Magnetic order in a spin-half interpolating square-triangle Heisenberg antiferromagnet

TL;DR

This study uses the coupled cluster method to analyze the zero-temperature phase diagram of a spin-half Heisenberg antiferromagnet on an anisotropic 2D lattice, revealing two quantum phase transitions between different magnetic orders.

Contribution

It provides the first quantitative determination of the critical points for phase transitions in the $J_{1}$--$J_{2}'$ model, highlighting the role of quantum fluctuations.

Findings

First-order transition from Néel to helical order at κ ≈ 0.80

Second-order transition from helical to stripe order at κ ≈ 1.8

Quantum fluctuations favor first-order transitions over classical second-order ones

Abstract

Using the coupled cluster method we study the zero-temperature phase diagram of a spin-half Heisenberg antiferromagnet (HAF), the so-called $J_{1}$--$J_{2}'$ model, defined on an anisotropic 2D lattice. With respect to an underlying square-lattice geometry the model contains antiferromagnetic ($J_{1} > 0$) bonds between nearest neighbors and competing ($J_{2}'>0$) bonds between next-nearest neighbors across only one of the diagonals of each square plaquette, the same diagonal in every square. Considered on an equivalent triangular-lattice geometry the model may be regarded as having two sorts of nearest-neighbor bonds, with $J_{2}' \equiv \kappa J_{1}$ bonds along parallel chains and $J_{1}$ bonds providing an interchain coupling. Hence, the model interpolates between a spin-half HAF on the square lattice at one extreme ($\kappa = 0$) and a set of decoupled spin-half chains at the other ($\kappa \to \infty$), with the spin-half HAF on the triangular lattice in between at $\kappa = 1$. We find strong evidence that quantum fluctuations favor a first-order transition from quasiclassical N\'{e}el order to a quantum helical state at a first critical point at $\kappa_{c_{1}} = 0.80 \pm 0.01$, by contrast with the corresponding second-order transition between the equivalent classical states at $\kappa_{{\rm cl}} = 0.5$. We also find strong evidence for a second critical point at $\kappa_{c_{2}} = 1.8 \pm 0.4$ where another first-order transition occurs, this time from the quantum helical phase to a collinear stripe-ordered phase. This latter result provides quantitative verification of a recent qualitative prediction of Starykh and Balents [Phys.\ Rev. Lett. {\bf 98}, 077205 (2007)] for the $J_{1}$--$J_{2}'$ model that did not, however, evaluate the corresponding critical point.