We study the effects of magnetoelastic couplings on pyrochlore antiferromagnets. We employ Landau theory, extending an investigation begun by Yamashita and Ueda for the case of S = 1, and semiclassical analyses to argue that such couplings generate bond order via a spin-Peierls transition. This is followed by, or concurrent with, a transition into one of several possible low-temperature Néel phases, with most simply collinear, but also coplanar or mixed spin patterns. In a collinear Néel phase, a dispersionless string-like magnon mode dominates the resulting excitation spectrum, providing a distinctive signature of the parent geometrically frustrated state. We comment on the experimental situation.Geometrically frustrated magnets [1][2][3] are examples of strongly interacting systems: the vast degeneracy of their classical ground states makes them highly susceptible even to small perturbations. By analogy with quantum Hall systems, where the Landau levels are also macroscopically degenerate, one expects a variety of phases in perturbed frustrated magnets, from Néel states to spin glasses or liquids, with valence-bond solids along the way.Probably the world's most frustrated spin system is the classical Heisenberg antiferromagnet on the pyrochlore lattice ( Fig. 1) where spins reside at vertices of tetrahedra. The number of its classical ground states, which are attained when total spin on each tetrahedron S tot = 4 i=1 S i = 0, is so large that, exceptionally, it does not order at any finite temperature [4]. In real compounds, deviations from the classical Heisenberg model (e. g. dipolar interactions, single-ion anisotropy or quantum fluctuations) determine which ground state is selected at the lowest temperatures.
FIG. 1. The pyrochlore latticeIn this note, we discuss an elegant mechanism for lifting the frustration through a coupling between spin and lattice degrees of freedom. The high symmetry of the pyrochlore lattice and the spin degeneracy drive a distortion of tetrahedra via a magnetic Jahn-Teller ("spinTeller") effect. The resulting state exhibits a reduction from cubic to tetragonal symmetry and the development of bond order in the spin system with unequal spin correlations S i · S j on different bonds of a tetrahedron. In the ordered phase, there are 4 strong and 2 weak bonds per tetrahedron-or vice versa. This phenomenon was uncovered by Yamashita and Ueda [5] for pyrochlore antiferromagnets with spins S = 1, for which they described an AKLT-style wavefunction [6] with the requisite bond order. In the following we study this phenomenon in the semiclassical limit with added insight from Landau theory, and discuss its consequences for the excitation spectrum. As many of the candidate systems have moderately large spins and order at finite temperatures, our methods should work well-in particular, they allow us to treat the Néel order that can (and experimentally does) appear in addition to the bond order.We begin by identifying a two-component bond order parameter at the level of a single tetrahedron an...