High-temperature spin dynamics in an amorphous ferromagnet

Abstract

We have carried out an inelastic-neutron-scattering investigation of the high-temperature spin-wave excitations and the critical dynamics in the amorphous ferromagnet ${({\mathrm{Fe}}_{65}{\mathrm{Ni}}_{35})}_{75}$${\mathrm{P}}_{16}$${\mathrm{B}}_{6}$${\mathrm{Al}}_{3}$ (${T}_{C}=572$ K). Well-defined spin-wave excitations are observed for wave vectors $0.06\ensuremath{\le}\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ensuremath{\le}0.18$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and for temperatures up to 555 K. The spin-wave dispersion relation over this $q$ range is well described by the expression $\ensuremath{\hbar}\ensuremath{\omega}=\ensuremath{\Delta}+D{q}^{2}$, where $\ensuremath{\Delta}(T=0)\ensuremath{\simeq}0.05$ meV and $D=115[1\ensuremath{-}0.45{(\frac{T}{{T}_{C}})}^{\frac{5}{2}}]$ meV ${\mathrm{\AA{}}}^{2}$; the $\frac{5}{2}$ 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 $\ensuremath{\Gamma}(q)\ensuremath{\sim}{q}^{4}{\mathrm{ln}}^{2}[\frac{{k}_{B}T}{\ensuremath{\hbar}\ensuremath{\omega}(q)}]$. In the critical region the spin-wave stiffness is found to follow the power law $D\ensuremath{\sim}{(1\ensuremath{-}\frac{T}{{T}_{C}})}^{0.5\ifmmode\pm\else\textpm\fi{}0.1}$ for $0.02\ensuremath{\le}1\ensuremath{-}\frac{T}{{T}_{C}}\ensuremath{\le}0.2$, while at ${T}_{C}$ the energy width is consistent with ${\ensuremath{\Gamma}}_{C}(q)\ensuremath{\sim}{q}^{2.7\ifmmode\pm\else\textpm\fi{}0.2}$ for $0.05\ensuremath{\le}q\ensuremath{\le}0.18$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$. 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.