Michel J. P. Gingras

Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets

The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare-earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Spin ices provide one of very few experimentally realized examples of fractionalization because their elementary excitations can be regarded as magnetic monopoles and, over some temperature range, spin ice materials are best described as liquids of these emergent charges. In the presence of quantum fluctuations, one can obtain, in principle, a quantum spin liquid descended from the classical spin ice state characterized by emergent photon-like excitations. Whereas in classical spin ices the excitations are akin to electrostatic charges with a mutual Coulomb interaction, in the quantum spin liquid these charges interact through a dynamic and emergent electromagnetic field. In this review, we describe the latest developments in the study of such a quantum spin ice, focusing on the spin liquid phenomenology and the kinds of materials where such a phase might be found.

Long-Range Order at Low Temperatures in Dipolar Spin Ice

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.

Monte Carlo studies of the dipolar spin ice model

We present a detailed theoretical overview of the thermodynamic properties of the dipolar spin ice model, which has been shown to be an excellent quantitative descriptor of the Ising pyrochlore materials Dy_2Ti_2O_7 and Ho_2Ti_2O_7. We show that the dipolar spin ice model can reproduce an effective quasi macroscopically degenerate ground state and spin-ice behavior of these materials when the long-range nature of dipole-dipole interaction is handled carefully using Ewald summation techniques. This degeneracy is, however, ultimately lifted at low temperature. The long-range ordered state is identified via mean field theory and Monte Carlo simulation techniques. Finally, we investigate the behavior of the dipolar spin ice model in an applied magnetic field, and compare our predictions with experimental results. We find that a number of different long-range ordered states are favored by the model depending on field direction.We present a detailed overview of numerical Monte Carlo studies of the dipolar spin ice model, which has been shown to be an excellent quantitative descriptor of the Ising pyrochlore materials Dy2Ti2O7 and Ho2Ti2O7. We show that the dipolar spin ice model can reproduce an effective quasi-macroscopically degenerate ground state and spin ice behaviour of these materials when the long range nature of dipole–dipole interaction is handled carefully using Ewald summation techniques. This degeneracy is, however, ultimately lifted at low temperature. The long range ordered state is identified via Monte Carlo simulation techniques. Finally, we investigate the behaviour of the dipolar spin ice model in an applied magnetic field and compare our predictions to experimental results. We find that a number of different long range ordered ground states are favoured by the model, depending on field direction.

Dynamically induced frustration as a route to a quantum spin ice state in Tb2Ti2O7 via virtual crystal field excitations and quantum many-body effects.

The Tb2Ti2O7 pyrochlore magnetic material is attracting much attention for its spin liquid state, failing to develop long-range order down to 50 mK despite a Curie-Weiss temperature thetaCW approximately -14 K. In this Letter we reinvestigate the theoretical description of this material by considering a quantum model of independent tetrahedra to describe its low-temperature properties. The naturally tuned proximity of this system near a Néel to spin ice phase boundary allows for a resurgence of quantum fluctuation effects that lead to an important renormalization of its effective low-energy spin Hamiltonian. As a result, Tb2Ti2O7 is argued to be a quantum spin ice. We put forward an experimental test of this proposal using neutron scattering on a single crystal.

Dy2Ti2O7 Spin Ice: a Test Case for Emergent Clusters in a Frustrated Magnet

Dy2Ti2O7 is a geometrically frustrated magnetic material with a strongly correlated spin ice regime that extends from 1 K down to as low as 60 mK. The diffuse elastic neutron scattering intensities in the spin ice regime can be remarkably well described by a phenomenological model of weakly interacting hexagonal spin clusters, as invoked in other geometrically frustrated magnets. We present a highly refined microscopic theory of Dy2Ti2O7 that includes long-range dipolar and exchange interactions to third nearest neighbors and which demonstrates that the clusters are purely fictitious in this material. The seeming emergence of composite spin clusters and their associated scattering pattern is instead an indicator of fine-tuning of ancillary correlations within a strongly correlated state.

Neutron scattering investigation of the spin ice state in Dy2Ti2O7

Dy2Ti2O7 has been advanced as an ideal spin ice material. We present a neutron scattering investigation of a single-crystal sample of (Dy2Ti2O7)-Dy-162. The scattering intensity has been mapped in zero applied field in the h,h,l and h,k,0 planes of reciprocal space at temperatures between 0.05 and 20 K. The measured diffuse scattering has been compared with that predicted by the dipolar spin ice model. The comparison is good, except at the Brillouin-zone boundaries where extra scattering appears in the experimental data. It is concluded that the dipolar spin ice model provides a successful basis for understanding Dy2Ti2O7, but that there are issues which remain to be clarified.

Rods of Neutron Scattering Intensity in Yb2Ti2O7: Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide

Paramagnetic correlations in the magnetic material Yb(2)Ti(2)O(7) have been investigated via neutron scattering, revealing a [111] rod of scattering intensity. Assuming interactions between the Yb(3+) ions composed of all symmetry-allowed nearest neighbor exchange interactions and long-range dipolar interactions, we construct a model Hamiltonian that allows for an excellent description of the neutron scattering data. Our results provide compelling evidence for significant anisotropic exchange interactions in an insulating magnetic pyrochlore oxide. We also compute the real space correlations leading to the [111] rod of scattering.

Induced random fields in the LiHoxY1-xF4 quantum Ising magnet in a transverse magnetic field.

The LiHoxY1-xF4 magnetic material in a transverse magnetic field Bx x perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the Bx-induced magnetization along the x direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho3+ ions, random fields along the Ising z direction. This identifies LiHoxY1-xF4 in Bx as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin-glass transition with increasing Bx and render the Bx-induced quantum criticality in LiHoxY1-xF4 likely inaccessible.

Finite-temperature transitions in dipolar spin ice in a large magnetic field.

We use Monte Carlo simulations to identify the mechanism that allows for phase transitions in dipolar spin ice to occur and survive for applied magnetic field, H, much larger in strength than that of the spin-spin interactions. In the most generic and highest symmetry case, the spins on one out of four sublattices of the pyrochlore decouple from the total local exchange+dipolar+applied field. In the special case where H is aligned perfectly along the [110] crystallographic direction, spin chains perpendicular to H show a transition to q=X long range order, which proceeds via a one to three dimensional crossover. We propose that these transitions are relevant to the origin of specific heat features observed in powder samples of the Dy2Ti2O7 spin ice material for H above 1 Tesla.

Evidence for gapped spin-wave excitations in the frustrated Gd2Sn2O7 pyrochlore antiferromagnet from low-temperature specific heat measurements

We have measured the low-temperature specific heat of the geometrically frustrated pyrochlore Heisenberg antiferromagnet Gd2Sn2O7 in zero magnetic field. The specific heat is found to drop exponentially below approximately 350 mK. This provides evidence for a gapped spin-wave spectrum due to an anisotropy resulting from single-ion effects and long-range dipolar interactions. The data are well fitted by linear spin-wave theory, ruling out unconventional low-energy magnetic excitations in this system, and allowing a determination of the pertinent exchange interactions in this material.