Transverse Magnetic Susceptibility of a Frustrated Spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg Antiferromagnet on a Bilayer Honeycomb Lattice

Abstract

We use the coupled cluster method (CCM) to study a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg antiferromagnet on a bilayer honeycomb lattice with $AA$ stacking. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor antiferromagnetic (AFM) exchange interactions are present in each layer, with respective exchange coupling constants $J_{1}>0$ and $J_{2} \equiv κJ_{1} > 0$. The two layers are coupled with NN AFM exchanges with coupling strength $J_{1}^{\perp}\equiv δJ_{1}>0$. We calculate to high orders of approximation within the CCM the zero-field transverse magnetic susceptibility $χ$ in the Néel phase. We thus obtain an accurate estimate of the full boundary of the Néel phase in the $κδ$ plane for the zero-temperature quantum phase diagram. We demonstrate explicitly that the phase boundary derived from $χ$ is fully consistent with that obtained from the vanishing of the Néel magnetic order parameter. We thus conclude that at all points along the Néel phase boundary quasiclassical magnetic order gives way to a nonclassical paramagnetic phase with a nonzero energy gap. The Néel phase boundary exhibits a marked reentrant behavior, which we discuss in detail.