Temperature dependence of the magnetic excitations in iron

The neutron coherent inelastic-scattering technique has been used to study the temperature dependence of the magnetic excitations in iron from room temperature to well above the ferromagnetic transition temperature. Most of the measurements were taken on a large single crystal of ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ (12-at.% Si), although a less extensive set of data was obtained with a single crystal of pure iron. In contrast to the behavior previously observed in the small-wave-vector region, we find that the spin waves at larger values of $\overrightarrow{\mathrm{q}}$ are only moderately renormalized up to $T_C$, and persist as excitations up to the highest temperature measured ($\sim 1.4T_C$). No further renormalization of the dispersion relation is observed above $T_C$. Measurements of the spin-wave linewidths show that as the temperature increases to $T_C$ the widths rapidly increase, but above $T_C$ no additional broadening occurs. In the paramagnetic phase the ratios of the energy widths divided by the excitation energies for $E\gtrsim 8$ meV are found to be less than one ($\frac{\Delta E}{E}<1\mathrm{}$), which has been used as the criterion for the definition of a spin-wave excitation. As the energy decreases below ∼ 8 meV, the scattering evolves continuously into the critical scattering around the origin ($\overrightarrow{\mathrm{q}}=0\mathrm{}$, $\omega =0\mathrm{}$), whereas with increasing energy $\frac{\Delta E}{E}$ decreases. The dynamical correlation range corresponds to a sphere with a diameter ∼ 10 Å, and this correlation range is, within experimental error, independent of the temperature. The over-all spin-wave intensities are reduced at elevated temperatures, but the abrupt decrease in the spin-wave intensity at high energies, interpreted in terms of the band model of magnetism as the intersection of the spin-wave spectrum with the Stoner continuum of spin-flip excitations, is found to be independent of the temperature. The spin-wave energies, as well as the linewidths, are isotropic in $\overrightarrow{\mathrm{q}}$ over the entire temperature range covered, and no interaction of the spin waves with the phonons is observed. These experimental results are in disagreement with present theoretical estimates of the generalized susceptbility at elevated temperatures.