Ferrimagnetic Slater insulator phase of the Sn/Ge(111) surface

We perform semilocal and hybrid density-functional theory (DFT) studies of the Sn/Ge(111) surface to identify the origin of the observed insulating sqrt[3]×sqrt[3] phase below ∼30  K. In contrast with the semilocal DFT calculation predicting a metallic 3×3 ground state, the hybrid DFT calculation including van der Waals interactions shows that the insulating ferrimagnetic structure with a sqrt[3]×sqrt[3] structural symmetry is energetically favored over the metallic 3×3 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.