Low-temperature properties of classical, geometrically frustrated antiferromagnets

TL;DR

This paper investigates the low-temperature and ground-state properties of classical frustrated antiferromagnets on kagome and pyrochlore lattices, revealing universal behaviors and the absence of freezing transitions.

Contribution

It provides a systematic analysis of degeneracies, ground-state selection, and spin dynamics in classical frustrated antiferromagnets, including explicit ground-state constructions for pyrochlore lattices.

Findings

Thermal fluctuations select ground states only in models with minimal degeneracy.

Pyrochlore ground states are not separated by energy barriers.

Relaxation time at low T scales as hbar/(k_B T), with no freezing transition.

Abstract

We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbour antiferromagnetic interactions on a class of geometrically frustrated lattices which includes the kagome and pyrochlore lattices. We explore the behaviour of these magnets that results from their large ground-state degeneracies, emphasising universal features and systematic differences between individual models. We investigate the circumstances under which thermal fluctuations select a particular subset of the ground states, and find that this happens only for the models with the smallest ground-state degeneracies. For the pyrochlore magnets, we give an explicit construction of all ground states, and show that they are not separated by internal energy barriers. We study the precessional spin dynamics of the Heisenberg pyrochlore antiferromagnet. There is no freezing transition or selection of preferred states. Instead, the relaxation time at low temperature, T, is of order hbar/(k_B T). We argue that this behaviour can also be expected in some other systems, including the Heisenberg model for the compound SrCr_8Ga_4O_{19}.