Spin-Wave Dispersion in Ferromagnetic Ni and fcc Co

Inelastic scattering of polarized neutrons by the diffraction technique from Ni and fcc Co at room temperature have yielded constants in the dispersion relation of the spin-wave energy versus wave vector, $\ensuremath{\hbar}\ensuremath{\omega}=D{q}^{2}(1\ensuremath{-}\ensuremath{\beta}{q}^{2})$. The results for fcc Co ($D=384\ifmmode\pm\else\textpm\fi{}20$ meV ${\mathrm{\AA{}}}^{2}$, $\ensuremath{\beta}=3.1\ifmmode\pm\else\textpm\fi{}1.0$ ${\mathrm{\AA{}}}^{2}$) indicate that this metal is similar to Fe and hcp Co in showing a quartic term even for relatively small wave vector ($\frac{q}{{q}_{max}}\ensuremath{\le}0.15$). In Ni, on the other hand ($D=374\ifmmode\pm\else\textpm\fi{}20$ meV ${\mathrm{\AA{}}}^{2}$, $\ensuremath{\beta}=0\ifmmode\pm\else\textpm\fi{}1.0$ ${\mathrm{\AA{}}}^{2}$), a more nearly quadratic relation is found in the same range of $q$. It is argued that these results, when compared with others for Fe and Ni-Fe alloys, are inconsistent with an attempt to interpret the magnetism of these metals in terms of a generalized Heisenberg model with long-range interactions.