Partial order from disorder in a classical pyrochlore antiferromagnet

Abstract

We investigate theoretically the phase diagram of a classical Heisenberg antiferromagnet on the pyrochlore lattice perturbed by a weak second-neighbor interaction ${J}_{2}$. The huge ground-state degeneracy of the nearest-neighbor Heisenberg spins is lifted by ${J}_{2}$ and a magnetically ordered ground state sets in upon approaching zero temperature. We have found a new, partially ordered phase with collinear spins at finite temperatures for a ferromagnetic ${J}_{2}$. In addition to a large nematic order parameter, this intermediate phase also exhibits a layered structure and a bond order that breaks the sublattice symmetry. Thermodynamic phase boundaries separating it from the fully disordered and magnetically ordered states scale as $1.87{J}_{2}{S}^{2}$ and $0.26{J}_{2}{S}^{2}$ in the limit of small ${J}_{2}$. The phase transitions are discontinuous. We analytically examine the local stability of the collinear state and obtain a boundary $T\ensuremath{\sim}{J}_{2}^{2}/{J}_{1}$ in agreement with Monte Carlo simulations.