Phase diagram of the spin-1 Heisenberg model with three-site interactions on the square lattice

Abstract

We study the spin S=1 antiferromagnetic Heisenberg model on the square lattice with, in addition to the nearest-neighbor interaction, a three-site interaction of the form (S_i S_j)*(S_j S_k) + h.c.. This interaction appears naturally in a strong coupling exansion of the two-orbital, half-filled Hubbard model. For spin 1/2, this model reduces to a Heisenberg model with bilinear interactions up to third neighbors, with a second-neighbor interaction twice as large the third-neighbor one, a very frustrated model with an infinite family of helical classical ground states in a large parameter range. Using a variety of analytical and numerical methods, we show that the spin-1 case is also very frustrated, and that its phase diagram is even richer, with possibly the succession of seven different phases as a function of the ratio of the three-site interaction to the bilinear one. The phases are either purely magnetic phases with collinear order, or of mixed magnetic and quadrupolar character with helical order.

9 pages, 14 figures

References in corpus (8)

• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
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• First-order Néel-cVBS transition in a model square lattice $S=1$ antiferromagnet
• Hysteresis behaviors of a spin-1 anisotropic Heisenberg model
• Alternating-spin S=3/2 and sigma=1/2 Heisenberg chain with three-body exchange interactions
• Magnetic properties of delta- and kagome-like chains with competing interactions
• A systematic approach to determine the spectral characteristics of molecular magnets
• Deconfined criticality for the two-dimensional quantum S=1-spin model with the three-spin and biquadratic interactions