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

A distinct approach for calculations of Dzyaloshinskii-Moriya interactions in molecules and crystals is proposed. It is based on the exact perturbation expansion of the 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 the 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 the spin-orbit coupling. Test calculations for La₂CuO₄ give the value of the canting angle in agreement with experimental data.