Helicity and size dependence of skyrmions in Mn$_{1-x}$Fe$_x$Ge mediated by the Dzyaloshinskii-Moriya interaction

We carry out first-principles electronic structure calculations for bulk alloys of Mn$_{1-x}$Fe$_x$Ge and MnSi in the B20 compound where skyrmions are seen to vary in size and chiral order. We utilize the Virtual Crystal Approximation to vary the concentration of Fe/Mn atoms within the unit cell. Using a first order perturbation approach with spin-orbit coupling applied to spin-spiral calculations we observe the Dzyaloshinski-Moriya vector changes sign and magnitude with the concentration of the transition metal ion.