Ground-state phases of the frustrated spin-1/2 J1-J2-J3 Heisenberg ferromagnet (J1andlt;0) on the honeycomb lattice with J3=J2andgt;0

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

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We study the ground-state (GS) properties of the frustrated spin-1/2 J1-J2-J3 Heisenberg model on the two-dimensional honeycomb lattice with ferromagnetic nearest-neighbor (J1=−1) exchange and frustrating antiferromagnetic next-nearest-neighbor (J2andgt;0) and next-next-nearest-neighbor (J3andgt;0) exchanges, for the case J3=J2. We use the coupled-cluster method implemented to high orders of approximation, complemented by the Lanczos exact diagonalization of a large finite lattice with 32 sites, in order to calculate the GS energy, magnetic order parameter, and spin-spin correlation functions. In one scenario we find a quantum phase transition point between regions characterized by ferromagnetic order and a form of antiferromagnetic (“striped”) collinear order at J2c≈0.1095±0.0005, which is below the corresponding hypothetical transition point at J2cl=1/7 (≈0.143) for the classical version of the model, in which we momentarily ignore the intervening noncollinear spiral phase in the region 1/10andlt;J2andlt;1/5. Hence we see that quantum fluctuations appear to stabilize somewhat the collinear antiferromagnetic order in preference to the ferromagnetic order in this model. We compare results for the present ferromagnetic case (with J1=−1) to previous results for the corresponding antiferromagnetic case (with J1=+1). The magnetic order parameter is found to behave similarly for the ferromagnetic and the antiferromagnetic models for large values of the frustration parameter J2. However, there are considerable differences in the behavior of the order parameters for the two models for J2/|J1|?0.6. For example, the quasiclassical collinear magnetic long-range order for the antiferromagnetic model (with J1=+1) breaks down at J2c2≈0.60, whereas the “equivalent” point for the ferromagnetic model (with J1=−1) occurs at J2c≈0.11. Unlike in the antiferromagnetic model (with J1=+1), where a plaquette valence-bond crystal phase intrudes between the two corresponding quasiclassical antiferromagnetic phases (with Néel and striped order) for J2c1andlt;J2andlt;J2c2, with J2c1≈0.47, we find no clear indications at all in the ferromagnetic model for an intermediate magnetically disordered phase between the corresponding phases exhibiting ferromagnetic and striped order. Instead the evidence for the ferromagnetic model (with J1=−1) points to one of two scenarios: either there is a direct first-order transition between the two magnetically ordered phases, as mentioned above; or there exists an intervening phase between them in the very narrow range 0.10?J2?0.12, which is probably a remnant of the spiral phase that exists in the classical counterpart of the model over the larger range 1/10andlt;J2andlt;1/5.
Original languageEnglish
JournalPhys. Rev. B
Issue number8
Publication statusE-pub ahead of print - 21 Feb 2012


  • heisenbrg ferromagnet


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