Long-wavelength spin-wave energies and linewidths of the amorphous Invar alloy ${\mathrm{Fe}}_{100\mathrm{-}\mathrm{x}}$${\mathrm{B}}_{\mathrm{x}}$

Neutron inelastic scattering experiments have been performed to investigate the long-wavelength spin dynamics of the amorphous isotropic ferromagnet ${\mathrm{Fe}}_{100\mathrm{-}\mathrm{x}}$ ${\mathrm{B}}_{\mathrm{x}}$ (for x=14 and 18). At both iron concentrations this system exhibits Invar behavior. The spin-wave energies are found to be well described by a quadratic dispersion relation E=D(T)$q^2$+Δ, where D(T) is the stiffness parameter and Δ is a small (∼0.05 meV) energy gap originating primarily from dipole interactions. The stiffness parameter D renormalizes with temperature as predicted by the two-magnon interaction theory of the Heisenberg ferromagnet, although the renormalization is more dramatic than expected for short-range interactions. The T=0 stiffness parameters obtained from the neutron scattering measurements are 131 and 122 meV A${̊}^2$ for two samples of nominal concentration x=14, and 165 meV A${̊}^2$ for x=18. These values are almost twice as large as those derived from low-temperature magnetization measurements. It has been argued that possible mechanisms that could explain this discrepancy are the existence of additional low-lying magnetic excitations, and/or anomalous magnon linewidths that would contribute to the rapid decrease of the magnetization. Our extensive analysis of the damping of the long-wavelength spin-wave excitations in ${\mathrm{Fe}}_{86}$ ${\mathrm{B}}_{14}$ has revealed that the temperature and wave-vector dependence of the spin-wave intrinsic linewidths are in good agreement with the predictions of the conventional two-magnon interaction theory of a Heisenberg ferromagnet. We therefore conclude that the discrepancy between the stiffness parameter derived from neutron scattering and magnetization measurements is likely a consequence of additional low-lying magnetic excitations, which contribute to the rather rapid renormalization of the spin-wave stiffness parameter with temperature.