Order induced by dipolar interactions in a geometrically frustrated antiferromagnet

TL;DR

This paper investigates how dipolar interactions induce order in a geometrically frustrated antiferromagnet on a pyrochlore lattice, combining mean-field analysis and fluctuation studies to identify two ordered phases.

Contribution

It provides a theoretical analysis of dipolar and exchange interactions leading to ordering in a frustrated antiferromagnet, extending previous experimental and theoretical work.

Findings

Identification of two types of ordered phases depending on interaction ratios

Reproduction and extension of prior theoretical results on Gd2Ti2O7

Analysis of low-temperature ordering mechanisms in the model

Abstract

We study the classical Heisenberg model for spins on a pyrochlore lattice interacting via long range dipole-dipole forces and nearest neighbor exchange. Antiferromagnetic exchange alone is known not to induce ordering in this system. We analyze low temperature order resulting from the combined interactions, both by using a mean-field approach and by examining the energy cost of fluctuations about an ordered state. We discuss behavior as a function of the ratio of the dipolar and exchange interaction strengths and find two types of ordered phase. We relate our results to the recent experimental work and reproduce and extend the theoretical calculations on the pyrochlore compound, Gd$_2$Ti$_2$O$_7$, by Raju \textit{et al.}, Phys. Rev. B {\bf 59}, 14489 (1999).