Spin-Wave Dispersion Relations in Ferromagnetic Fe-Si Alloys

Spin-wave dispersion relations, in the momentum range $0.1\le q\le 0.3$ ${\mathrm{\AA }}^{-1\mathrm{}}$, have been measured in ${\mathrm{Fe}}_{0.93}$ ${\mathrm{Si}}_{0.07}$ and ${\mathrm{Fe}}_{0.85}$ ${\mathrm{Si}}_{0.15}$ ferromagnetic alloys by means of the so-called diffraction method in conjunction with polarized neutrons. By fitting the experimental points with the law $\hslash \omega =D{q}^2(1-\beta q^2+\gamma q^4)$, the stiffness constant $D$ has been found to be 273±3 and 233±11 meV ${\mathrm{\AA }}^2$, respectively, for the two alloys. Values of 3.7±0.2 and 4±2 ${\mathrm{\AA }}^2$ were obtained for the parameter $\beta$. These values of $\beta$, as well as the concentration dependence of the stiffness constants, appear to be inconsistent with a nearest-neighbor Heisenberg model.