Self-consistent tight-binding method for the prediction of magnetic spin structures in solids: Application to MnF₂ and MnO₂

We introduce a self-consistent tight-binding approach to the modeling and prediction of magnetic structure in solids. The method is similar to a charge self-consistent tight-binding method which we introduced earlier, but here we add information concerning the dependence of the ion energy on the total ion spin in the on-site matrix elements of the tight-binding Hamiltonian. We self-consistently determine both spins and charges of the ions during calculation. We illustrate with studies of MnF₂ and the rutile form of MnO₂. In the first case we find without adjustment that the well-known two sublattice spin structure is predicted. In the second case we find that a disordered spin phase is predicted, contrary to experimental evidence, but a small adjustment of the parametrization yields the spiral spin structure suggested by experiments.