  We study a spin-one Heisenberg model with exchange interaction, J, uniaxial
single-ion exchange anisotropy, D, and Zeeman coupling to a magnetic field, B,
parallel to the symmetry axis. We com- pute the (D/J,B/J) quantum phase diagram
for square and simple cubic lattices by combining an- alytical and Quantum
Monte Carlo approaches, and find a transition between XY-antiferromagnetic and
ferronematic phases that spontaneously break the U(1) symmetry of the model. In
the language of bosonic gases, this is a transition between a Bose-Einstein
condensate (BEC) of single bosons and a BEC of pairs. Our work opens up new
avenues for measuring this transition in real magnets.
