Self-consistent tight-binding method for the prediction of magnetic spin structures in solids: Application to (formula presented) and (formula presented)

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 (formula presented) and the rutile form of (formula presented) 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.