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

TL;DR

This study investigates magnetic ordering in coupled spin-half and spin-one Heisenberg chains on an anisotropic triangular lattice, revealing how inter-chain coupling influences phase stability and the emergence of magnetic order.

Contribution

It provides a detailed analysis of magnetic phases in anisotropic triangular-lattice Heisenberg models, highlighting the effects of frustration and coupling strength on phase stability.

Findings

Non-colinear spiral phases can be stabilized at arbitrarily small inter-chain coupling in spin-half models.

Critical inter-chain coupling for magnetic order in spin-one chains is larger in frustrated geometries.

Colinear phase is absent in the spin-one Heisenberg model.

Abstract

We study spin-half and spin-one Heisenberg models in the limit where one dimensional (1-D) linear chains, with exchange constant J1, 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 non-colinear spiral phases that arise classically in the model and the colinear antiferromagnet that has been recently proposed for the spin-half model by Starykh and Balents using a Renormalization Group approach. We find that such phases can be stabilized in the spin-half model for arbitrarily small coupling between the chains. For vanishing coupling between the chains the energy of each phase must approach that of decoupled linear chains. With increasing inter-chain coupling, the non-colinear 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 an unfrustrated manner, the critical coupling is very small (~0.01J1) and agrees well with previous chain mean-field studies. When they are coupled in the frustrated triangular-lattice geometry, the critical coupling required to develop magnetic order is substantially larger (> 0.3J1). The colinear phase is not obtained for the spin-one Heisenberg model.