Dipolar spin correlations in classical pyrochlore magnets

TL;DR

This paper investigates the nature of spin correlations in classical pyrochlore antiferromagnets, proposing a dipolar form driven by local constraints, and confirms this through simulations and analytical expansions for various N values.

Contribution

The authors conjecture and verify that local constraints lead to dipolar spin correlations in pyrochlore antiferromagnets for all N except 2, supported by simulations and analytical methods.

Findings

Dipolar form of spin correlations in pyrochlore antiferromagnets.

Analytical expressions fit well for N=1 and N=3.

Connection to spin ice and water ice models.

Abstract

We study spin correlations for the highly frustrated classical pyrochlore lattice antiferromagnets with O(N) symmetry in the limit T->0. We conjecture that a local constraint obeyed by the extensively degenerate ground states dictates a dipolar form for the asymptotic spin correlations, at all N $\ne$ 2 for which the system is paramagnetic down to T=0. We verify this conjecture in the cases N=1 and N=3 by simulations and to all orders in the 1/N expansion about the solvable N=infinity limit. Remarkably, the N=infinity formulae are an excellent fit, at all distances, to the correlators at N=3 and even at N=1. Thus we obtain a simple analytical expression also for the correlations of the equivalent models of spin ice and cubic water ice, I_h.