Theory of severe slowdown in the relaxation of rings and clusters with antiferromagnetic interactions

TL;DR

This paper explains the universal power-law temperature dependence of relaxation in antiferromagnetic rings and nanoclusters, showing it is governed by quadrupolar fluctuations rather than lowest excitations, with a key energy scale set by the spin gap.

Contribution

It introduces a new understanding that quadrupolar fluctuations dominate relaxation in the severe slowdown regime, contrasting with previous focus on lowest excitation lines.

Findings

Relaxation governed by quadrupolar fluctuations, not lowest excitations.

Universal power-law behavior of correlation frequency with exponent near 4.

Rescaling temperature by the spin gap aligns data across different clusters.

Abstract

We show that in the severe slowing down temperature regime the relaxation of antiferromagnetic rings and similar magnetic nanoclusters is governed by the quasi-continuum portion of their quadrupolar fluctuation spectrum and not by the lowest excitation lines. This is at the heart of the intriguing near-universal power-law temperature dependence of the electronic correlation frequency $\omega_c$ with an exponent close to 4. The onset of this behavior is defined by an energy scale which is fixed by the lowest spin gap $\Delta_0$. This explains why experimental curves of $\omega_c$ for different cluster sizes and spins nearly coincide when $T$ is rescaled by $\Delta_0$.