Exchange interactions and the spin-wave spectrum of terbium

The inelastic neutron scattering data of Møller and Houmann for spin waves in terbium at 90 °K are analysed on the basis of a model consisting of Heisenberg exchange and axial and hexagonal crystal field terms. By considering the conditions required to fit the calculated spin-wave energies to the experimental results at points of high symmetry in the Brillouin zone a set of interatomic exchange constants extending to sixth-nearest neighbours is deduced. These provide a reasonably good interpolation scheme for obtaining spin-wave energies throughout the Brillouin zone, as is required for the study of thermodynamic properties and spin-wave renormalization. The question of how well the theory of Ruderman and Kittel, Kasuya and Yosida accounts for the exchange interactions in terbium is also considered. The pertinent quantities S(Jo - Jq) and Svertical barJqprime vertical bar are calculated in the free-electron approximation and a striking disagreement is found between the calculated and experimental results for S(Jo - Jq) in the outer part of the `ab plane' of the Brillouin zone.