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

Using the coupled cluster method we investigate spin-$s$ $J_{1}$-$J_{2}'$ 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 ($J_{2}' > 0$) 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 $J_{2}' \equiv κJ_{1}$ 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 $κ= 0$ and a set of decoupled chains at $κ\rightarrow \infty$, with the isotropic HAF on the triangular lattice in between at $κ= 1$. For both the $s=1$ and the $s=3/2$ models we find a second-order quantum phase transition at $κ_{c}=0.615 \pm 0.010$ and $κ_{c}=0.575 \pm 0.005$ respectively, between a Néel antiferromagnetic state and a helical state. In both cases the ground-state energy $E$ and its first derivative $dE/dκ$ are continuous at $κ=κ_{c}$, 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 $κ= κ_{c}$ 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 $κ_{c}=0.80 \pm 0.01$. 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).

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