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

2013/07/31 by F. Michaud, Frédéric Michaud, Frédéric Mila +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Frustration #Geometry #Heisenberg model #Hubbard model #Ising model #Lattice (music) #Magnetic properties of thin films #Mathematics #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Spin (aerodynamics) #Spin model #Square (algebra) #Square lattice #Superconductivity #Thermodynamics #cond-mat.str-el #k-nearest neighbors algorithm

paper · pdf · doi:10.1103/physrevb.88.094435

9 pages, 14 figures

arxiv created 2013/07/31 · openalex publication_date 2013/09/26 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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\ifmmode⋅\else\textperiodcentered\fiS_j)(S_j\ifmmode⋅\else\textperiodcentered\fiS_k)+H.c. This interaction appears naturally in a strong coupling expansion 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 as 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.

Citations

• Microscopic origin of isotropic non-Heisenberg behavior inS=1magnetic systems
• Plaquette order in theJ1−J2−J3model: Series expansion analysis
• Spin-liquid phase for the frustrated quantum Heisenberg antiferromagnet on a square lattice
• Spin Waves and Electronic Interactions inLa2CuO4
• Plaquette valence-bond crystal in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics
• Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet
• Anisotropic Superexchange Interaction and Weak Ferromagnetism

Cited by

• Alternating-spin S = 3/2 and σ = 1/2 Heisenberg chain with isotropic three-body exchange interactions

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