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 (Fe₆₅Ni₃₅)₇₅{P}₁₆B₆{Al}₃$ (${T}C=572$ K). Well-defined spin-wave excitations are observed for wave vectors $0.06{≤}{{→}}{q}{≤}0.18$ ${{{}}}^{{-}1}$ and for temperatures up to 555 K. The spin-wave dispersion relation over this $q$ range is well described by the expression ${}{ω}={Δ}+D{q}²$, where ${Δ}(T=0){}0.05$ meV and $D=115[1{-}0.45{({T}{{T}C})}5/2]$ meV ${{{}}}²$; the $5/2$ power law appears to hold up to 450 K. Measurements at $T=450$ K show that the spin-wave damping is consistent with the Heisenberg-model prediction ${Γ}(q){~}{q}⁴{ln}²[{{k}BT}{{}{ω}(q)}]$. In the critical region the spin-wave stiffness is found to follow the power law $D{~}{(1{-}{T}{{T}C})}^{0.5±{}0.1}$ for $0.02{≤}1{-}{T}{{T}C}{≤}0.2$, while at ${T}C$ the energy width is consistent with ${{Γ}}C(q){~}{q}^{2.7±{}0.2}$ for $0.05{≤}q{≤}0.18$ ${{{}}}^{{-}1}$. 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.