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Antiferromagnetic state in bilayer graphene

Motivated by the recent experiment of Velasco Jr. {\em et al.} [J. Velasco Jr. {\em et al.}, Nat. Nanotechnology 7, {\bf 156} (2012)], we develop a mean-field theory of the interaction-induced antiferromagnetic (AF) state in bilayer graphene at charge neutrality point at arbitrary perpendicular magnetic field B. We demonstrate that the AF state can persist at all $B$. At higher $B$, the state continuously crosses over to the AF phase of the $ν=0$ quantum Hall ferromagnet, recently argued to be realized in the insulating $ν=0$ state. The mean-field quasiparticle gap is finite at B=0 and grows with increasing B, becoming quasi-linear in the quantum Hall regime, in accord with the reported behavior of the transport gap. By adjusting the two free parameters of the model, we obtain a simultaneous quantitative agreement between the experimental and theoretical values of the key parameters of the gap dependence -- its zero-field value and slope at higher fields. Our findings suggest that the insulating state observed in bilayer graphene in Ref. 1 is antiferromagnetic (canted, once the Zeeman effect is taken into account) at all magnetic fields.