Magnetoelastic model for the relaxation of lanthanide ions in YBa2Cu3O7-delta observed by neutron scattering

Established physical properties of ceramic superconductors and lanthanide i ons suggest lattice vibrations are significant in the paths for relaxation of the ions as substitutional impurities in such high-T-c materials. Here, the 4f electrons of a lanthanide ion substituting for Y in YBa2Cu3O7-delta are described with a crystal-field potential (symmetry D-2h) and a magnetoe lastic interaction, which is linear in the normal modes of vibration of the paramagnetic ion and anions. The most significant matrix elements of the i nteraction are determined using selection rules and wave functions for the crystal-field states. Applied to Tb3+, Ho3+, and Tm3+, calculations for the ground state and first excited state indicate that the dynamic properties of the lanthanide ions are adequately described by a simple three-state mod el not unlike the one introduced by Orbach for the interpretation of electr on paramagnetic resonance signals from a lanthanide ion in dilute concentra tion in a salt. The cross section for inelastic scattering of neutrons by t he lanthanide ion is derived by constructing a pseudospin model (spin=1) an d treating the magnetoelastic interaction as a perturbation on the three cr ystal-field states. In the case of Tb3+, the energy of the first excited st ate relative to the ground state is found to be very much smaller than the energy of any other state, the scattering of neutrons is thus a quasielasti c process and the width in energy or, alternatively, the relaxation rate is proportional to {exp(Delta/k(B)T)-1}(-1), when T is the temperature and De lta is the energy of the third, intermediate crystal-field state at which t he density of phonon states probed. The value of Delta suggested by the cal culation and the law predicted for the temperature dependence of the relaxa tion rate are in accord with measurements, on metallic and nonmetallic samp les. Equally impressive accounts are given of data published on the relaxat ion rates of Ho3+ and Tm3+ in metallic YBa2Cu3O7-delta.