Describing Dzyaloshinskii–Moriya spirals from first principles

In magnetic systems lacking spatial inversion symmetry it is observed that the Dzyaloshinskii–Moriya interaction can entail long-ranged spin spirals with a unique sense of rotation. Here, we present a computationally efficient scheme to calculate these large magnetic structures within density functional theory and extract the interaction parameters using perturbative approaches of different order. We analyze the accuracy of these methods by investigating thin Fe films on W(1 1 0) and Mo(1 1 0) substrates.