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The zero-temperature quantum phase diagram of the spin-$\frac{1}{2}$$J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model on an $AA$-stacked bilayer honeycomblattice is investigated using the coupled cluster method (CCM). The modelcomprises two monolayers in each of which the spins, residing onhoneycomb-lattice sites, interact via both nearest-neighbor (NN) andfrustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenbergexchange iteractions, with respective strengths $J_{1} > 0$ and $J_{2} \equiv\kappa J_{1}>0$. The two layers are coupled via a comparable Heisenbergexchange interaction between NN interlayer pairs, with a strength$J_{1}^{\perp} \equiv \delta J_{1}$. The complete phase boundaries of twoquasiclassical collinear AFM phases, namely the N\'{e}el and N\'{e}el-IIphases, are calculated in the $\kappa \delta$ half-plane with $\kappa > 0$.Whereas on each monolayer in the N\'{e}el state all NN pairs of spins areantiparallel, in the N\'{e}el-II state NN pairs of spins on zigzag chains alongone of the three equivalent honeycomb-lattice directions are antiparallel,while NN interchain spins are parallel. We calculate directly in thethermodynamic (infinite-lattice) limit both the magnetic order parameter $M$and the excitation energy $\Delta$ from the $s^{z}_{T}=0$ ground state to thelowest-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 orderinglies along the $z$ direction) for both quasiclassical states used (separately)as the CCM model state, on top of which the multispin quantum correlations arethen calculated to high orders ($n \leq 10$) in a systematic series ofapproximations involving $n$-spin clusters. The sole approximation made is thento extrapolate the sequences of $n$th-order results for $M$ and $\Delta$ to theexact limit, $n \to \infty$.

journal of magnetism and magnetic materials

Collinear antiferromagnetic phases of a frustrated spin-$\frac{1}{2}$  $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg model on an $AA$-stacked bilayer  honeycomb lattice