Quantum Effects in a Half-Polarized Pyrochlore Antiferromagnet

We study quantum effects in a spin-3/2 antiferromagnet on the pyrochlore lattice in an external magnetic field, focusing on the vicinity of a plateau in the magnetization at half the saturation value, observed in CdCr₂O₄ and HgCr₂O₄. Our theory, based on quantum fluctuations, predicts the existence of a symmetry-broken state on the plateau, even with only nearest-neighbor microscopic exchange. This symmetry-broken state consists of a particular arrangement of spins polarized parallel and antiparallel to the field in a 3∶1 ratio on each tetrahedron. It quadruples the lattice unit cell, and reduces the space group from Fd3̅ m to P4₃32. We also predict that for fields just above the plateau, the low-temperature phase has transverse spin order, describable as a Bose-Einstein condensate of magnons. Other comparisons to and suggestions for experiments are discussed.