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Diagrammatic Perturbation Theory for a Spin–Phonon System
Author(s) -
Barker G. C.,
Tucker J. W.
Publication year - 1981
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221040134
Subject(s) - diagrammatic reasoning , phonon , paramagnetism , perturbation theory (quantum mechanics) , condensed matter physics , physics , ion , lattice (music) , matrix (chemical analysis) , quantum mechanics , chemistry , computer science , chromatography , acoustics , programming language
In a diagrammatic expansion of the phonon Green function for a coupled spin–phonon system an essential quantity that enters the calculation is the polarisation matrix associated with the generalised spin susceptibility. Averages of time‐ordered products of spin operators that occur have been conveniently expressed in terms of semi‐invariants and are evaluated using a diagrammatic technique. Hitherto, only the zeroth‐ and second‐order contributions to the polarisation matrix are derived for a system of paramagnetic ions coupled to the phonons of the host lattice through an interaction that is linear in the strain. Near a spin resonance frequency, higherorder terms in the polarisation matrix become important. The complete expression for the fourthorder contribution to the polarisation matrix is reported. The result is valid for all temperatures and the concentration dependence of the paramagnetic ions is accounted for.