Thermodynamic properties of a S=1 spin-phonon system: specific heat of Fe2+in MgO

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Abstract
The thermodynamic properties of a coupled spin-phonon system with S=1 are examined using a diagrammatic expansion of the free energy. The evaluation of the thermal averages of products of spin operators is facilitated by use of the drone- fermion representation. The specific heat contribution from the spin-phonon interaction is examined in detail for the case of ferrous ions in MgO and it is found to be negligible compared with the usual Schottky anomaly. This is in agreement with the experimental observation of Smith and Seidel (1970). The importance of using the full spin-phonon Hamiltonian as dictated by crystal symmetry is stressed because there is a large cancellation from the terms in the interaction that give 'resonances' at zero, omega 0 and 2 omega 0. If it was not for this cancellation the specific heat contribution from the spin-phonon interaction would be a factor omega m/ omega 0 times larger and hence observable experimentally.