Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model

Abstract

The zero-temperature phase diagram of the frustrated spin-1 2 J1-J2-J ⊥ 1 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 J ⊥ 1 ≡ 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.