Order by disorder in classical kagome antiferromagnets with chiral interactions

Abstract

The Heisenberg antiferromagnet on the kagome lattice is an archetypal instance of how large ground state degeneracies arise, and how they may get resolved by thermal and quantum fluctuations. Augmenting the Heisenberg model by chiral spin interactions has proved to be of particular interest in the discovery of certain chiral quantum spin liquids. Here we consider the classical variant of this chiral kagome model and find that it exhibits, similar to the classical Heisenberg antiferromagnet, a remarkably large and structured ground-state manifold, which combines continuous and discrete degrees of freedom. This allows for a rich set of order-by-disorder phenomena. Degeneracy lifting occurs in a highly selective way, choosing already at the harmonic level specific triaxial states which however retain an emergent $Z_2$ degree of freedom (absent in the conventional Heisenberg model). We also study the competition of entropic and energetic ground state selection as the model interpolates between the purely chiral and Heisenberg cases. For this mixed model, we find a "proximate ordered-by-disorder" finite-temperature regime where fluctuations overcome the energetic ground state preference of the perturbation. Finally, a semiclassical route to a spin liquid is provided by quantum order by disorder in the purely chiral models, where the aforementioned $Z_2$ degrees of freedom are elevated to the role of an emergent gauge field.

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Cited by in corpus (7)

• A Classical Chiral Spin-Liquid from Chiral Interactions on the Pyrochlore Lattice
• Unified tensor network theory for frustrated classical spin models in two dimensions
• Chiral Broken Symmetry Descendants of the Kagomé Lattice Chiral Spin Liquid
• Chiral crossroads in $\mathrm{H}{\mathrm{o}}_3\mathrm{Sc}{\mathrm{O}}_6$: a tale of frustration in maple leaf lattice
• Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet
• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices
• Entropic selection of magnetization in a frustrated 2D magnetic model