On the measurement of the stiffness of spin waves in the Fe$_{0.75}$Co$_{0.25}$Si helimagnet by the small-angle neutron scattering method

The stiffness of spin waves in the Fe$_{0.75}$Co$_{0.25}$Si helimagnet with the Dzyaloshinskii–Moriya interaction in a state fully magnetized by an external field has been measured by the small-angle neutron scattering method. It has been shown that the dispersion of magnons in this state is anisotropic because the neutron scattering pattern consists of two circles for neutrons with 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 $\pm \mathbf{k}_s$ measured in inverse nanometers. The radius of the circles is directly related to the stiffness of spin waves and depends on the magnitude of the magnetic field. It has been shown that the stiffness of spin waves $A$ for the helimagnet is equal to $46.0$ meV Å$^2$ at $T=0$ K and decreases weakly (by $20\%$) with increasing temperature up to the critical value $T_c = 38$ K.