International Workshop on Quantum Spin Ice

CdEr2Se4, a spinel, was shown to be the first spin ice in a crystal structure other than the rare earth pyrochlore [1]. Although it has the correct entropy, the exact nature of the spin ice state therein, especially the form of the spin correlation function was not further established. A further particularity was the spin relaxation time, which, at low temperature, was found to display a similar activation energy to that of a canonical spin ice, yet the dynamics are three orders of magnitude faster. Using diffuse neutron scattering, we established that the spin correlations in both CdEr2Se4 and CdEr2S4 are well modeled by the dipolar spin ice Hamiltonian, and used this to parameterize the magnetic Coulomb gas existing in each compound. Both are dilute and non-interacting, as in canonical spin ices, so the monopole population alone cannot account for the enhanced dynamics. By a combination of conventional and high frequency susceptibility measurements, and neutron spin echo spectroscopy, we examine the full temperature dependence of the relaxation time, locating the previously known low temperature thermally activated regime [1], and the uncharacterized intermediate plateau and high temperature thermally activated regime, all as in a canonical spin ice but with much faster timescales. Following the approach of Tomasello et al.[2], we find that the crystal field Hamiltonian of CdEr2X4, as parameterized by our inelastic neutron scattering experiments, supports the faster monopole dynamics primarily through increased susceptibility to transverse fields. Ultimately CdEr2X4 are dipolar spin ices with dilute magnetic Coulomb gases, in which fast monopole dynamics are produced by an increased hopping rate.

Superconductivity research has traditionally been discovery driven. Of course, Tc is a non-universal quantity that cannot be predicted, hence off-limits to theorists. Nevertheless, it must be possible to reach intelligent predictions for superconductors that are interesting for reasons other than high Tc per se. Of particular interest are topological superconductors under pursuit as a platform for quantum computing. Here, I will present the strategy of using the spin-spin correlation of quantum spin ice to achieve topological superconductivity at the interface between metal and quantum spin ice.

We present an experimental study of the quantum spin ice candidate pyrochlore compound Pr2Zr2O7 by means of magnetization measurements, specic heat and neutron scattering. We confirm that the spin excitation spectrum is essentially inelastic [1] and consists in a broad flat mode centered at about 0.4 meV with a magnetic structure factor which resembles the spin ice pattern. The new experimental results obtained under an applied magnetic field, interpreted in the light of mean field calculations, draw a new picture where quadrupolar interactions play a major role and overcome the magnetic exchange coupling. We determine a range of acceptable parameters able to account for the observations and propose that the actual ground state of this material is an antiferroquadrupolar liquid with spin-ice like excitations [2]. The influence of disorder is also discussed.

"Quantum spin ice" materials have been widely discussed in terms of an XXZ model on a pyrochlore lattice, which is accessible to quantum Monte Carlo simulation for unfrustrated interactions J_\pm > 0. Here we argue that the properties of this model may become even more interesting once it is "frustrated". Using a combination of large-scale classical Monte Carlo simulation, semi-classical molecular dynamics, symmetry analysis and analytic field theory we explore the new phases which arise for J_\pm < 0. We find that the model supports not one, but three distinct forms of spin liquid: spin ice, a U(1) spin liquid; a disguised version of the U(1) x U(1) x U(1) spin-liquid found in the Heisenberg antiferromagnet on a pyrochlore lattice; and another entirely new form of spin liquid described by a U(1) x U(1) gauge group. At low temperatures this novel spin liquid undergoes a thermodynamic phase transition into a ground state with hidden, spin-nematic order. We present explicit predictions for inelastic neutron scattering experiments carried out on the three different spin liquids [M. Taillefumier et al., arXiv:1705.00148].

Motivated by the rapid experimental progress of quantum spin ice materials, we study the dynamical properties of pyrochlore spin ice in the U(1) spin liquid phases. In particular, we focus on the spinon excitations that appear in high energies and show up as an excitation continuum in the dynamic spin structure factor. The keen connection between the crystal symmetry fractionalization of the spinons and the spectral periodicity of the spinon continuum is emphasized and explicitly demonstrated. The enhanced spectral periodicity of the spinon continuum provides a sharp physical observable to detect the spin quantum number fractionalization and U(1) spin liquid. Our prediction can be immediately examined by inelastic neutron scattering experiments among quantum spin ice materials with Kramers' doublets. Further application to the non-Kramers' doublets is discussed. If time permits, I will present some of our recent work in this field.

We report highly unusual heat conduction generated by the spin degrees of freedom in spin liquid states of the pyrochlore magnets Yb2Ti2O7 and Pr2Zr2O7. In Yb2Ti2O7, the excitations propagate a long distance without being scattered, in contrast to the diffusive nature of classical monopoles. In Pr2Zr2O7, the thermal conductivity unexpectedly shows a dramatic enhancement at very low temperature. The low-lying excitations are discussed in terms of a possible emergent photons, coherent gapless spin excitations in a spin-ice manifold.

Pyrochlore Pr2Ir2O7 is a rare material with various unique properties such as geometrical frustration, c-f hybridization and Fermi node in the band structure. Although Pr3+ carries the effective moment of ~3B with Curie-Weiss temperature  ~ 20 K, no long-range order is observed down to the partial freezing at Tf ~ 0.3 K, suggesting the geometrical frustration [1]. Magnetic Grüneisen ratio diverges mag ~ T-3/2 without tuning any parameter, indicating the zero-field quantum criticality [2]. Besides, recent angle-resolved photoemission spectroscopy (ARPES) measurement reveals the Fermi node at  point in Pr2Ir2O7, which can be an origin of the various topological phases such as topological insulator and Weyl semimetal [3]. One of the most interesting and striking properties of Pr2Ir2O7 is non-trivial anomalous Hall effect: spontaneous Hall effect appears even in the absence of any spin freezing, which is attributed to the chiral spin liquid state [4]. In this presentation, we will discuss the recent results for the anomalous Hall effect for various samples of Pr2Ir2O7.

Numerical Linked Cluster (NLC) expansions can accurately compute thermal properties of quantum spin models in the thermodynamic limit in certain parameter regimes. In classical spin-ice models, where all correlations remain short-ranged down to T=0, these expansions can be convergent even at low T. However, for quantum spin-ice models, they converge only when either temperatures are not too small or there is a strong magnetic field present. To turn these studies into a spectroscopy of exchange parameters, when multiple exchange constants are relevant, is a challenge both because of the limited temperature-range of validity of effective spin-half models and difficulties in isolating magnetic properties in experiments at intermediate and high temperatures. We discuss ways in which such a spectroscopy can proceed.