Critical properties of highly frustrated pyrochlore antiferromagnets

The pyrochlore form of FeF₃ (pyr-FeF₃) exhibits an unusual noncoplanar form of long-range magnetic order below 16 K. This is a result of the topological frustration inherent in the lattice of corner-sharing tetrahedra formed by the iron atoms. Neutron-diffraction experiments fix the critical exponent {β} at 0.18(2), which does not correspond to any known universality class. Monte Carlo simulations on the same lattice with Heisenberg spins confirm this value of {β} and also determine that {ν}=0.38(2), {γ}=1.1(1), and {α}=0.6(1). The power of Ferrenberg and Swendsen's histogram method of Monte Carlo data analysis is discussed, as well as careful checks for weak first-order behavior in the transition. The recently discovered universality classes in triangular-lattice antiferromagnets are compared to the situation in pyr-FeF₃.