Nematic order in square lattice frustrated ferromagnets

We present a new scenario for the breakdown of ferromagnetic order in a two--dimensional quantum magnet with competing ferromagnetic and antiferromagnetic interactions. In this, dynamical effects lead to the formation of two--magnon bound states, which undergo Bose--Einstein condensation, giving rise to bond--centered nematic order. This scenario is explored in some detail for an extended Heisenberg model on a square lattice. In particular, we present numerical evidence confirming the existence of a state with d-- wave nematic correlations but no long range magnetic order, lying between the saturated ferromagnetic and collinear antiferromagnetic phases of the ferromagnetic $J_1$--$J_2$ model. We argue by continuity of spectra that this phase is also present in a model with 4--spin cyclic exchange. The case of the multiple spin exchange model on a triangular lattice, relevant to magnetism of solid ${}^3$He films, is also discussed.