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 $J_{2} \equiv κJ_{1}>0$. 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 $κ_{c_{1}} \approx 1.00 \pm 0.01$ (as does the classical model at $κ_{\rm cl}=1$) between two antiferromagnetic phases, viz., a quasiclassical Néel phase (for $κ< κ_{c_{1}}$) and one of the infinitely degenerate family of quasiclassical phases (for $κ> κ_{c_{1}}$) that exists in the classical model for $κ> κ_{\rm cl}$, 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 $κ_{c_{2}} \approx 2.0 \pm 0.5$ in the spin-1 model, such that for $κ> κ_{c_{2}}$ 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 $κ> κ_{c_{2}}$.