Quantum effects on a graphene-like material with four-sublattice

A Heisenberg model is formed by a graphene-like material with four-sublattice, which the intralayer exchange coupling of upper layer is ferromagnetic and that of bottom layer is antiferrimagnetic. The retarded Green's function and the linear spin-wave approximation are introduced to study the magnetic properties of the system. The effects of various parameters in the ground state properties of the system, such as the spin-wave spectra, energy gap and the magnetization have been studied. Two energy gaps are found in the spin-wave spectra. The antiferrimagnetic couplings and spin quantum numbers play important roles on energy gaps and sublattice magnetization.