Spin-Peierls phases in pyrochlore antiferromagnets

In the highly frustrated pyrochlore magnet spins form a lattice of corner-sharing tetrahedra. We show that the tetrahedral ``molecule'' at the heart of this structure undergoes a Jahn-Teller distortion when lattice motion is coupled to the antiferromagnetism. We extend this analysis to the full pyrochlore lattice by means of Landau theory and argue that it should exhibit ``spin-Peierls'' phases with bond order but no spin order. We find a range of N\'eel phases, with collinear, coplanar, and noncoplanar order. While collinear N\'eel phases are easiest to generate microscopically, we also exhibit an interaction that gives rise to a coplanar state instead.