Critical and Spin-Wave Scattering of Neutrons from Iron

The wavelength and frequency dependence of neutrons magnetically scattered from iron has been studied with high resolution from low temperatures to $1.05T_c$. At low temperatures, the spin waves can be satisfactorily described in terms of a model Hamiltonian containing Heisenberg and dipole-dipole terms. The spin-wave energies vary as $1-\frac{T}{T_c}$ to the power 0.37±0.03 over a temperature range $0.005<1-\frac{T}{T_c}<0.2\mathrm{}$. At a temperature a few degrees below $T_c$, the spin waves become over-critically damped. In the spin-wave region, no peak corresponding to a diffusive mode has been observed in the scattering, in contrast to the antiferromagnet RbMn${\mathrm{F}}_3$, where the existence of such a peak has been clearly demonstrated. Above $T_c$, in the hydrodynamic region, the scattering can be described in terms of a diffusion equation. The diffusion constant and static susceptibility vary as $1-\frac{T_c}{T}$ to the powers 0.14±0.04 and 1.30±0.06, respectively, over the temperature range $0.008<1-\frac{T_c}{T}<0.05\mathrm{}$. The observed power laws indicate that near the Curie temperature the spin-wave energies vary with temperature in the same way as the magnetization, while the diffusion constant varies more slowly with temperature than has been predicted. In agreement with earlier measurements, the data for the static susceptibility indicate that the power law of the divergence is close to 1.30. Values in the range 1.33-1.43 are predicted by high-temperature expansion techniques. There is evidence for the existence of a strongly damped propagating mode in the transition region at and above $T_c$. At the critical temperature, linewidths scale as the wave vector to the power 2.7±0.3; within error, this is the same as the power 2.5 predicted on the basis of the dynamic scaling laws.