Frustrated order by disorder: The pyrochlore anti-ferromagnet with bond disorder

Abstract

The classical Heisenberg antiferromagnet on the pyrochlore lattice is macroscopically and continuously degenerate and the system remains disordered at all temperatures, even in the presence of weak dilution with nonmagnetic ions. We show that, in stark contrast, weak bond disorder lifts the ground state degeneracy in favour of locally collinear spin configurations. We present a proof that for a single tetrahedron the ground state is perfectly collinear but identify two mechanisms which preclude the establishment of a globally collinear state; one due to frustration and the other due to higher-order effects. We thus obtain a rugged energy landscape, which is necessary to account for the glassy phenomena found in real systems such as the pyrochlore Y2Mo2O7 recently reported by Booth et al.[1] to contain a substantial degree of bond disorder.

Order in the Heisenberg pyrochlore: The magnetic structure ofGd2Ti2OChampion1, Wills2, Fennell3 et al. 2001Phys. Rev. B14610861View full textAdd to dashboardCite

“…These materials show spin freezing transitions in the absence of long range order and spin correlations characteristic of the pure Heisenberg system [5,17,18]. Thus our results support the idea that quenched chemical disorder is a strongly relevant perturbation in the pyrochlore system that is responsible for the glassy ground states often observed [19]. The theory of Raju et al [6] encompasses the experimental behaviour of Gd 2 Ti 2 O 7 in that it predicts an h h h propagation vector.…”

Magnetic frustration in the context of pseudo-dipolar ionic disorder

“…Imposing the constraint leads to a significant slowing of the dynamics, but with 10 7 MCS/s q EA remains below 0.05 even at T /|J ab | = 0.01. As already noted, this behaviour is in strong contrast with that of HPAFM with weak random bond disorder [19,20]. Figure 2 shows the variation of the order parameter m…”

Spin-glass transition in geometrically frustrated antiferromagnets with weak disorder

“…14 and 15, and an earlier investigation by others of the problem we consider is described in Ref. 16. A short account of some of our work has been given in a previous publication 17 by two of the authors.…”