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 ${\mathrm{CdCr}}_2{\mathrm{O}}_4$ and ${\mathrm{HgCr}}_2{\mathrm{O}}_4$. 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 $Fd\overline{3}m$ to $P{4}_{3}32$. 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.

• Received 6 October 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.097207