Cubic magnetic anisotropy in $B$20 magnets: Interplay of anisotropy and magnetic order in Fe${}_{1-x}$Co${}_x$Si

Abstract

The metallic systems MnSi and Fe${}_{1-x}$Co${}_x$Si are known to feature a generic magnetic phase diagram primarily determined by the isotropic exchange and Dzyaloshinskii-Moriya interactions. However, additional weaker anisotropies, lowest in the hierarchy of energy scales, play a crucial role: they determine the relative order of phases in the phase diagram and may even enable skyrmion stability far below the ordering temperature. Among cubic B20 helimagnets, the insulator Cu${}_2$OSeO${}_3$ is currently the only known example exhibiting a low-temperature, anisotropy-induced skyrmion pocket. In this manuscript, we present a systematic study of cubic magnetocrystalline anisotropy by means of angle-resolved SQUID magnetization measurements in MnSi and Fe${}_{1-x}$Co${}_x$Si ($0.08\le x\le 0.70$) single crystals and provide quantitative values of the anisotropy constants. For Fe${}_{1-x}$Co${}_x$Si, the cubic anisotropy is found to be strongly dependent on the Co concentration $x$. In particular, for low Co concentrations ($x\sim 0.10$), the anisotropy is sufficiently strong to stabilize a low-temperature skyrmion lattice, in agreement with theoretical predictions. This finding suggests that Fe${}_{1-x}$Co${}_x$Si may represent the first chiral metallic system to exhibit a low-temperature skyrmion phase controllably stabilized by cubic anisotropy for specific directions of the magnetic field.