High-temperature spin dynamics in an amorphous ferromagnet

We have carried out an inelastic-neutron-scattering investigation of the high-temperature spin-wave excitations and the critical dynamics in the amorphous ferromagnet ${\left({\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35}\right)}_{75}$ ${\mathrm{P}}_{16}$ ${\mathrm{B}}_6$ ${\mathrm{Al}}_3$ ($T_C=572\mathrm{}$ K). Well-defined spin-wave excitations are observed for wave vectors $0.06\le \overrightarrow{\mathrm{q}}\le 0.18$ ${\mathrm{\AA }}^{-1\mathrm{}}$ and for temperatures up to 555 K. The spin-wave dispersion relation over this $q$ range is well described by the expression $\hslash \omega =\Delta +D{q}^2$, where $\Delta \mathrm{}(T=0\mathrm{})\mathrm{}\simeq 0.05$ meV and $D=115[1-0.45\mathrm{}{\left(\frac{T}{T_C}\right)}^{\frac{5}{2}}]$ meV ${\mathrm{\AA }}^2$; the $\frac{5}{2}$ power law appears to hold up to 450 K. Measurements at $T=450\mathrm{}$ K show that the spin-wave damping is consistent with the Heisenberg-model prediction $\Gamma \mathrm{}\left(q\right)\mathrm{}\sim q^4{\ln }^2\left[\frac{k_{B}T}{\hslash \omega \mathrm{}\left(q\right)\mathrm{}}\right]$. In the critical region the spin-wave stiffness is found to follow the power law $D\sim {(1-\frac{T}{T_C})}^{0.5\pm 0.1}$ for $0.02\le 1-\frac{T}{T_C}\le 0.2$, while at $T_C$ the energy width is consistent with ${\Gamma }_C\mathrm{}\left(q\right)\mathrm{}\sim q^{2.7\pm 0.2}$ for $0.05\le q\le 0.18$ ${\mathrm{\AA }}^{-1\mathrm{}}$. These results are in satisfactory agreement with dynamical scaling theory for the Heisenberg ferromagnet and further they are in good accord with similar, albeit more-detailed, measurements in the crystalline transition metals Fe, Co, and Ni.