Ground-state phases of the frustrated spin-1/2 $J_{1}$--$J_{2}$--$J_{3}$ Heisenberg ferromagnet ($J_{1}<0$) on the honeycomb lattice with $J_{3}=J_{2}>0$

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

doi:10.1103/PhysRevB.85.085115

paper

Ground-state phases of the frustrated spin-1/2 $J_{1}$ -- $J_{2}$ -- $J_{3}$ Heisenberg ferromagnet ( $J_{1} < 0$ ) on the honeycomb lattice with $J_{3} = J_{2} > 0$

arXiv:1109.6229 · doi:10.1103/PhysRevB.85.085115

Abstract

We study the ground-state (gs) properties of the frustrated spin-1/2 $J_{1}$ -- $J_{2}$ -- $J_{3}$ Heisenberg model on a honeycomb lattice with ferromagnetic (FM) nearest-neighbor ( $J_{1} = - 1$ ) exchange and frustrating antiferromagnetic (AFM) next-nearest-neighbor ( $J_{2} > 0$ ) and next-next-nearest-neighbor ( $J_{3} > 0$ ) exchanges, for the case $J_{3} = J_{2}$ . We use the coupled cluster method in high orders of approximation, complemented by the exact diagonalization of a lattice with 32 sites, and calculate the gs energy, magnetic order parameter, and spin-spin correlation functions. We find a quantum phase transition between regions characterized by FM order and a form of AFM ("striped") collinear order at $J_{2}^{c} \approx 0.1095 \pm 0.0005$ . We compare results for the FM case (with $J_{1} = - 1$ ) to previous results for the corresponding AFM case (with $J_{1} = + 1$ ). While the magnetic order parameters behave similarly for the FM and the AFM models for large values of the frustration parameter $J_{2}$ , there are considerable differences between them for $J_{2} /∣ J_{1} ∣ ≲ 0.6$ . For example, the quasiclassical collinear magnetic long-range order for the AFM model (with $J_{1} = + 1$ ) breaks down at $J_{2}^{c_{2}} \approx 0.60$ , whereas the "equivalent" point for the FM model (with $J_{1} = - 1$ ) occurs at $J_{2}^{c} \approx 0.11$ . Unlike in the AFM model (with $J_{1} = + 1$ ), where a plaquette valence-bond crystal phase intrudes between the two corresponding quasiclassical AFM phases (with Néel and striped order) for $J_{2}^{c_{1}} < J_{2} < J_{2}^{c_{2}}$ , with $J_{2}^{c_{1}} \approx 0.47$ , we find no clear indications in the FM model for an intermediate magnetically disordered phase between the phases exhibiting FM and striped order. Instead, the evidence points strongly to a direct first-order transition between the two ordered phases of the FM model.

21 pages, 6 figures (a & b)

Ground-state phases of the frustrated spin-1/2 $J_{1}$ -- $J_{2}$ -- $J_{3}$ Heisenberg ferromagnet ( $J_{1} < 0$ ) on the honeycomb lattice with $J_{3} = J_{2} > 0$

Abstract

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Ground-state phases of the frustrated spin-1/2 J1​--J2​--J3​ Heisenberg ferromagnet (J1​<0) on the honeycomb lattice with J3​=J2​>0

Abstract

References in corpus (26)

Cited by in corpus (26)

Ground-state phases of the frustrated spin-1/2 $J_{1}$ -- $J_{2}$ -- $J_{3}$ Heisenberg ferromagnet ( $J_{1} < 0$ ) on the honeycomb lattice with $J_{3} = J_{2} > 0$