Spin-liquid phase and order by disorder of classical Heisenberg spins on the swedenborgite lattice

Abstract

Frustration refers to the inability to satisfy competing interactions simultaneously, often leading to a large number of degenerate ground states. This can suppress ordering tendencies, sometimes resulting in a spin-liquid phase. An intrinsic effect lifting this degeneracy is entropic order by disorder. We present strong evidence that a classical nearest-neighbor Heisenberg model on the swedenborgite lattice exhibits both an extended spin-liquid phase as well as entropic order-by-disorder choosing coplanar configurations after a first-order transition. We argue that this observation renders magnetic insulators such as ${R\mathrm{BaCo}}_{4}{\mathrm{O}}_{7}$, where $R$ denotes a rare-earth atom, prime candidates for displaying spin-liquid behavior and entropic order-by-disorder physics due to their large exchange constant.