Square root relaxation: two possible mechanisms

TL;DR

This paper investigates two mechanisms explaining square root magnetic relaxation in large spin molecular paramagnets, highlighting the roles of dipole and hyperfine interactions and their dependence on nuclear spin relaxation rates.

Contribution

It introduces a new hyperfine interaction-based mechanism and analyzes how nuclear spin relaxation rates influence short-time magnetic relaxation behaviors.

Findings

Square root relaxation can arise from hyperfine interactions under certain conditions.

Different relaxation regimes depend on the nuclear spin relaxation speed.

The behavior is especially relevant in dilute systems.

Abstract

Magnetic relaxation in large spin molecular paramagnets is often found to behave as the square root of time at short times t. This behaviour was explained by Prokofiev & Stamp as arising from dipole interactions between molecular spins. However, as observed by Miyashita & Saito, the same behaviour can arise from a different mechanism which, in the present work, is related to hyperfine interactions. The Miyashita-Saito scheme is found to be possible at short times if the nuclear longitudinal spin relaxation is very slow. In the case of moderately slow nuclear spin relaxation, the electronic magnetization variation is initially proportional to t, then to the square root of t and finally to decay exponentially. This behaviour may be mostly expected in dilute systems.