Doping effects and higher-order magnetic interactions in skyrmionic B20 compounds

Skyrmionic B20 compounds based on FeSi and CoSi doped with 3d, 4d and 5d transition metals are studied theoretically using a combination of density functional theory and dynamical mean-field theory. Using the magnetic force theorem, we obtain a detailed picture of magnetic interactions, including Heisenberg, Dzyaloshinskii-Moriya (DM), and symmetric anisotropic exchange. From these calculated interactions, we perform micromagnetic simulations under external field and find non-collinear magnetic phases with a small spatial period. Our results demonstrate that 4d and 5d doping enhances substantially the effect of the DM interaction compared to the 3d-doped case, such as the experimentally studied (Fe_1-xCo_x)Si B20 system. We have also extended the theoretical framework, in order to explore the higher-order multispin interactions, which can contribute significantly to skyrmion stability and dynamics.