Frustrated spin-[Formula presented] Heisenberg magnet on an AA-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the J₁–J₂–J₁^⊥ model

The zero-temperature phase diagram of the frustrated spin-[Formula presented]J₁–J₂–J₁^⊥ Heisenberg magnet on an AA-stacked honeycomb bilayer lattice is studied using the coupled cluster method implemented to very high orders. On each monolayer the spins interact via nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic Heisenberg interactions with respective strength parameters J₁>0 and J₂≡κJ₁>0. The two layers are coupled such that NN interlayer pairs of spins also interact via a similar isotropic Heisenberg interaction of strength J₁^⊥≡δJ₁, which may be of either sign. In particular, we locate with high accuracy the complete phase boundaries in the κ–δ half-plane with κ>0 of the two quasiclassical collinear antiferromagnetic phases with Néel or Néel-II magnetic order in each monolayer, and the interlayer NN pairs of spins either aligned (for δ<0) or anti-aligned (for δ>0) to one another. Compared to the two-sublattice Néel order, in which all NN intralayer pairs of spins are antiparallel to one another, the four-sublattice Néel-II order is characterized by NN intralayer pairs of spins on the honeycomb lattice being antiparallel to one another along zigzag (or sawtooth) chains in a specified direction from among the three equivalent honeycomb-lattice directions, and parallel to one another for the corresponding interchain pairs.