Origin of Spin Ice Behavior in Ising Pyrochlore Magnets with Long Range Dipole Interactions: an Insight from Mean-Field Theory

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 ferromagnetic nearest neighbor spin ice model proposed by Harris {\it et al.}, Phys. Rev. Lett. {\bf 79}, 2554 (1997). The manifestation of spin ice behavior in these systems {\it 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 nearest neighbor interactions is only very weakly lifted by the long range interactions. Such behavior only appears beyond a cut-off distance corresponding to $O(10^2)$ 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.Comment: 7 Color POSTSCRIPT figures included. To appear in Canadian Journal of Physics for the Proceedings of the {\it Highly Frustrated Magnetism 2000 Conference}, Waterloo, Ontario, Canada, June 11-15, 2000 Contact: [email protected]

Long Range Order at Low Temperature in Dipolar Spin Ice

Recently it has been suggested that long range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$. We report here numerical results on the low temperature properties of the dipolar spin ice model, obtained via a new loop algorithm which greatly improves the dynamics at low temperature. We recover the previously reported missing entropy in this model, and find a first order transition to a long range ordered phase with zero total magnetization at very low temperature. We discuss the relevance of these results to ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$.Comment: New version of the manuscript. Now contains 3 POSTSCRIPT figures as opposed to 2 figures. Manuscript contains a more detailed discussion of the (i) nature of long-range ordered ground state, (ii) finite-size scaling results of the 1st order transition into the ground state. Order of authors has been changed. Resubmitted to Physical Review Letters Contact: [email protected]

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 ${\rm Ho_{2}Ti_{2}O_{7}}$ and ${\rm Dy_{2}Ti_{2}O_{7}}$. We suggest that the nearest neighbor exchange in ${\rm Dy_{2}Ti_{2}O_{7}}$ is {\it antiferromagnetic} and that spin ice behavior is induced by long range dipolar interactions.Comment: 4 postscript figures included. Submitted to Physical Review Letters Contact: [email protected]