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 $J_2\equiv \kappa J_1>0$. The two layers are coupled with NN AFM exchanges with coupling strength $J_1^{\perp }\equiv \delta J_1>0$. We calculate to high orders of approximation within the CCM the zero-field transverse magnetic susceptibility $\chi$ in the Néel phase. We thus obtain an accurate estimate of the full boundary of the Néel phase in the $\kappa \delta$ plane for the zero-temperature quantum phase diagram. We demonstrate explicitly that the phase boundary derived from $\chi$ 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.

References in corpus (14)

• Quantum magnetism and criticality
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice
• The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality
• Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice
• Spin susceptibility of quantum magnets from high to low temperatures
• The frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ isotropic $XY$ model on the honeycomb lattice
• Complete phase diagram of the spin-1/2 $J_1$-$J_2$-$J_3$ model (with $J_3=J_2$) on the honeycomb lattice
• Phase diagram of a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$ $XXZ$ model on the honeycomb lattice
• A frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ model
• Large-$s$ expansions for the low-energy parameters of the honeycomb-lattice Heisenberg antiferromagnet with spin quantum number $s$
• Highly frustrated spin-lattice models of magnetism and their quantum phase transitions: A microscopic treatment via the coupled cluster method
• Self consistent study of the quantum phases in a frustrated antiferromagnet on the bilayer honeycomb lattice

Cited by in corpus (2)

• 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
• 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