Orbit-lattice interaction of paramagnetic ions in ionic crystals: acoustic resonance of Dy3+in CaF2

Abstract

The orbit-lattice interaction of a paramagnetic ion coupled by Coulomb forces to displacements of its neighbouring point ions is derived. Systematic techniques are used to find this interaction. In particular the attenuation coefficient beta of a longitudinal acoustic wave is calculated in a crystal doped with rare-earth ions; group theory is used to simplify the interaction and calculation of transition probabilities. For Dy³⁺ in CaF₂ the model gives beta approximately 10⁴ cm^-1, which is about 10⁴ times greater than measured; the g values, however, are consonant with experiment. The experimental uncertainties in inhomogeneous broadening and in the fraction of ions on cubic sites reduce beta by about 5*10², and the point-charge model is thus not necessarily a bad one.