Frustrated Heisenberg antiferromagnet on the checkerboard lattice: J 1-J 2 model

R. F. Bishop, P. H.Y. Li, D. J.J. Farnell, J. Richter, C. E. Campbell

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Abstract

We study the zero-temperature ground-state (gs) phase diagram of the spin-12 anisotropic planar pyrochlore (or crossed chain) model using the coupled cluster method (CCM). The model is equivalently described as a frustrated J 1-J 2 antiferromagnet on the two-dimensional checkerboard lattice, with nearest-neighbor exchange bonds of strength J 10 and next-nearest-neighbor bonds of strength J 2 κJ 10. Using various antiferromagnetic (AFM) classical ground states as CCM reference states, we present results for the gs energy, average local on-site magnetization, and the susceptibilities of these states against the formation of plaquette valence-bond crystal (PVBC) and crossed-dimer valence-bond crystal (CDVBC) ordering. We show that the AFM quasiclassical state with Néel ordering is the gs phase for κ<κ c1 0.80±0.01, but that none of the infinitely degenerate set of AFM states that form the gs phase for the classical version (s→) of the model (for κ1) survive the quantum fluctuations to form a stable magnetically ordered gs phase for the s=1/2 case. Instead, our calculations indicate a PVBC-ordered phase for κ c1<κ<κ c2 1.22±0.02, and a CDVBC-ordered phase for all κκ c2. Both transitions are likely to be direct ones, although we cannot exclude very narrow coexistence regions confined to 0.79κ 0.81 and 1.20κ 1.22, respectively.

Original languageEnglish (US)
Article number205122
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume85
Issue number20
DOIs
StatePublished - May 11 2012

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