Use of the drone-fermion representation. II. Phonon scattering by paramagnetic ions

Abstract

For pt. I see abstr. A37362 of 1971. In an interacting spin-phonon system, coherences in the phonon scattering from different ions lead to coupled spin-phonon modes and the thermal resistance arises from the finite lifetime of the coupled excitations. The phonon Green function is derived here by means of a diagrammatic method employing the drone-fermion representation for spin-¹/₂ operators. Comparison of the phonon lifetime with previous treatments is made, with particular attention being given to the dependence on phonon frequency and ionic concentration. The relationship to the single-ion perturbation-theory calculation is then established and the implications of these results for the analysis of thermal conductivity data are discussed.