Frustrated classical Heisenberg and XY models in 2 dimensions with nearest neighbor exchange: exact solution for the ground state phase diagram

Abstract

The ground state phase diagram is determined exactly for the frustrated classical Heisenberg model plus nearest-neighbor biquadratic exchange interactions on a 2-dimensional lattice. A square- and a rhombic-symmetry version are considered. There appear ferromagnetic, incommensurate-spiral, "up-up-down-down" (uudd) and canted ferromagnetic states, a non-spiral coplanar state that is an ordered vortex lattice, plus a non-coplanar ordered state (a "conical vortex lattice"). In the rhombic case, which adds biquadratic terms to the Heisenberg model used widely for insulating manganites, the uudd state found is the E-type state observed; this along with accounting essentially for the variety of ground states found in these materials, shows that this model probably contains the long-sought mechanism behind the uudd state.

8 pages, 7 figures. Significance as a theory for the essential aspects of the variety of ground-state magnetic structures in the insulating perovskites RMnO3 clarified. A seeming contradiction concerning 3- and 4-spin terms vs claims for this significance fixed (pg. 4).

References in corpus (2)

• Microscopic origin of isotropic non-Heisenberg behavior in highly correlated systems
• Frustrated classical Heisenberg model in 1 dimension with added nearest-neighbor biquadratic exchange interactions

Cited by in corpus (19)

• Higher-order exchange interactions in two-dimensional magnets
• Theory of spin-phonon coupling in multiferroic Mn perovskites
• General method for atomistic spin-lattice dynamics with first principles accuracy
• Biquadratic and ring exchange interactions in orthorhombic perovskite manganites
• Tuning the multiferroic mechanisms of TbMnO3 by epitaxial strain
• Quantum renormalization group of XY model in two dimensions
• Relationship between crystal structure and multiferroic orders in orthorhombic perovskite manganites
• Single-axis dependent structural and multiferroic properties of orthorhombic RMnO${}_3$ (R = Gd - Lu)
• Orthogonal spin arrangement as possible ground state of three - dimensional Shastry - Sutherland network in Ba3Cu3In4O12
• $XY$ model with antinematic interaction
• New ordered phase in geometrically frustrated generalized $XY$ model
• Phase diagrams of antiferromagnetic $XY$ model on a triangular lattice with higher-order interactions
• Interpretation of magnetoelectric phase states using the praphase concept and exchange symmetry
• Incommensurate Single-Angle Spiral Orderings of Classical Heisenberg Spins on Zigzag Ladder Lattices
• Classical Heisenberg and planar spin models on the windmill lattice
• Influence of the biquadratic exchange interaction in the classical ground state magnetic response of the antiferromagnetic icosahedron
• Phases of frustrated quantum antiferromagnets on the square and triangular lattices
• XY model with competing higher-order interactions
• Investigation of frustrated and dimerized classical Heisenberg chains