Resonant scattering of phonons by iron impurities in zinc sulphide

A phenomenological model has been proposed for the resonant scattering of phonons due to magnetic impurities. The expression for the defect relaxation rate, which also includes Rayleigh scattering of phonons, is of the form ${\tau }_{\mathrm{defect}}^{-1\mathrm{}}=A_{\mathrm{defect}}{\omega }^4+\Sigma \stackrel{}{i}{H}_i\frac{\omega }{{(\omega -{\omega }_{0i})}^2}{F}_i\mathrm{}\left(T\right)\mathrm{},$ where $A_{\mathrm{defect}}$ is the Rayleigh scattering strength; $i (=1,2,3,\dots )$ denotes a particular phonon-induced electronic transition; $H_i$ represents the strength of spin-phonon coupling; and $F_i\mathrm{}\left(T\right)\mathrm{}$ is the fractional electron population difference between the levels involved in the i th electronic transition. The model has been applied to explain resonance structure of $K$ vs $T$ curves of iron-doped ZnS. The success of the model lies in the fact that it gives consistently excellent agreement between theory and experiment for lightly as well as for heavily doped specimens. The model is, however, a simplification and does not consider, among other concepts, phonon dispersion, phonon polarization, phonon normal process, and phonon scattering by Raman processes.