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

Abstract

Using the coupled cluster method we study the zero-temperature phase diagram of a spin-half Heisenberg antiferromagnet (HAF), the so-called $J_1$--$J_2^{\prime }$ 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 ($J_2^{\prime }>0$) 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 $J_2^{\prime }\equiv \kappa J_1$ 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 Néel 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 ${\kappa }_{\mathrm{cl}}=0.5$. 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 $J_1$--$J_2^{\prime }$ model that did not, however, evaluate the corresponding critical point.

28 pages, 8 figures

References in corpus (7)

• Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet
• Ordering in spatially anisotropic triangular antiferromagnets
• Quantum $J_1$--$J_2$ antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering
• Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet
• Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• The quantum $J_1$--$J_1^{\prime }$--$J_2$ spin-1 Heisenberg model: Influence of the interchain coupling on the ground-state magnetic ordering in 2D
• Magnetic order in coupled spin-half and spin-one Heisenberg chains in anisotropic triangular-lattice geometry

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