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

TL;DR

This study maps the zero-temperature phase diagram of a frustrated spin-1/2 Heisenberg model on an AA-stacked honeycomb bilayer, revealing the boundaries of collinear magnetic phases with high precision using the coupled cluster method.

Contribution

It provides the first high-order coupled cluster analysis of the complete phase boundaries for the $J_1$--$J_2$--$J_1^ot$ model on an AA-stacked honeycomb bilayer, including detailed characterization of N{é}el and N{é}el-II phases.

Findings

Accurate phase boundaries for N{é}el and N{é}el-II phases in the $$-$$ plane.

Identification of interlayer spin alignment effects depending on the sign of $J_1^ot$.

High-order coupled cluster method effectively characterizes complex magnetic orderings.

Abstract

The zero-temperature phase diagram of the frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ 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 $J_{1}>0$ and $J_{2}\equiv\kappa J_{1}>0$. The two layers are coupled such that NN interlayer pairs of spins also interact via a similar isotropic Heisenberg interaction of strength $J_{1}^{\perp}\equiv \delta J_{1}$, which may be of either sign. In particular, we locate with high accuracy the complete phase boundaries in the $\kappa$-$\delta$ half-plane with $\kappa>0$ of the two quasiclassical collinear antiferromagnetic phases with N\'{e}el or N\'{e}el-II magnetic order in each monolayer, and the interlayer NN pairs of spins either aligned (for $\delta<0$) or anti-aligned (for $\delta > 0$) to one another. Compared to the two-sublattice N\'{e}el order, in which all NN intralayer pairs of spins are antiparallel to one another, the four-sublattice N\'{e}el-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.