Order by Disorder and a Classical Spin Liquid on the Kagome Lattice: A Heisenberg Antiferromagnet With Chiral Interactions
The kagome Heisenberg antiferromagnet (KHAFM) has an extensive zero temperature entropy, in direct violation of the third law of thermodynamics. Nonetheless, its statictical mechanics predict the onset of order which is not present in the ground state manifold, and this has been verified in Monte Carlo simulations for decades. A similar effect has been demonstrated by means of a different physical mechanism in the pyrochlore antiferromagnet. It too has a large classical ground state manifold, but linear spin-wave calculations indicate that semiclassical corrections favor collinear ground states over generic ground states. In the following work, I describe an extension of the KHAFM by introducing a three-body interaction which imposes a chirality on the kagome lattice triangles. The conditions for the above effects are demonstrated for the chiral kagome Heisenberg antiferromagnet. The order by disorder mechanisms are even more discriminating than those of the pure antiferromagnet, and give rise to a classical Z2 spin liquid, and a phase whose defects combine according to a non-Abelian group, namely the binary octahedral group, 2O.