Dynamical Scaling as a Signature of Multiple Phase Competition in Yb_{2}Ti_{2}O_{7}

Yb_{2}Ti_{2}O_{7} is a celebrated example of a pyrochlore magnet with highly frustrated, anisotropic exchange interactions. To date, attention has largely focused on its unusual, static properties, many of which can be understood as coming from the competition between different types of magnetic order. Here we use inelastic neutron scattering with exceptionally high energy resolution to explore the dynamical properties of Yb_{2}Ti_{2}O_{7}. We find that spin correlations exhibit dynamical scaling, analogous to behavior found near to a quantum critical point. We show that the observed scaling collapse can be explained within a phenomenological theory of multiple-phase competition, and confirm that a scaling collapse is also seen in semiclassical simulations of a microscopic model of Yb_{2}Ti_{2}O_{7}. These results suggest that dynamical scaling may be general to systems with competing ground states.

Understanding Reentrance in Frustrated Magnets: The Case of the Er_{2}Sn_{2}O_{7} Pyrochlore

Reentrance, the return of a system from an ordered phase to a previously encountered less-ordered one as a controlled parameter is continuously varied, is a recurring theme found in disparate physical systems, yet its microscopic cause is often not investigated thoroughly. Here, through detailed characterization and theoretical modeling, we uncover the microscopic mechanism behind reentrance in the strongly frustrated pyrochlore antiferromagnet Er_{2}Sn_{2}O_{7}. We use single crystal heat capacity measurements to expose that Er_{2}Sn_{2}O_{7} exhibits multiple instances of reentrance in its magnetic field B vs temperature T phase diagram for magnetic fields along three cubic high symmetry directions. Through classical Monte Carlo simulations, mean field theory, and classical linear spin-wave expansions, we argue that the origins of the multiple occurrences of reentrance observed in Er_{2}Sn_{2}O_{7} are linked to soft modes. These soft modes arise from phase competition and enhance thermal fluctuations that entropically stabilize a specific ordered phase, resulting in an increased transition temperature for certain field values and thus the reentrant behavior. Our work represents a detailed examination into the mechanisms responsible for reentrance in a frustrated magnet and may serve as a template for the interpretation of reentrant phenomena in other physical systems.

Rank-2 U(1) Spin Liquid on the Breathing Pyrochlore Lattice

Higher-rank generalizations of electrodynamics have recently attracted considerable attention because of their ability to host "fracton" excitations, with connections to both fracton topological order and gravity. However, the search for higher-rank gauge theories in experiment has been greatly hindered by the lack of materially relevant microscopic models. Here we show how a spin liquid described by rank-2 U(1) gauge theory can arise in a magnet on the breathing pyrochlore lattice. We identify Yb-based breathing pyrochlores as candidate systems, and make explicit predictions for how the rank-2 U(1) spin liquid would manifest itself in experiment.

Quantum Spin Ice with Frustrated Transverse Exchange: From a π-Flux Phase to a Nematic Quantum Spin Liquid

Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalization, numerical linked-cluster and series expansions, we find that the previously studied U(1) quantum spin liquid, in its π-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point.

Clustering of Topological Charges in a Kagome Classical Spin Liquid

Fractionalization is a ubiquitous phenomenon in topological states of matter. In this work, we study the collective behavior of fractionalized topological charges and their instabilities, through the J_{1}-J_{2}-J_{3} Ising model on a kagome lattice. This model can be mapped onto a Hamiltonian of interacting topological charges under the constraint of Gauss' law. We find that the recombination of topological charges gives rise to a yet unexplored classical spin liquid. This spin liquid is characterized by an extensive residual entropy, as well as the formation of hexamers of same-sign topological charges. The emergence of hexamers is reflected by a half-moon signal in the magnetic structure factor, which provides a signature of this new spin liquid in elastic neutron-scattering experiments. To study this phase, a worm algorithm has been developed which does not require the usual divergence-free condition.

Spin ice Thin Film: Surface Ordering, Emergent Square ice, and Strain Effects

Motivated by recent realizations of Dy_{2}Ti_{2}O_{7} and Ho_{2}Ti_{2}O_{7} spin ice thin films, and more generally by the physics of confined gauge fields, we study a model spin ice thin film with surfaces perpendicular to the [001] cubic axis. The resulting open boundaries make half of the bonds on the interfaces inequivalent. By tuning the strength of these inequivalent "orphan" bonds, dipolar interactions induce a surface ordering equivalent to a two-dimensional crystallization of magnetic surface charges. This surface ordering may also be expected on the surfaces of bulk crystals. For ultrathin films made of one cubic unit cell, once the surfaces have ordered, a square ice phase is stabilized over a finite temperature window. The square ice degeneracy is lifted at lower temperature and the system orders in analogy with the well-known F transition of the 6-vertex model. To conclude, we consider the addition of strain effects, a possible consequence of interface mismatches at the film-substrate interface. Our simulations qualitatively confirm that strain can lead to a smooth loss of Pauling entropy upon cooling, as observed in recent experiments on Dy_{2}Ti_{2}O_{7} films.

A spin-liquid with pinch-line singularities on the pyrochlore lattice

The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell's theory of electromagnetism to Einstein's theory of general relativity. More recently it has become clear that gauge theories also emerge in condensed matter, a prime example being the spin-ice materials which host an emergent electromagnetic gauge field. In spin-ice, the underlying gauge structure is revealed by the presence of pinch-point singularities in neutron-scattering measurements. Here we report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. Remarkably, these features may already have been observed in the pyrochlore material Tb₂Ti₂O₇.

Neutron scattering measurements of spin-ice materials contain signature pinch-point singularities, demonstrating the existence of an emergent electromagnetic gauge field. Here, the authors propose a system in which correlations manifest in pinch lines, which may have already been observed experimentally.

Are Multiphase Competition and Order by Disorder the Keys to Understanding Yb(2)Ti(2)O(7)?

If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is perhaps no less fascinating, providing an avenue for the exploration and discovery of unconventional behaviors. Here, we study a realistic minimal model where a number of such mechanisms converge, which, incidentally, pertain to the perplexing quantum spin ice candidate Yb(2)Ti(2)O(7). Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder selection, conspire to expand the stability region of a degenerate continuous U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb(2)Ti(2)O(7). The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb(2)Ti(2)O(7) [Lhotel et al., Phys. Rev. B 89, 224419 (2014)]. By combining a gamut of numerical techniques, we obtain compelling evidence that such multiphase competition is a natural engine for the substantial sample-to-sample variability observed in Yb(2)Ti(2)O(7) and is the missing key to ultimately understand the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores.

Crystal shape-dependent magnetic susceptibility and Curie law crossover in the spin ices Dy2Ti2O7 and Ho2Ti2O7

We present an experimental determination of the isothermal magnetic susceptibility of the spin ice materials Dy2Ti2O7 and Ho2Ti2O7 in the temperature range 1.8-300 K. The use of spherical crystals has allowed accurate correction for demagnetizing fields and allowed the true bulk isothermal susceptibility χT(T) to be estimated. This has been compared against a theoretical expression based on a Husimi tree approximation to the spin ice model. Agreement between experiment and theory is excellent at T > 10 K, but systematic deviations occur below that temperature. Our results largely resolve an apparent disagreement between neutron scattering and bulk measurements that has been previously noted. They also show that the use of non-spherical crystals in magnetization studies of spin ice may introduce very significant systematic errors, although we note some interesting--and possibly new--systematics concerning the demagnetizing factor in cuboidal samples. Finally, our results show how experimental susceptibility measurements on spin ices may be used to extract the characteristic energy scale of the system and the corresponding chemical potential for emergent magnetic monopoles.

Analysis of a fully packed loop model arising in a magnetic Coulomb phase

The Coulomb phase of spin ice, and indeed the I(c) phase of water ice, naturally realize a fully packed two-color loop model in 3D. We present a detailed analysis of the statistics of these loops: we find loops spanning the system multiple times hosting a finite fraction of all sites while the average loop length remains finite. We contrast the behavior with an analogous 2D model. We connect this body of results to properties of polymers, percolation and insights from Schramm-Loewner evolution processes. We also study another extended degree of freedom, called worms, which appear as "Dirac strings" in spin ice. We discuss implications of these results for the efficiency of numerical cluster algorithms, and address implications for the ordering properties of a broader class of magnetic systems, e.g., with Heisenberg spins, such as CsNiCrF(6) or ZnCr(2)O(4).

Magnetic monopole dynamics in spin ice

One of the most remarkable examples of emergent quasi-particles is that of the 'fractionalization' of magnetic dipoles in the low energy configurations of materials known as 'spin ice' into free and unconfined magnetic monopoles interacting via Coulomb's 1/r law (Castelnovo et al 2008 Nature 451 42-5). Recent experiments have shown that a Coulomb gas of magnetic charges really does exist at low temperature in these materials and this discovery provides a new perspective on otherwise largely inaccessible phenomenology. In this paper, after a review of the different spin ice models, we present detailed results describing the diffusive dynamics of monopole particles starting both from the dipolar spin ice model and directly from a Coulomb gas within the grand canonical ensemble. The diffusive quasi-particle dynamics of real spin ice materials within the 'quantum tunnelling' regime is modelled with Metropolis dynamics, with the particles constrained to move along an underlying network of oriented paths, which are classical analogues of the Dirac strings connecting pairs of Dirac monopoles.

Spin ice under pressure: symmetry enhancement and infinite order multicriticality

We study the low-temperature behavior of spin ice when uniaxial pressure induces a tetragonal distortion. There is a phase transition between a Coulomb liquid and a fully magnetized phase. Unusually, it combines features of discontinuous and continuous transitions: the order parameter exhibits a jump, but this is accompanied by a divergent susceptibility and vanishing domain wall tension. All these aspects can be understood as a consequence of an emergent SU(2) symmetry at the critical point. We map out a possible experimental realization.

Three-dimensional Kasteleyn transition: spin ice in a [100] field

We examine the statistical mechanics of spin-ice materials with a [100] magnetic field. We show that the approach to saturated magnetization is, in the low-temperature limit, an example of a 3D Kasteleyn transition, which is topological in the sense that magnetization is changed only by excitations that span the entire system. We study the transition analytically and using a Monte Carlo cluster algorithm, and compare our results with recent data from experiments on Dy2Ti2O7.