Breakdown of Dynamic Scaling Analysis in Isotropic Ferromagnets

The predictions of dynamic scaling theory are shown to be in disagreement with the observed wave-vector and temperature dependence of the inelastic neutron scattering from iron and nickel above $T_c$, outside the region of small wave vectors. This breakdown becomes particularly severe when the characteristic energy of the fluctuations becomes comparable to $\mathrm{kT}$, which occurs at considerably smaller reduced wave vectors for metallic ferromagnets such as Fe, Co, and Ni than for Heisenberg insulators such as EuO.