Inelastic neutron scattering investigation of spin waves and magnetic interactions in α‐Fe₂O₃

Abstract

Abstract Spin waves in antiferromagnetic α‐Fe 2 O 3 have been studied at temperatures of 240 and 290° K by means of inelastic neutron scattering. We report here the first determination of the acoustical branch throughout the entire Brillouin zone and the first observation of the optical branch. The latter shows little dispersion throughout the zone, and has an energy of 1125° K (97 meV) at the zone centre. At the zone boundaries a gap of 20 to 70° K exists between the two branches. Heisenberg interaction parameters J m defined through a Hamiltonian \documentclass{article}\pagestyle{empty}\begin{document}$ H\, = \, - \,\sum\limits_{i,j} {J_m } (r_{ij} )S_i \cdot S_j $\end{document} were obtained through fitting of the data to theoretical expressions for the dispersion relations. The following values were obtained for the first five nearest neighbours: J 1 = 6.0 ± 1.6° K, J 2 = 1.6 ± 0.6° K, J 3 = −29.7 ± ± 2.0° K, J 4 = −23.2 ± 1.0° K and J 5 = −1.0 ± 1.0° K. Interactions to farther neighbours were found to be weak. Neutron intensity data were partly invoked in obtaining the interaction parameters, as two sets of parameters could fit the energy data almost equally well, but they predicted different relative intensities for the two branches in certain regions of the reciprocal space. All spin waves of energy larger than 80° K, including the entire optical branch, were found to be unaffected by the Morin spin‐flip transition at 261° K temperature. The spin‐wave data were used to calculate the sublattice magnetization, the Néel and the Curie‐Weiss temperatures, the perpendicular susceptibility at low temperatures and the density of spin‐wave state spectrum.