  Magnetic frustration can lead to peculiar magnetic orderings that break a
discrete symmetry of the lattice in addition to the fundamental magnetic
symmetries (i.e., spin rotation invariance and time-reversal symmetry). In this
work, we focus on frustrated quantum magnets and study the nature of the
quantum phase transition between a paramagnet and a magnetically ordered state
with broken threefold ($Z_3$) crystal rotation symmetry. We predict the
transition to happen in two stages, giving rise to an intermediate nematic
phase in which rotation symmetry is broken but the system remains magnetically
disordered. The nematic transition is described by the three-state Potts model.
This prediction is based on an analysis of bound states formed from two-magnon
excitations in the paramagnet, which become gapless while single-magnon
excitations remain gapped. By considering three different lattice models, we
demonstrate a generic instability towards two-magnon bound state formation in
the Potts-nematic nematic channel. We present both numerical results and a
general analytical perturbative formula for the bound state binding energy
similar to BCS theory. We further discuss a number of different materials that
realize key features of the model considered, and thus provide promising venues
for possible experimental observation.
