Spin-wave stiffness in the Dzyaloshinskii-Moriya helimagnets Mn1−xFexSi

Abstract

The small-angle neutron scattering is used to measure the spin-wave stiffness in the field-polarized state of the Dzyaloshinskii-Moriya helimagnets ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}\mathrm{Si}$ with $x=0.03$, 0.06, 0.09, and 0.10. The ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}\mathrm{Si}$ compounds are helically ordered below ${T}_{c}$ and show a helical fluctuation regime above ${T}_{c}$ in a wide range up to ${T}_{\text{DM}}$. The critical temperatures ${T}_{c}$ and ${T}_{\text{DM}}$ decrease with $x$ and tend to 0 at $x=0.11$ and 0.17, respectively. We have found that the spin-wave stiffness $A$ change weakly with temperature for each individual Fe-doped compound. On the other hand, the spin-wave stiffness $A$ decreases with $x$ duplicating the ${T}_{\text{DM}}$ dependence on $x$, rather than ${T}_{c}(x)$. These findings classify the thermal phase transition in all ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}\mathrm{Si}$ compounds as an abrupt change in the spin state caused, most probably, by the features of an electronic band structure. Moreover, the criticality in these compounds is not related to the value of the ferromagnetic interaction but demonstrates the remarkable role of the Dzyaloshinskii-Moriya interaction as a factor destabilizing the magnetic order.