Exchange Interactions and the Spin-Wave Spectrum of Terbium

The spin-wave spectrum of terbium obtained by Mo/ller and Houmann by inelastic neutron scattering at 90°K has been analyzed on the basis of a model consisting of Heisenberg exchange and axial and hexagonal crystal-field terms. By examining the conditions required to fit the calculated spin-wave energies to the experimental results at certain points of high symmetry in the Brillouin zone, values were found for the interatomic exchange constants Jij extending out to sixth-nearest neighbors. These provide a convenient interpolation scheme for obtaining the spin-wave energies throughout the Brillouin zone. The effect of interactions among spin waves arising from the strong crystal-field terms has also been studied. With the aid of an approximation often employed in spin-wave studies of magnetic anisotropy, it was found that the crystal-field parameters of the noninteracting case become multiplied by appropriate powers of the reduced magnetization. This accounts for about half of the temperature dependence of the spin-wave energies measured by Mo/ller and Houmann.