Correlated band theory of spin and orbital contributions to Dzyaloshinskii-Moriya interactions

A new approach for calculations of Dzyaloshinskii-Moriya interactions in molecules and crystals is proposed. It is based on the exact perturbation expansion of total energy of weak ferromagnets in the canting angle with the only assumption of local Hubbard-type interactions. This scheme leads to a simple and transparent analytical expression for Dzyaloshinskii-Moriya vector with a natural separation into spin and orbital contributions. The main problem was transferred to calculations of effective tight-binding parameters in the properly chosen basis including spin-orbit coupling. Test calculations for La$_2$CuO$_4$ give the value of canting angle in a good agreement with experimental data.