Heisenberg antiferromagnet on the pyrochlore lattice: order from distortion

The Heisenberg antiferromagnet on the pyrochlore lattice is an example of a highly frustrated system with a large degeneracy of the ground state. The classical model with nearest-neighbor interactions shows no signs of magnetic order down to very low temperatures. The quantum analog, with short enough spins, was considered a prime candidate for a quantum-disordered ground state, such as a valence-bond liquid or solid. At the same time, the large degeneracy makes this magnet susceptible to a variety of nominally small perturbations. A spin-lattice coupling leads to a spin-Peierls-like distortion of the lattice. In contrast to spin chains, the spin-Peierls distortion in a pyrochlore antiferromagnet occurs for any spin length $S$ remaining robust even in the classical limit. A recent experimental characterization of the $S=3/2$ prototype CdCr$_2$O$_4$ [1] provided a test for the theoretical model. This antiferromagnetic spinel exhibits a tetragonal lattice distortion with an elongated unit cell $a=b