Magnetic properties of a doped graphene-like bilayer

A doped graphene-like bilayer is described using a four-sublattice Heisenberg model both ferromagnetic and antiferrimagnetic couplings. The magnetic properties of the bilayer system are studied using the Heisenberg model, retarded Green's function and the linear spin-wave approximation. The spin-wave spectra, energy gap, and the magnetization and quantum fluctuation of the system at the ground state are calculated with various intra- and interlayer couplings. The results indicate that the effect of antiferromagnetic exchange coupling on the magnetic properties of the system is significant. Magnetizations at low temperature show intersection points due to the quantum effects.