Abstract
The constraints which must be applied to lattice dynamical models are investigated. These constraints are translational and rotational invariance conditions and symmetry conditions on the elastic constants. The results are applied to models for MnF2. In addition to a shell model, two variations are considered which attempt to take account of the static dipole on the fluorine ions. A reasonable fit to experimental data is obtained for the shell model, with nine of the twelve optically active frequencies being in error by less than 4% and the largest error being 12%; the elastic constants are fitted to better than 19% while the dielectric constants fit only to about 30%. There are eight free parameters in this model. No significant improvement is found with the other two models. A comparison is made between the frequency distribution function found from the shell model and the phonon sideband associated with an exciton-magnon transition.
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