Condensed Matter

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.

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.

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.

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.

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.

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.

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.

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.

In this talk we present a study of the “breathing” pyrochlore compound Ba3Yb2Zn5O11. Due to the nearly decoupled nature of its tetrahedral units, this compound serves as an ideal testbed for exploring the nature of anisotropic exchange in a theoretically and experimentally tractable rare-earth system. The relevant low-energy model of the Yb3+ tetrahedra is parametrized by four anisotropic exchange constants and is capable of reproducing the inelastic neutron scattering data, specific heat, and magnetic susceptibility with high fidelity. Using this model, we predict the appearance of an unusual non-Kramers octupolar paramagnet at low temperatures. We further speculate on possible collective, inter-tetrahedron physics of these non-Kramers doublets and discuss applications to about anisotropic exchange in other rare-earth magnets.

The XY pyrochlore Er2Ti2O7 has garnered much attention due to the possibility that its ground state selection could originate from an order-by-disorder mechanism [1,2]. However, recently, theoretical work has exploited the fact that the symmetry breaking in this system is a rare case of high discrete symmetry (Z6) [3]. This work studied the effect of a magnetic field on the Z6 symmetry breaking and predicted rich and controllable magnetothermodynamic properties. Indeed, the authors predict numerous domains transitions in the low field regime that strongly depends on the field direction. In this talk, I will present neutron scattering data on Er2Ti2O7 with a magnetic field applied along different high symmetry directions which provides the first experimental evidence for this rich Z6 domain phase behavior [4].

In recent years, there has been a resurgence of interest in the study of chiral spin liquids (CSLs), topologically ordered states of matter that are closely related to the celebrated fractional quantum Hall states. This resurgence has been driven by the introduction of exact parent Hamiltonians and a number of numerical studies that have identified CSLs in local spin models. However, our understanding of how and why these states emerge is still lacking. I will discuss evidence supporting one particularly intuitive mechanism in which they arise as "quantum-disordered" descendants of certain non-coplanar magnetic parent states, uniting many of the CSLs found so far under a common framework.