Observation of spin-wave renormalization effects in iron and nickel

This is the authors' abstract. We don't add key points for this paper.

Angular distributions characteristic of the small-angle scattering of neutrons by long-wavelength spin waves have been observed at temperatures up to and above the Curie temperature in iron and nickel. For temperatures below 0·9 T c the spin-wave stiffness D , the spin-wave scattering cross section and the spin-wave lifetime have been obtained directly from the measured angular distributions, and the results are compared with the predictions of spin-wave interaction theories. For temperatures up to 0·42 T c in iron a good fit to the variation of D can be obtained using an expression of the form D 0 - D 1 T 2 - D 2 T 5/2 based on the itinerant electron model, but above 0·42 T c the fit becomes progressively poorer and D decreases faster than the fitted expression. The cross section for spin-wave scattering shows a temperature dependence additional to that contained in the thermodynamic factor alone; for iron at temperatures up to 0·7 T c this additional dependence has the form < S z >{1-(0·30±0·08) T / T c } and is stronger than the variation with < S z > predicted by Marshall and Murray in a calculation of the effects of kinematic interactions between spin waves in the Heisenberg model. The observed spin-wave lifetimes have the same form of temperature dependence as is obtained from a nearest-neighbour Heisenberg model calculation by Cooke and Gersch. At temperatures above 0·9 T c the observed angular distributions were corrected for critical scattering using calculated cross sections for the latter due to Villain. D is found to fall slowly on passing through the Curie temperature in both iron and nickel, and is still of the order of a quarter of the room temperature value when the spin-wave scattering intensity falls below the threshold of observability.