Hubbard model calculation of (2 × 1) reconstructed (111) surfaces of diamond-structure solids

From a Hubbard Hamiltonian for the electrons in the dangling bond orbitals of a (111) surface of diamond-type solids, different superstructures of periodicity (2 × 1) are calculated. The most stable one is an antiferromagnetic ordering of the electron spins, where alternating rows of orbitals show alternating magnetization. This superstructure vanishes in a second order phase transition at a critical temperature, above which the surface shows the unreconstructed (1 × 1) periodicity.