Quantum Matter

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.

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.

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.

"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].

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.

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.

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.

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.

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.

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.

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.

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.