that the observed insulating phase is attributed to the Slater mechanism via itinerant magnetic order rather than the hitherto accepted Mott-Hubbard mechanism via electron correlations.

• Received 10 June 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.106403