Phase transitions in bilayer Heisenberg model with general couplings

The ground state properties and phase diagram of bilayer Heisenberg model on the square lattice are studied in a wide range of parameter space of intralayer exchange couplings, assuming an antiferromagnetic coupling between constituent layers. In the classical limit, the model exhibits three phases: two of these are ordered phases specified by the ordering wave vectors (pi, pi; pi) and (0, 0; pi); where the third component of each indecates the antiferromagnetic orientation between layers, and another one is ''canted'' phase, stabilized by competing interactions. The effects of quantum fluctuations in the model with S = 1/2 have been explored in terms of dimer mean-field theory exact diagonalization of 2 root 2 x 2 root 2 x 2 clusters, and higher-order perturbation expansions about the interlayer dimer limit.