Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the spin ice model proposed by Harris et al. Phys. Rev. Lett. 79, 2554(1997. We discuss the dipolar energy scale present in both these materials and consider how they can display spin ice behavior 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 Ho2Ti2O7 and Dy2Ti2O7. We suggest that the nearest neighbor exchange in Dy2Ti2O7 is antiferromagnetic and that spin ice behavior is induced by long range dipolar interactions.An exciting development has occurred in the last two years with the discovery of an apparent analogy between the low temperature physics of the geometrically frus- and Dy 3+ of these particular materials reside on the pyrochlore lattice of corner sharing tetrahedra. Single-ion effects conspire to make their magnetic moments almost ideally Ising-like, but with their own set of local axes. In particular, each moment has its local Ising axis along the line connecting its site to the middle of a tetrahedron to which it belongs (see inset of Fig. 1).In a simple model of nearest neighbor ferromagnetic (FM) interactions, such a system has the same 'ice rules' for the construction of its ground state as those for the ground state of real ice [3,4]. In both cases, these rules predict a macroscopically degenerate ground state, a feature that a number of geometrically frustrated systems possess [5][6][7][8].In Ho 2 Ti 2 O 7 , µSR data indicates a lack of ordering down to ∼ 50 mK despite a Curie-Weiss temperature θ cw ∼ 1.9 K, while single crystal neutron scattering data suggests the development of short-range FM correlations, but the absence of ordering down to at least 0.35 K [1]. Ho 2 Ti 2 O 7 also displays field dependent behavior consistent with a spin ice picture [9]. Quite dramatically, thermodynamic measurements on Dy 2 Ti 2 O 7 [2] show a lack of any ordering feature in the specific heat data, with the measured ground state entropy within 5% of Pauling's prediction for the entropy of ice [3].However, both spin ice materials contain further interactions additional to the nearest neighbor exchange. Often, rare earth cations can have appreciable magnetic moments and, consequently, magnetic dipole-dipole interactions of the same order as, if not larger than the exchange coupling, can occur. Furthermore, it has been suggested that the nearest neighbor exchange interaction in Ho 2 Ti 2 O 7 is actually antiferromagnetic (AF) [10], which by itself should cause a phase transition to a long range ordered ground state. Thus, how these systems actually display spin ice-like behavior is most puzzling. For examp...

In a recent letter [Phys. Rev. Lett. 82, 1012(1999] it was found that the Tb 3+ magnetic moments in the Tb2Ti2O7 pyrochlore lattice of corner-sharing tetrahedra remain in a collective paramagnetic state down to 70mK. In this paper we present results from d.c. magnetic susceptibility, specific heat data, inelastic neutron scattering measurements, and crystal field calculations that strongly suggest that (1) the Tb 3+ ions in Tb2Ti2O7 possess a moment of approximatively 5µB, and (2) the ground state g−tensor is extremely anisotropic below a temperature of O(10 0 )K, with Ising-like Tb 3+ magnetic moments confined to point along a local cubic 111 diagonal (e.g. towards the middle of the tetrahedron). Such a very large easy-axis Ising like anisotropy along a 111 direction dramatically reduces the frustration otherwise present in a Heisenberg pyrochlore antiferromagnet. The results presented herein underpin the conceptual difficulty in understanding the microscopic mechanism(s) responsible for Tb2Ti2O7 failing to develop long-range order at a temperature of the order of the paramagnetic Curie-Weiss temperature θCW ≈ −10 1 K. We suggest that dipolar interactions and extra perturbative exchange coupling(s) beyond nearest-neighbors may be responsible for the lack of ordering of Tb2Ti2O7.

It has recently been suggested that long-range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets Dy2Ti2O7 and Ho2Ti2O7. 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 Dy2Ti2O7 and Ho2Ti2O7.

The pyrochlore material Ho2Ti2O7 has been suggested to show "spin ice" behaviour. We present neutron scattering and specific heat results that establish unambiguously that Ho2Ti2O7 exhibits spin ice correlations at low temperature. Diffuse magnetic neutron scattering from Ho2Ti2O7 is found to be quite well described by a nearest neighbour spin ice model and very accurately described by a dipolar spin ice model. The heat capacity is well accounted for by the sum of a dipolar spin ice contribution and an expected nuclear spin contribution, known to exist in other Ho 3+ salts. These results settle the question of the nature of the low temperature spin correlations in Ho2Ti2O7 for which contradictory claims have been made.

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 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(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. PACS Nos.: 75.10-b, 75.10Hk, 75.20-g, 75.30-m