Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets

Abstract

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...

Microscopic aspects of magnetic lattice demagnetizing factors

“…We illustrate this explicitly by a numerical MC simulation of the so-called dipolar spin ice model, which has been found to reproduce a number of properties of the Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 dipolar spin ice materials [33,34,55,56]. The Hamiltonian for this model consists of the dipolar term defined in Eq.…”

Magnetic ordering in the frustratedJ1−J2Ising chain candidateBaNd2O4

“…Due to the magnetic frustration inherent in these materials, non-collinear magnetic ground states often form that can lead to multiferroic behavior [5]. In other cases, conventional long-range magnetic order is replaced by short-range alternatives, including spin glasses [6], spin liquids [7,8], and spin ices [9][10][11].…”

Structural properties of the geometrically frustrated pyrochloreTb2Ti2OHan1, Gardner2, Booth3 2004Phys. Rev. B513320View full textAdd to dashboardCite

“…This makes corner-sharing tetrahedral spin systems with antiferromagnetic exchange ideal candidates for threedimensional, low temperature spin-liquids. A spin-liquid state may not form if further interactions such as crystal field anisotropy, 5 , long-range exchange or dipolar interactions perturb the classical spin models. 6 However, since any amount of lattice disorder can precipitate a spin-glass phase, 7 geometrically-frustrated systems that do not magnetically order to the lowest temperatures are extremely rare.…”