Temperature Dependence of the Linewidth in Critical Spin Fluctuation

Starting from the kinetic equations obeyed by the time-dependent spin-correlation functions, we have calculated the homogeneous function which appears in the dynamical scaling expression for the linewidth of critical fluctuations in ferromagnets and antiferromagnets. In agreement with recent experimental findings, this function shows a minimum for $\frac{\kappa }{q}\equiv \mathrm{inverse}$ correlation $\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}/\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\ne 0$.