Magnetic order in coupled spin-half and spin-one Heisenberg chains in an anisotropic triangular-lattice geometry

Abstract

We study spin-half and spin-one Heisenberg models in the limit where one-dimensional (1D) linear chains, with exchange constant ${J}_{1}$, are weakly coupled in an anisotropic triangular-lattice geometry. Results are obtained by means of linked-cluster series expansions at zero temperature around different magnetically ordered phases. We study the noncollinear spiral phases that arise classically in the model and the collinear antiferromagnet that has been recently proposed for the spin-half model by Starykh and Balents [Phys. Rev. Lett. 98, 077205 (2007)] using a renormalization group approach. We find some evidence that such phases can be stabilized in the spin-half model for arbitrarily small coupling between the chains, though convergence of the sublattice-magnetization series remains unsatisfactory. For vanishing coupling between the chains the energy of each phase must approach that of decoupled linear chains. With increasing interchain coupling, the noncollinear phase appears to have a lower energy in our calculations. For the spin-one chain, we find that there is a critical interchain coupling needed to overcome the Haldane gap. When spin-one chains are coupled in the frustrated triangular-lattice geometry, the critical coupling required to close the Haldane gap is enhanced by an order of magnitude compared to unfrustrated interchain couplings in the square-lattice geometry. The collinear phase is not obtained for the spin-one Heisenberg model.