Order-disorder transitions in bilayer Heisenberg models on the triangular lattice

Abstract

The triangular-lattice bilayer Heisenberg model with antiferromagnetic interlayer coupling ${J}_{0}$ is studied using strong-coupling perturbation theory and bond-operator mean-field theory. It is found that the model with ferromagnetic intralayer coupling $J<0$ undergoes a quantum order-disorder transition at a strong-${J}_{0}$ critical point ${J}_{0c}=\ensuremath{-}3.83J.$ While for the model with $J>0,$ the transition point is very small, ${J}_{0c}=0.15J.$ The result implies that the single-layer triangular Heisenberg antiferromagnet only has small long-range order parameter (if ordered) so that it is very sensitive to the interlayer perturbation.