Magnon Scattering of Polarized Neutrons by the Diffraction Method: Measurements on Magnetite

The acoustic branch of the spin-wave spectrum of a ferromagnet may be measured by the inelastic scattering of neutrons. It is shown that when polarized neutrons are employed in conjunction with the diffraction method, data may be secured over a sufficient range of the magnon wave vector $q$ to test the applicability of the Heisenberg model. The procedures for utilizing this technique are described. In particular, the methods used for correcting for the instrumental resolution and for converting the data into the form of a dispersion relation are explained. This procedure has been applied to a study of ${\mathrm{Fe}}_3$ ${\mathrm{O}}_4$ at room temperature for values of $\frac{q}{q_{max}}$ up to ∼0.3. The results are in very good agreement with measurements by direct energy analysis and with the predictions of the Heisenberg theory. A value of 2.35×${10}^{-3\mathrm{}}$ eV is obtained for the exchange integral. Additional data taken at 77°K show that the dispersion relation in magnitite is substantially the same in the high- and low-temperature phases (i.e., above and below the $A-B$ site ordering transition at 119°K).