Study of time-dependent hyperfine interactions by PAC, Mossbauer effect, μSR and NMR: a review of stochastic models

Abstract

Time-dependent hyperfine interactions constitute a useful nuclear tool for probing interactions in condensed matter. The hyperfine coupling between, say, a nucleus and its surrounding electrons in an atom, is rendered time dependent when the atom becomes a component of a many-body system. The time dependence can arise from a variety of effects, e.g., interaction of the electronic shell of the nucleus with phonons, magnons, other electrons, etc., or modulation of the electronic environment of the nucleus owing to defect kinetics, etc. The experimental methods usually employed for studying hyperfine interactions consist of the perturbed angular correlation (PAC) of γ-rays, the Mossbauer effect, nuclear magnetic resonance (NMR), or muon spin rotation (μSR). The aim of this review is to provide a common theoretical basis for analyzing time-dependent hyperfine spectra by the above-mentioned techniques. This is achieved by expressing the experimentally measured quantity in each case in terms of an object termed the perturbation factor. With a view to calculating the latter, the time-dependent hyperfine interaction is modelled in terms of a stochastic hamiltonian. Two distinct kinds of stochastic models are considered, and their applications illustrated within a random-phase-like approximation. Various physical examples are then investigated. These include fluctuating electric quadrupolar and magnetic dipolar interactions. Comparison of the computed plots of the perturbation factor brings out the similarities and dissimilarities between the PAC, Mossbauer, μSR and NMR techniques.