Origin of spin-ice behavior in Ising pyrochlore magnets with long-range dipole interactions: an insight from meanfield theory

Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the ferromagnetic nearest-neighbor spin-ice model proposed by Harris et al. Phys. Rev. Lett. 79, 2554 (1997). The manifestation of spin-ice behavior in these systems despite the energetic constraints introduced by the strength and the long-range nature of dipole–dipole interactions, remains difficult to understand. We report here results from a mean-field analysis that shed some light on the origin of spin-ice behavior in (111) Ising pyrochlores. Specifically, we find that there exist a large frustrating effect of the dipolar interactions beyond the nearest neighbor, and that the degeneracy established by effective ferromagnetic nearestneighbor interactions is only very weakly lifted by the long-range interactions. Such behavior only appears beyond a cut-off distance corresponding to O(102) nearest neighbor. Our mean-field analysis shows that truncation of dipolar interactions leads to spurious ordering phenomena that change with the truncation cut-off distance.