  The field induced quantum critical properties of the three dimensional
spin-1/2 anisotropic antiferromagnetic Heisenberg model has been studied. We
have investigated the quantum phase transition between the spiral order and
field induced ferromagnetic order by means of Bose-Einstein condensation of
magnons in terms of a bosonic representation. The effect of in-plane anisotropy
on the critical properties has been studied via the bosonic model by Green's
function approach. We have found an analytic expression for the gap exponent in
addition to numerical results for the critical magnetic field in terms of
anisotropy parameter. The in-plane anisotropy breaks the U(1) symmetry
explicitly which changes the universal behavior by a drastic change on the gap
exponent. Moreover, the critical magnetic field depends strongly on the
in-plane anisotropies. The divergence of the transverse structure factor at the
antiferromagnetic wave vector confirms the onset of the magnetic order which
scales with the negative value of gap exponent as the magnetic field approaches
the critical one. The transverse staggered magnetization as an order parameter
vanishes with exponent $\beta=0.5$ when the magnetic field reaches its critical
value in low field region.
