Refrustration and competing orders in the prototypicalDy2Ti2O7spin ice material

Abstract

Spin ices, frustrated magnetic materials analogous to common water ice, have emerged over the past fifteen years as exemplars of high frustration in three dimensions. Recent experimental developments aimed at interrogating anew the low-temperature properties of these systems, in particular whether the predicted transition to long-range order occurs, behoove researchers to scrutinize our current dipolar spin ice model description of these materials. In this work we do so by combining extensive Monte Carlo simulations and mean-field theory calculations to analyze data from previous magnetization, elastic neutron scattering and specific heat measurements on the paradigmatic Dy2Ti2O7 spin ice material. In the present work, we also reconsider the possible importance of the nuclear specific heat, Cnuc, in Dy2Ti2O7. We find that Cnuc is not entirely negligible below a temperature ∼ 0.5 K and must therefore be taken into account in a quantitative analysis of the calorimetric data of this compound below that temperature. We find that in this material, small effective spin-spin exchange interactions compete with the magnetostatic dipolar interaction responsible for the main spin ice phenomenology. This causes an unexpected "refrustration" of the long-range order that would be expected from the incompletely self-screened dipolar interaction and which positions the material at the boundary between two competing classical long-range ordered ground states. This allows for the manifestation of new physical low-temperature phenomena in Dy2Ti2O7, as exposed by recent specific heat measurements. We show that among the four most likely causes for the observed upturn of the specific heat at low temperature -an exchange-induced transition to long-range order, quantum non-Ising (transverse) terms in the effective spin Hamiltonian, the nuclear hyperfine contribution and random disorder -only the last appears to be reasonably able to explain the calorimetric data.

Out-of-equilibrium dynamics and extended textures of topological defects in spin ice

“…Such interactions might be present in spin-ice materials [65][66][67] and be of importance for quantum spin ices where virtual crystal field excitations can induce coupling beyond nearest-neighbors 68,69 . The J 2 = J 3 condition is an arguably strong constraint, but very useful by its simplicity in order to serve as a basis for perturbative approaches.…”

Microscopic aspects of magnetic lattice demagnetizing factors

“…Exchange interactions, even when known in detail (e.g., for Dy 2 Ti 2 O 7 [33,34]), have not been included in our theoretical models. This is because demagnetizing fields arise solely from the long-range dipolar interactions.…”

“…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.…”

“…The inset of the figure compares the uncorrected susceptibility data and the data derived from assuming N = 1/3 for both samples. The predicted theoretical continuation of the experimental data below 2 K (dashed curves) is based on a generalized version of the dipolar spin ice model [33,34]. [2].…”

“…The localized-moment paramagnet Dy 2 Ti 2 O 7 (a spin ice) is well suited to this purpose as it has a large susceptibility, is crystallographically well defined (in the cubic space group F d3m) with no evidence of crystal distortion [32], and can be accurately cut into high-quality single-crystal samples of different shape. Since its spin Hamiltonian has been established in great detail [33,34], it is convenient to adopt Dy 2 Ti 2 O 7 as a model system for studying the demagnetizing factor.…”