## Abstract

The regions of stability of two collinear quasiclassical phases within the zero-temperature quantum phase diagram of the spin-½

*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 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*= 0 ground state to the lowest-lying |^{z}_{T}*s*| = 1 excited state (where^{z}_{T}*s*is the total^{z}_{T }*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 ∆ to the exact limit,*n*→ ∞.Original language | English |
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Pages (from-to) | 262-273 |

Number of pages | 12 |

Journal | Journal of Magnetism and Magnetic Materials |

Volume | 482 |

Early online date | 8 Mar 2019 |

DOIs | |

Publication status | Published - 2019 |

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_{1}–

*J*

_{2}–

*J*

_{1}

^{⊥}Heisenberg model on an

*AA*-stacked bilayer honeycomb lattice'. Together they form a unique fingerprint.