Collinear antiferromagnetic phases of a frustrated spin-12 J1–J2–J1⊥Heisenberg model on an AA-stacked bilayer honeycomb lattice

Abstract The regions of stability of two collinear quasiclassical phases within the zero-temperature quantum phase diagram of the spin- 1 2 J 1 – J 2 – J 1 ⊥ 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 J 1 > 0 and J 2 ≡ κ J 1 > 0 . The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength J 1 ⊥ ≡ δ J 1 . The complete phase boundaries of two quasiclassical collinear AFM phases, namely the Neel and Neel-II phases on each monolayer, with the two layers coupled so that NN spins between them are antiparallel, are calculated in the κ δ half-plane with κ > 0 . Whereas on each monolayer in the Neel state all NN pairs of spins are antiparallel, in the Neel-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 Δ from the s T z = 0 ground state to the lowest-lying | s T z | = 1 excited state (where s T z 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 involving n -spin clusters. The sole approximation made is then to extrapolate the sequences of n th-order results for M and Δ to the exact limit, n → ∞ .