Spin freezing in geometrically frustrated antiferromagnets with weak disorder

We investigate the consequences for geometrically frustrated antiferromagnets of weak disorder in the strength of exchange interactions. Taking as a model the classical Heisenberg antiferromagnet with nearest neighbor exchange on the pyrochlore lattice, we examine low-temperature behavior. We show that spatial modulation of exchange generates long-range effective interactions within the extensively degenerate ground states of the clean system. Using Monte Carlo simulations, we find a spin glass transition at a temperature set by the disorder strength. Disorder of this type, which is generated by random strains in the presence of magnetoelastic coupling, may account for the spin freezing observed in many geometrically frustrated magnets.