Small-angle critical neutron scattering from cobalt

Total and inelastic-neutron-scattering measurements have been made of the small-angle critical scattering from polycrystalline cobalt both above and below its Curie temperature $T_C$. Below $T_C$ the scattering is dominated by well-defined spin-wave modes which exhibit quadratic dispersion, $\hslash \omega \mathrm{}\left(q\right)=D{q}^2$. Within the hydrodynamic region, the spin-wave stiffness constant is found to have the power-law temperature dependence $D \propto {(T-T_C)}^x$ where $x=0.39\mathrm{}\pm 0.05$. As $T_C$ is approached, the spin waves renormalize and broaden but no evidence of a central peak indicative of the longitudinal component of the susceptibility is observed. Above $T_C$, the exponents $\gamma =1.23\mathrm{}\pm 0.05$ and $\nu =0.65\mathrm{}\pm 0.04$, describing the power-law dependences of the static susceptibility and the inverse correlation range, respectively, have been obtained from the small-angle scans after taking full account of the inelasticity of the scattering. In addition, the critical scattering has been calibrated directly against the nuclear incoherent scattering and in this way the interaction range $r_1$, which appears in the classical and modified Ornstein-Zernike expressions for the asymptotic form of the spin pair correlation function, has also been determined. The linewidths of the quasielastic critical scattering have been measured over a range of wave vectors at temperatures up to 150°C above $T_C$. At $T_C$ the linewidths vary with $q$ to the 2.4±0.2 power. Above $T_C$, the linewidths are well described by a dynamical scaling function which, however, differs from that previously found for iron.