Temperature-dependent scattering parameter in the Shubnikov-de Haas effect

Study of the Shubnikov-de Haas effect in samples of ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$ at temperatures up to and through the structural phase transition show contributions to the Dingle scattering parameter from the soft transverse-optic phonons associated with the phase transition and from the formation of domain walls in the samples at the transition. The variation of the cross-sectional area of the Fermi surfaces through the transition is found to agree with Bangert's predictions based on band-structure parameters which fit the reported variation with carrier concentration and Sn composition dependence of Fermi-surface anisotropy and of effective mass in the cubic phase of ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$.