Spin-Wave Dispersion Relation in Dysprosium Metal

Abstract

The spin-wave dispersion relation for the $c$ direction of dysprosium metal in the ferro-magnetic phase at 78\ifmmode^\circ\else\textdegree\fi{}K and in the helical magnetic phase at 98\ifmmode^\circ\else\textdegree\fi{}K has been measured by triple-axis neutron spectrometry. The energy gap measured in the ferromagnetic phase at $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}=0$ is in poor agreement with that calculated from the macroscopic magnetostriction and crystal-field anisotropy constants. The Fourier-transformed exchange interaction $J(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})\ensuremath{-}J(0)$ in the ferromagnetic phase posses a peak near the wave vector that gives the periodicity of the helical structure just above the Curie temperature.