Recent experiments suggest that the Ising pyrochlore magnets ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ display qualitative properties of the nearest-neighbor “spin ice” model. We discuss the dipolar energy scale present in both these materials and discuss how spin-ice behavior can occur despite the presence of long-range dipolar interactions. We present results of numerical simulations and a mean field analysis of Ising pyrochlore systems. Based on our quantitative theory, we suggest that the spin-ice behavior in these systems is due to long-range dipolar interactions, and that the nearest-neighbor exchange in ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ is antiferromagnetic.

• Received 8 November 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.3430