Abstract
The metallic helimagnet MnSi has been found to exhibit skyrmionic spin textures when subjected to magnetic fields at low temperatures. The Dzyaloshinskii-Moriya (DM) interaction plays a key role in stabilizing the skyrmion state. With the help of first-principles calculations, crystal field theory and a tight-binding model we study the electronic structure and the origin of the DM interaction in the B20 phase of MnSi. The strength of $\vec{D}$ parameter is determined by the magnitude of the spin-orbit interaction and the degree of orbital mixing, induced by the symmetry-breaking distortions in the B20 phase. We find that, strong coupling between Mn-$d$ and Si-$p$ states lead to a mixed valence ground state $|d^{7-x}p^{2+x}\rangle$ configuration. The experimental magnetic moment of $0.4~\mu_B$ is consistent with the Coulomb-corrected DFT+$U$ calculations, which redistributes electrons between the majority and minority spin channels. We derive the magnetic interaction parameters $J$ and $\vec{D}$ for Mn-Si-Mn superexchange paths using Moriya's theory assuming the interaction to be mediated by $e_g$ electrons near the Fermi level. Using parameters from our calculations, we get reasonable agreement with the observations.