LAUSR

By using magnetization and small-angle neutron scattering measurements, we have investigated the magnetic behavior of the $\mathrm{M}{\mathrm{n}}_{1\ensuremath{-}x}\mathrm{I}{\mathrm{r}}_{x}\mathrm{Si}$ system to explore the effect of increased carrier density and spin-orbit interaction on the magnetic properties of MnSi. We determine estimates of the spin wave stiffness and the Dzyaloshinskii-Moriya (DM) interaction strength and compare with $\mathrm{M}{\mathrm{n}}_{1\ensuremath{-}x}\mathrm{C}{\mathrm{o}}_{x}\mathrm{Si}$ and $\mathrm{M}{\mathrm{n}}_{1\ensuremath{-}x}\mathrm{F}{\mathrm{e}}_{x}\mathrm{Si}$. Despite the large differences in atomic mass and size of the substituted elements, $\mathrm{M}{\mathrm{n}}_{1\ensuremath{-}x}\mathrm{C}{\mathrm{o}}_{x}\mathrm{Si}$ and $\mathrm{M}{\mathrm{n}}_{1\ensuremath{-}x}\mathrm{I}{\mathrm{r}}_{x}\mathrm{Si}$ show nearly identical variations in their magnetic properties with substitution. We find a systematic dependence of the transition temperature, the ordered moment, the helix period, and the DM interaction strength with electron count for $\mathrm{M}{\mathrm{n}}_{1\ensuremath{-}x}\mathrm{I}{\mathrm{r}}_{x}\mathrm{Si},\mathrm{M}{\mathrm{n}}_{1\ensuremath{-}x}\mathrm{C}{\mathrm{o}}_{x}\mathrm{Si}$, and $\mathrm{M}{\mathrm{n}}_{1\ensuremath{-}x}\mathrm{F}{\mathrm{e}}_{x}\mathrm{Si}$, indicating that the magnetic behavior is primarily dependent upon the additional carrier density, rather than on the mass or size of the substituting species. This indicates that the variation in magnetic properties, including the DM interaction strength, is primarily controlled by the electronic structure, as Co and Ir are isovalent. Our work suggests that although the rigid band model of electronic structure, along with Moriya's model of weak itinerant magnetism, describes this system surprisingly well, phenomenological models for the DM interaction strength are not adequate to describe this system.