Collinear antiferromagnetic phases of a frustrated spin-½ J₁–J₂–J₁^⊥ Heisenberg model on an AA-stacked bilayer honeycomb lattice

The regions of stability of two collinear quasiclassical phases within the zero-temperature quantum phase diagram of the spin-½ J₁–J₂–J₁^⊥ model on an
AA-stacked bilayer honeycomb lattice are investigated using the coupled cluster method (CCM).  The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange interactions, with respective strengths J₁ > 0 and J₂ ≡ κJ₁ > 0.  The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength J₁^⊥≡ δJ₁.  The complete phase boundaries of two quasiclassical collinear AFM phases, namely the Néel and Néel-II phases on each monolayer, with the two layers coupled so that NN spins between them are antiparallel, are calculated in the κδ half-plane with κ > 0.  Whereas on each monolayer in the Néel state all NN pairs of spins are antiparallel, in the Néel-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel.  We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter M and the excitation energy ∆ from the s^z_T= 0 ground state to the lowest-lying |s^z_T| = 1 excited state (where s^z_T is the total z component of spin for the system as a whole, and where the collinear ordering lies along the z direction), for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders (n ≤ 10) in a systematic series of approximations involvingn-spin clusters.  The sole approximation made is then to extrapolate the sequences of nth-order results for M and ∆ to the exact limit, n → ∞.