Spin-wave stiffness of the Dzyaloshinskii-Moriya helimagnet compounds Fe1−xCoxSi studied by small-angle neutron scattering

Abstract

The spin wave stiffness was measured by small-angle neutron scattering method in the Dzyaloshinskii-Moriya helimagnet compounds ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}\mathrm{Si}$ with $x=0.25,0.30,0.50$. It has been shown that the spin wave dispersion in the fully polarized state is anisotropic due to Dzyaloshinskii-Moriya interaction. It is reflected in the neutron scattering pattern as two circles for neutrons obtaining and losing the magnon energy, respectively. The centers of the circles are shifted by the momentum transfer oriented along the applied magnetic field $\mathbf{H}$ and equal to the wave vector of the spiral $\ifmmode\pm\else\textpm\fi{}{\mathbf{k}}_{s}$. The radius of the circles is directly related to the stiffness of spin waves and depends on the magnetic field. We have found that the spin-wave stiffness $A$ change weakly with temperature for each individual compound. On the other hand, the spin-wave stiffness $A$ increases linearly with $x$ in contrast to the $x$ dependences of the critical temperature ${T}_{c}$ and the low-temperature ordered moment. Experimentally obtained values of the stiffness $A$ approve quantitative applicability of the Bak-Jensen model for the compounds under study.