A frustrated spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet: An anisotropic planar pyrochlore model

Abstract

The zero-temperature ground-state (GS) properties and phase diagram of a frustrated spin-1 $J_1$--$J_2$ Heisenberg model on the checkerboard square lattice are studied, using the coupled cluster method. We consider the case where the nearest-neighbour exchange bonds have strength $J_1>0$ and the next-nearest-neighbour exchange bonds present (viz., in the checkerboard pattern of the planar pyrochlore) have strength $J_2\equiv \kappa J_1>0$. We find significant differences from both the spin-1/2 and classical versions of the model. We find that the spin-1 model has a first phase transition at ${\kappa }_{c_1}\approx 1.00\pm 0.01$ (as does the classical model at ${\kappa }_{\mathrm{cl}}=1$) between two antiferromagnetic phases, viz., a quasiclassical Néel phase (for $\kappa <{\kappa }_{c_1}$) and one of the infinitely degenerate family of quasiclassical phases (for $\kappa >{\kappa }_{c_1}$) that exists in the classical model for $\kappa >{\kappa }_{\mathrm{cl}}$, which is now chosen by the {\it order by disorder} mechanism as (probably) the "doubled Néel" (or Néel${}^{\ast }$) state. By contrast, none of this family survives quantum fluctuations to form a stable GS phase in the spin-1/2 case. We also find evidence for a second quantum critical point at ${\kappa }_{c_2}\approx 2.0\pm 0.5$ in the spin-1 model, such that for $\kappa >{\kappa }_{c_2}$ the quasiclassical (Néel${}^{\ast }$) ordering melts and a nonclassical phase appears, which, on the basis of preliminary evidence, appears unlikely to have crossed-dimer valence-bond crystalline (CDVBC) ordering, as in the spin-1/2 case. Unlike in the spin-1/2 case, where the Néel and CDVBC phases are separated by a phase with plaquette valence-bond crystalline (PVBC) ordering, we find very preliminary evidence for such a PVBC state in the spin-1 model for all $\kappa >{\kappa }_{c_2}$.

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