Abstract
The coupling between magnetic and lattice degrees of freedom in magnetic crystals is taken into account in the framework of the Heisenberg model by the simple assumption that the exchange integral depends on the instantaneous positions of atoms changing as a result of their thermal vibrations. In the standard approach, the exchange integral is expanded in a power series in terms of the displacement of atoms from the equilibrium positions, and only the first and the second terms of the expansion are retained. The first term of the expansion leads to the Heisenberg Hamiltonian describing the spin interaction in the rigid lattice, and the second one describes the interaction between the spins (magnetic moments) and the lattice vibrations (the spin-phonon interaction). The lattice vibrations are assumed to be harmonic. This is the harmonic model. It was extensively developed in numerous papers [1–13] and used to explain the properties of ferromagnetic crystals. The assumptions made in the harmonic model restrict its application to the cases where the displacements of the atoms from equilibrium positions are small relative to inter-atomic spacing.
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Plakida, N.M., Konwent, H. (1976). The Spin-Phonon Interaction in Anharmonic Ferromagnetic Crystals. In: Łopuszański, J.T., Pękalski, A., Przystawa, J. (eds) Magnetism in Metals and Metallic Compounds. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0016-9_25
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