Magnetic field induced semimetal-to-canted-antiferromagnet transition on the honeycomb lattice

It is shown that the semimetallic state of the two-dimensional honeycomb lattice with a pointlike Fermi surface is unstable toward a canted antiferromagnetic insulator upon application of an in-plane magnetic field. This instability is already present at the mean-field level; the magnetic field shifts the up- and the down-spin cones in opposite directions thereby generating a finite density of states at the Fermi surface and a perfect nesting between the up- and the down-spin Fermi sheets. This perfect nesting triggers a canted antiferromagnetic insulating state. Our conclusions, based on mean-field arguments, are confirmed by auxiliary field projective quantum Monte Carlo methods on lattices up to 12 x 12 unit cells.