Dispersion Relation for Spin Waves in a fcc Cobalt Alloy

The technique of neutron spectrometry has been used to measure the dispersion curve of the spin waves in a metal for the first time. The momentum distributions of inelastically scattered neutrons from a single crystal of fcc cobalt containing 8% of iron have been observed under constant energy transfer conditions. The observed neutron groups (which satisfied momentum and energy conservation between the neutrons and the spin-wave quanta) enabled the dispersion relation to be established. The response of the intensity of the neutron groups to an applied magnetic field was used to identify those of spin-wave origin. The dispersion relation is in agreement with the form predicted by the Bloch-Heisenberg spin-wave theory. Over the range of measurements, which was limited by the available spectrum of neutron energies, approximate isotropy was observed to hold. The value of the product of the exchange integral and the atomic spin is found to be $JS=(1.47\mathrm{}\pm 0.15)\times {10}^{-2\mathrm{}}$ ev. Assuming $S=0.92\mathrm{}$ the value for $J$ is in poor agreement with a value obtained from the spin-wave interpretation of low-temperature magnetization data. Study of the widths of the neutron groups leads to the conclusion that the mean lifetimes of some of the spin waves are greater than 3×${10}^{-13\mathrm{}}$ sec.