On Spin‐Lattice Interactions in the Heisenberg Ferromagnet

The properties of the compressible Heisenberg model are discussed. The spin‐phonon interactions are taken into account by an expansion of the exchange coupling in powers of the atomic displacements. The coupled system of spins and phonons is treated by a series of unitary and Bogolyubov transformations. Expressions are derived for the lowering of the magnetic critical temperature due to first and second derivatives of the exchange integral and for the phonon spectrum as renormalized by the magnetic coupling. The change in the excitation spectrum of the spins at high temperatures induced by the presence of phonons is also found by using Callen's decoupling for the spin propagator in the random phase approximations. Where appropriate, the results are in qualitative agreement with previous work and experiment.