**Collin Broholm**, Johns Hopkins University

*Lobed phase diagram of single crystalline Yb2Ti2O7 in [111] magnetic field*

High quality single crystals of Yb2Ti2O7 synthesized using a traveling solvent floating zone method enable experiments that explore the anisotropic temperature-field phase diagram of this quantum spin ice candidate. We have examined the H//(111) orientation, which is interesting because a phase transition that breaks three fold rotation symmetry is possible in the presence of a magnetic field. Using specific heat, magnetization, and neutron diffraction we find an apparent enhancement of the critical temperature with applied field that is not accounted for by a classical Monte Carlo simulation of the established spin hamiltonian. I shall discuss possible explanations for the discrepancy, which include quantum fluctuations and long range dipolar interactions. A Scheie, J Kindervater, S Säubert, C Duvinage, C Pfleiderer, HJ Changlani, S Zhang, L Harriger, SM Koohpayeh, O Tchernyshyov, and C Broholm, arXiv:1703.06904 (2017). Work supported by U.S. DOE Basic Energy Sciences, Materials Sciences & Engineering through DE-FG02-08ER46544 and the Gordon and Betty Moore foundation.

**Gang Chen**, Fudan University

*The spectral periodicity of spinon continuum in quantum spin ice*

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.

**Radu Coldea**, University of Oxford

*Quasiparticle breakdown in the quantum pyrochlore Yb2Ti2O7 in magnetic field*

The pyrochlore magnet Yb2Ti2O7 has the remarkable property that it orders magnetically, but has no propagating magnons over wide regions of reciprocal space. Using inelastic neutron scattering we observe that at high magnetic fields, in addition to dispersive magnons there is also a two-magnon continuum, which grows in intensity upon reducing field, overlaps with one-magnon states at intermediate fields leading to strong dispersion renormalizations and magnon decays. We re-evaluate the Hamiltonian finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong quantum fluctuation effects observed at low fields. [J.D. Thompson, P.A. McClarty, D. Prabhakaran, I. Cabrera, T. Guidi, and R. Coldea, arXiv:1703.04506].

**Tom Fennell**, Paul Scherrer Institute

*Dipolar spin ice states with fast monopole hopping rate in the spinels CdEr2X4 (X=Se,S)*

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.

**Alannah Hallas**, McMaster University

*Experimental signatures of phase competition in the quantum XY pyrochlores*

The erbium and ytterbium rare earth pyrochlores exhibit local XY spin anisotropy. Experimental and theoretical investigations of XY pyrochlores have revealed a strong propensity for quantum magnetic phenomena, such as order-by-disorder and the quantum spin ice state. We have conducted a systematic investigation of the family of XY pyrochlores, Yb2B2O7 and Er2B2O7, spanning many non-magnetic B site cations (B = Ge, Ti, Pt, and Sn). We have characterized the magnetism of these XY pyrochlores using heat capacity, muon spin relaxation, neutron diffraction, and inelastic neutron scattering. A diversity of magnetic ground states and behaviours are represented among this family, ordered states ranging from ferromagnetic to antiferromagnetic, and in the case of one material, an absence of magnetic order to at least 100 mK. Moreover, we find that the magnetic ground state properties of these materials are strongly influenced by proximity to competing magnetic phases, consistent with theoretical predictions. We empirically demonstrate the signatures for phase competition in the frustrated XY pyrochlores: multiple heat capacity anomalies, suppressed TN or Tc, sample and pressure dependent ground states, and unconventional spin dynamics.

**Ludovic Jaubert**, Université de Bordeaux

*Living on the edge: multiphase competition in Yb2Ti2O7 and monopole crystal in Tb2Ti2O7*

Yb2Ti2O7 and Tb2Ti2O7 share the common point to sit at the edge between different phases. This multiphase competition makes the characterization of their low-temperature physics a challenge and, more generally, brings another degree of complexity to rare-earth pyrochlores. In this talk, we will take two different approaches to study these materials. For Yb2Ti2O7, we explicitly investigate the influence of thermal and quantum fluctuations in this competition, with finite-temperature order by disorder and quantum shifting of the phase boundaries. For Tb2Ti2O7, we will step away from the puzzling zero-field physics, and explain the undisputed order observed experimentally in a high [110] field. This order strongly supports the presence of magneto-electric coupling in Tb2Ti2O7, and offers a rare example of long-range order of magnetic monopoles.

**Eun-Ah Kim**, Cornell University

*Topological superconductivity in metal/quantum-spin-ice heterostructures*

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.

**Yong-Baek Kim,** University of Toronto

*Lightning review on emergent quantum electrodynamics in quantum spin ice*

We aim to provide a concise review on theoretical background on emergent quantum electrodynamics in pyrochlore quantum spin ice. We first introduce elementary excitations in quantum spin ice using a simple model and then extend the discussion to more realistic systems. Implications to experiments are also discussed.

**Bella Lake**, Helmholtz-Zentrum Berlin

*Recent measurements of dipolar-octupolar rare earth pyrochlores*

This talk will outline recent measurements on the dipolar-octupolar rare earth pyrochlores Nd2Zr2O7 and Nd2Hf2O7. Measurements of their crystal field excitations allows the wavefunction of their ground state Kramer’s doublet to be determined. Both compounds develop long-range magnetic order and their Hamiltonians are extracted by comparing inelastic neutron scattering data to spin-wave theory at low temperatures. The Hamiltonians are used to qualitatively explain AC magnetization measurements as well as neutron data collected in an applied magnetic field. Both system as predicted to lie close to a U(1) spin liquid and the excitation spectrum above the Néel temperature is compared to calculations for bosonic many body quantum spin ice.

**Elsa Lhotel**, Institute Neel

*Magnetic fragmentation and quantum effects in Nd2Zr2O7*

By means of neutron scattering measurements, we have observed magnetic fragmentation in the pyrochlore oxide Nd2Zr2O7, in which the Nd3+ ion has a strong Ising character and ferromagnetic interactions are inferred from the positive Curie-Weiss temperature θCW = 195 mK [2]. In this system, an “all in - all out” ordered state, with a reduced magnetic moment, coexists below TN = 285 mK with a fluctuating state [3]. Experimentally, the fragmentation manifests itself via the superposition of magnetic Bragg peaks, characteristic of the antiferromagnetic ordered phase, and a pinch point pattern, characteristic of the Coulomb phase [4]. The finite energy of the pinch point pattern and the dispersive modes that emerge from it, points out the quantum origin of the fragmentation in Nd2Zr2O7 [5], which comes from the very peculiar “dipolar-octopolar” nature of the Kramers Nd3+ doublet.

**Yuji Matsuda**, Kyoto University

*Possible observation of photons and monopoles in the frustrated pyrochlore Yb2Ti2O7 and Pr2Zr2O7*

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.

**Tyrel McQueen**, Johns Hopkins University

*The importance of defects and structural flexibility in the physics of quantum spin ices*

Harboring interpenetrating lattices of corner-sharing tetrahedra, materials with the pyrochlore structure type dominate exploration of the physics of quantum spin ices. Recent synthetic advances in the control of point defects, such as in Yb2Ti2O7 and Pr2Zr2O, have demonstrated that even sub-percent changes in the type and/or number of defects radically modulates the low temperature physics of these materials. This sensitivity to disorder is driven not only by the geometrically frustrated nature of the lattice, but also by the propensity of a corner sharing tetrahedral framework to undergo displacive motions, in a manner analogous to that of beta-crystabolite (quartz), either statically, or dynamically (as soft phonons). An outlook for continued improvements in our ability to control the chemistry behind quantum spin ices will also be presented.

**Shigeki Onoda**, RIKEN

*Quantum spin ice under a [111] magnetic field: from pyrochlore to kagome*

Quantum spin ice, modeled for magnetic rare-earth pyrochlores, has attracted great interest for hosting a U(1) quantum spin liquid, which involves spin-ice monopoles as gapped deconfined spinons, as well as gapless excitations analogous to photons. However, the global phase diagram under a [111] magnetic field remains open. Here we uncover by means of unbiased quantum Monte-Carlo simulations that a supersolid of monopoles, showing both a superfluidity and a partial ionization, intervenes the kagome spin ice and a fully polarized ionic monopole insulator, in contrast to classical spin ice where a direct discontinuous phase transition takes place. We also show that on cooling, kagome spin ice evolves towards a valence bond solid. Possible relevance to experiments is discussed.

**Sylvain Petit**, Centre d'Etudes de Saclay

*Antiferroquadrupolar correlations in the quantum spin ice candidate Pr2Zr2O7*

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.

**David Pomaranski**, University of Waterloo

*Low temperature specific heat characterization of the geometrically frustrated magnetic compound Yb2Ti2O7*

Yb2Ti2O7 is a geometrically frustrated magnet that proposed as a quantum spin liquid (QSL) candidate. This would have an emergent U(1) gauge structure, support emergent quasiparticles and a continuum of gapless spin excitations. A cubic power law dependence is expected in the specific heat down to zero temperature. [1,2] Identifying a power law is hindered by the presence of a sharp transition at 0.26K and a Schottky anomaly due to nuclear hyperfine interactions below 0.1K. [3] By preparing an isotopically enriched sample with 174-Yb and 48-Ti, we suppress the Schottky anomaly. This allows us to extend the specific heat to lower temperatures, revealing a polynomial behavior to at least 0.05 K that is suggestive of a quantum spin liquid.

**Jeffrey Rau**, University of Waterloo

*Microscopic aspects of insulating rare-earth pyrochlore magnets*

In this tutorial, we will review the microscopic aspects of rare-earth magnets relevant for quantum spin ice. We first discuss the single-ion properties of the variety of rare-earth atoms that appear in quantum spin ice candidate materials. Second, we consider the origin of the two-ion exchange interactions, including electric and magnetic multipolar interactions, super-exchange and virtual crystal field mediated interactions. We provide a detailed microscopic basis for the super-exchange interaction and discuss the implications of its multipolar structure for models of rare-earth materials. Finally, we introduce the generic symmetry allowed anisotropic exchange model for rare-earth pyrochlore magnets.

**Akito Sakai**, University of Tokyo

*Anomalous transport property in the nodal metallic spin ice Pr2Ir2O7*

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 ~3mB with Curie-Weiss temperature q ~ -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 Gmag ~ 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 G 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.

**Nicholas Shannon**, Okinawa Institute of Science and Technology

*Frustrating quantum spin ice: a tale of three spin liquids, and hidden order*

"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].

**Romain Sibill**e, Paul Scherrer Institute

*A summary of our results on the pyrochlore hafnates Tb2Hf2O7 and Pr2Hf2O7*

I will present our results on two hafnium-based pyrochlores. Firstly, I will summarize our findings on Tb2Hf2O7, where a sizeable gap isolates a non-Kramers ground state doublet with Ising-like anisotropy at low temperature. Long-range magnetic order is avoided down to the lowest temperatures, where Tb2Hf2O has correlations typical of a Coulomb phase. A large density of anion Frenkel defects leads to quenched random crystal fields, making this material relevant to theories of disorder-induced quantum entanglement in spin ices. Secondly, I will present our results on another non-Kramers pyrochlore with Ising-like moments, Pr2Hf2O, which displays macroscopic signatures that are consistent with spin ice-like correlations. Using the results of neutron scattering experiments I will demonstrate that Pr2Hf2O conforms to the predictions of the quantum-coherent regime of a QSI, where pinch-points are suppressed. Our result allows an estimate for the speed of light associated with magnetic photon excitations.

**Rajiv Singh**, University of California, Davis

*Numerical linked cluster spectroscopy of quantum spin ice*

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.

**Yixi Su**, Jülich Centre for Neutron Science

*Approaching the ground state of classical dipolar spin ice Dy2Ti2O7: a renewed study with neutron scattering*

The true magnetic ground state in thermally equilibrated classical spin ice compounds such as Dy2Ti2O7 remains an important but yet to be settled issue. In this talk, I will present our recent neutron scattering study of static and dynamic magnetic correlations in isotope-enriched 162Dy2Ti2O7 single-crystal samples. Implications within the context of possible quantum effects in dipolar spin ice based on our neutron results will be discussed as well.

**Yuan Wan**, Perimeter Institute

*Spinon dynamics in quantum spin ice*

In this talk, I will present our study on a minimal model for spinon propagation in quantum spin ice. I will demonstrate that the spinon motion can be thought of as a quantum walk with entropy-induced memory. Our numerical simulation shows that the spinon dynamics exhibits a remarkable renormalization phenomenon where the spinon propagates as a massive, nearly free quantum particle at low energy despite its strong coupling to a disordered spin background at the lattice scale. I will also present our ongoing work on the dynamical spin structure factor in a microscopic quantum spin ice model.

**Christopher Wiebe**, University of Winnipeg

*Confinement of magnetic monopole quasiparticles in a quantum spin ice*

We report direct spectroscopic evidence of correlations between monopoles in a quantum spin ice. A hierarchy of unequally spaced magnetic excitations has been observed via inelastic neutron spectroscopy in Pr2Sn2O7, resembling the confinement of spin defects in low-dimensional quantum magnets. Using a simple linear potential model to fit the excitations, we have estimated the monopole pair creation energy, and calculated a lower bound for the tension between monopole-like quasiparticles. The linear potential model provides a natural explanation as to why detection of these correlations have been so elusive in the canonical dipolar spin ices. This is the first spectroscopic measurement of an effective “Dirac string” between magnetic monopoles.