Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets

Recent experiments suggest that the Ising pyrochlore magnets ${\rm Ho_{2}Ti_{2}O_{7}}$and${\rm Dy_{2}Ti_{2}O_{7}}$ display qualitative properties of the spin ice model proposed by Harris {\it et al.} \prl {\bf 79}, 2554 (1997). We discuss the dipolar energy scale present in both these materials and consider how they can display spin ice behavior {\it despite} the presence of long range interactions. Specifically, we present numerical simulations and a mean field analysis of pyrochlore Ising systems in the presence of nearest neighbor exchange and long range dipolar interactions. We find that two possible phases can occur, a long range ordered antiferromagnetic one and the other dominated by spin ice features. Our quantitative theory is in very good agreement with experimental data on both $\mathrm{H}{\mathrm{o}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ and $\mathrm{D}{\mathrm{y}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$. We suggest that the nearest neighbor exchange in $\mathrm{D}{\mathrm{y}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ is {\it antiferromagnetic} and that spin ice behavior is induced by long range dipolar interactions.