Nematic phase and phase separation near saturation field in frustrated ferromagnets

We discuss effects of quantum fluctuations on magnetization process of quantum frustrated ferromagnets. It is found that, on general grounds, in a neighborhood of a ferromagnet/antiferromagnet classical 1st-order phase boundary in zero external field, a phase separation or non-classical phase must appear slightly below the saturation field in a quantum case, if the classical AF is not an eigenstate. Besides, we study the ferromagnetic $J_1$-$J_2$ $S=1/2$ Heisenberg model ($J_1<0$) on the bcc lattice from the viewpoint of the magnon Bose-Einstein condensation. For $-1.50097 \leq J_1/J_2 \leq -1.389$, the nematic phase is expected and for $-1.389 \leq J_1/J_2 \leq -0.48$ the phase separation appears under high magnetic field.