Magnetic order in spin-1 and spin-3/2 interpolating square-triangle Heisenberg antiferromagnets

Abstract

Using the coupled cluster method we investigate spin-$s$ $J_1$-$J_2^{\prime }$ Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, triangular lattice when the spin quantum number $s=1$ or $s=3/2$. With respect to a square-lattice geometry the model has antiferromagnetic ($J_1>0$) bonds between nearest neighbours and competing ($J_2^{\prime }>0$) bonds between next-nearest neighbours across only one of the diagonals of each square plaquette, the same one in each square. In a topologically equivalent triangular-lattice geometry, we have two types of nearest-neighbour bonds: namely the $J_2^{\prime }\equiv \kappa J_1$ bonds along parallel chains and the $J_1$ bonds producing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at $\kappa =0$ and a set of decoupled chains at $\kappa \to \infty$, with the isotropic HAF on the triangular lattice in between at $\kappa =1$. For both the $s=1$ and the $s=3/2$ models we find a second-order quantum phase transition at ${\kappa }_c=0.615\pm 0.010$ and ${\kappa }_c=0.575\pm 0.005$ respectively, between a Néel antiferromagnetic state and a helical state. In both cases the ground-state energy $E$ and its first derivative $dE/d\kappa$ are continuous at $\kappa ={\kappa }_c$, while the order parameter for the transition (viz., the average on-site magnetization) does not go to zero on either side of the transition. The transition at $\kappa ={\kappa }_c$ for both the $s=1$ and $s=3/2$ cases is analogous to that observed in our previous work for the $s=1/2$ case at a value ${\kappa }_c=0.80\pm 0.01$. However, for the higher spin values the transition is of continuous (second-order) type, as in the classical case, whereas for the $s=1/2$ case it appears to be weakly first-order in nature (although a second-order transition could not be excluded).

17 pages, 8 figues (Figs. 2-7 have subfigs. (a)-(d))

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Cited by in corpus (12)

• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
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• Ground-state properties of the triangular-lattice Heisenberg antiferromagnet with arbitrary spin quantum number $s$
• A frustrated honeycomb-bilayer Heisenberg antiferromagnet: The spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ model
• Ground-state phases of the spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet on the honeycomb lattice
• A high-order study of the quantum critical behavior of a frustrated spin-$\frac{1}{2}$ antiferromagnet on a stacked honeycomb bilayer
• Thermal evolution of quasi-1D spin correlations within the anisotropic triangular lattice of $\alpha$-NaMnO${}_2$
• Large-$s$ expansions for the low-energy parameters of the honeycomb-lattice Heisenberg antiferromagnet with spin quantum number $s$
• Stripe order and magnetic anisotropy in the $S=1$ antiferromagnet BaMoP${}_2$O${}_8$
• Frustrated Heisenberg antiferromagnet on the honeycomb lattice with spin quantum number $s\ge 1$
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_1$--$J_2$--$J_1^{\perp }$ model
• A frustrated spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model