Spin correlations in rare-earth paramagnetic systems; neutron linewidths and muSR spin-lattice relaxation rates

TL;DR

This paper analyzes spin correlation functions in rare-earth paramagnetic systems to understand temperature-dependent linewidths and relaxation rates, incorporating conduction electron and phonon mechanisms with theoretical models and phenomenological modifications.

Contribution

It introduces a combined theoretical framework using single-ion dynamics and RPA to interpret experimental spin relaxation data in rare-earth compounds, including insulators.

Findings

The models explain temperature dependence of linewidths and relaxation rates.

Phonon relaxation mechanisms are emphasized in simple crystal-field schemes.

A phenomenological modification improves data fitting for insulators.

Abstract

We consider the spin correlation functions for rare-earth compounds in their paramagnetic state with the aim to understand the temperature dependence of the quasi-elastic and crystal-field linewidths and the spin-lattice relaxation rates measured by the muon-spin-relaxation technique. Both the conduction electron and phonon relaxation mechanisms are treated. First the single-ion dynamics is described using an iterative method introduced by P. M. Richards. Then the case of a regular lattice of rare-earth ions is studied using the random-phase approximation (RPA). Applications to simple crystal-field level schemes are given with particular emphasis on the phonon relaxation mechanism. This allows us to investigate the domain of validity of our results. In order to account for data recorded on insulators, a phenomelogical modification is suggested.