  We study the 2D Kondo insulators in a uniform magnetic field using quantum
Monte Carlo simulations of the particle-hole symmetric Kondo lattice model and
a mean field analysis of the Periodic Anderson model. We find that the field
induces a transition to an insulating, antiferromagnetically ordered phase with
staggered moment in the plane perpendicular to the field. For fields in excess
of the quasi-particle gap, corresponding to a metal in a simple band picture of
the periodic Anderson model, we find that the metallic phase is unstable
towards the spin density wave type ordering for any finite value of the
interaction strength. This can be understood as a consequence of the perfect
nesting of the particle and hole Fermi surfaces that emerge as the field closes
the gap. We propose a phase diagram and investigate the quasi-particle and
charge excitations in the magnetic field. We find good agreement between the
mean-field and quantum Monte Carlo results.
