Dichotomous dynamics of magnetic monopole fluids.

A recent advance in the study of emergent magnetic monopoles was the discovery that monopole motion is restricted to dynamical fractal trajectories [J. N. Hallén et al., Science 378, 1218 (2022)], thus explaining the characteristics of magnetic monopole noise spectra [R. Dusad et al., Nature 571, 234 (2019); A. M. Samarakoon et al., Proc. Natl. Acad. Sci. U.S.A. 119, e2117453119 (2022)]. Here, we apply this novel theory to explore the dynamics of field-driven monopole currents, finding them composed of two quite distinct transport processes: initially swift fractal rearrangements of local monopole configurations followed by conventional monopole diffusion. This theory also predicts a characteristic frequency dependence of the dissipative loss angle for AC field-driven currents. To explore these novel perspectives on monopole transport, we introduce simultaneous monopole current control and measurement techniques using SQUID-based monopole current sensors. For the canonical material Dy2Ti2O7, we measure [Formula: see text], the time dependence of magnetic flux threading the sample when a net monopole current [Formula: see text] is generated by applying an external magnetic field [Formula: see text] These experiments find a sharp dichotomy of monopole currents, separated by their distinct relaxation time constants before and after t ~[Formula: see text] from monopole current initiation. Application of sinusoidal magnetic fields [Formula: see text] generates oscillating monopole currents whose loss angle [Formula: see text] exhibits a characteristic transition at frequency [Formula: see text] over the same temperature range. Finally, the magnetic noise power is also dichotomic, diminishing sharply after t ~[Formula: see text]. This complex phenomenology represents an unprecedented form of dynamical heterogeneity generated by the interplay of fractionalization and local spin configurational symmetry.

Revealing emergent magnetic charge in an antiferromagnet with diamond quantum magnetometry.

Whirling topological textures play a key role in exotic phases of magnetic materials and are promising for logic and memory applications. In antiferromagnets, these textures exhibit enhanced stability and faster dynamics with respect to their ferromagnetic counterparts, but they are also difficult to study due to their vanishing net magnetic moment. One technique that meets the demand of highly sensitive vectorial magnetic field sensing with negligible backaction is diamond quantum magnetometry. Here we show that an archetypal antiferromagnet-haematite-hosts a rich tapestry of monopolar, dipolar and quadrupolar emergent magnetic charge distributions. The direct read-out of the previously inaccessible vorticity of an antiferromagnetic spin texture provides the crucial connection to its magnetic charge through a duality relation. Our work defines a paradigmatic class of magnetic systems to explore two-dimensional monopolar physics, and highlights the transformative role that diamond quantum magnetometry could play in exploring emergent phenomena in quantum materials.

Dynamical Axions in U(1) Quantum Spin Liquids.

Since their proposal nearly half a century ago, physicists have sought axions in both high energy and condensed matter settings. Despite intense and growing efforts, to date, experimental success has been limited, with the most prominent results arising in the context of topological insulators. Here, we propose a novel mechanism whereby axions can be realized in quantum spin liquids. We discuss the necessary symmetry requirements and identify possible experimental realizations in candidate pyrochlore materials. In this context, the axions couple to both the external and the emergent electromagnetic fields. We show that the interaction between the axion and the emergent photon leads to a characteristic dynamical response, which can be measured experimentally in inelastic neutron scattering. This Letter sets the stage for studying axion electrodynamics in the highly tunable setting of frustrated magnets.

Dynamical fractal and anomalous noise in a clean magnetic crystal.

Fractals-objects with noninteger dimensions-occur in manifold settings and length scales in nature. In this work, we identify an emergent dynamical fractal in a disorder-free, stoichiometric, and three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is born from constraints on the dynamics of the magnetic monopole excitations in spin ice, which restrict them to move on the fractal. This observation explains the anomalous exponent found in magnetic noise experiments in the spin ice compound Dy2Ti2O7, and it resolves a long-standing puzzle about its rapidly diverging relaxation time. The capacity of spin ice to exhibit such notable phenomena suggests that there will be further unexpected discoveries in the cooperative dynamics of even simple topological many-body systems.

Enhanced diffusion in soft-walled channels with a periodically varying curvature.

The motion of particles along channels of finite width is known to be hindered by either the presence of energy barriers along the channel direction or by variations in the width of the channel in the transverse direction (rugged channel). Remarkably, when both features are present, they can interact to produce a counterintuitive result: adding energy barriers to a rugged channel can enhance the rate of diffusion along it. This is the result of competing energetic and entropic effects. Under the approximation of particles instantaneously in equilibrium in the transverse direction, one can tailor the energy barriers to the ruggedness to recover free diffusion. However, such fine-tuning and potentially restrictive approximations are not necessary to observe an enhanced rate of diffusion as we demonstrate by adding a range of (non-fine-tuned) energy barriers to a channel of sinusoidally varying curvature. Furthermore, this was observed to hold for systems with a finite characteristic timescale for motion in the transverse direction, thus, suggesting that the phenomenon lends itself to be exploited for practical applications.

Anomalous magnetic noise in an imperfectly flat landscape in the topological magnet Dy2Ti2O7.

Noise generated by motion of charge and spin provides a unique window into materials at the atomic scale. From temperature of resistors to electrons breaking into fractional quasiparticles, "listening" to the noise spectrum is a powerful way to decode underlying dynamics. Here, we use ultrasensitive superconducting quantum interference device (SQUIDs) to probe the puzzling noise in a frustrated magnet, the spin-ice compound Dy2Ti2O7 (DTO), revealing cooperative and memory effects. DTO is a topological magnet in three dimensions-characterized by emergent magnetostatics and telltale fractionalized magnetic monopole quasiparticles-whose real-time dynamical properties have been an enigma from the very beginning. We show that DTO exhibits highly anomalous noise spectra, differing significantly from the expected Brownian noise of monopole random walks, in three qualitatively different regimes: equilibrium spin ice, a "frozen" regime extending to ultralow temperatures, and a high-temperature "anomalous" paramagnet. We present several distinct mechanisms that give rise to varied colored noise spectra. In addition, we identify the structure of the local spin-flip dynamics as a crucial ingredient for any modeling. Thus, the dynamics of spin ice reflects the interplay of local dynamics with emergent topological degrees of freedom and a frustration-generated imperfectly flat energy landscape, and as such, it points to intriguing cooperative and memory effects for a broad class of magnetic materials.

Logarithmic Entanglement Growth from Disorder-Free Localization in the Two-Leg Compass Ladder.

We explore the finite-temperature dynamics of the quasi-1D orbital compass and plaquette Ising models. We map these systems onto a model of free fermions coupled to strictly localized spin-1/2 degrees of freedom. At finite temperature, the localized degrees of freedom act as emergent disorder and localize the fermions. Although the model can be analyzed using free-fermion techniques, it has dynamical signatures in common with typical many-body localized systems: Starting from generic initial states, entanglement grows logarithmically; in addition, equilibrium dynamical correlation functions decay with an exponent that varies continuously with temperature and model parameters. These quasi-1D models offer an experimentally realizable setting in which natural dynamical probes show signatures of disorder-free many-body localization.

Correlation holes and slow dynamics induced by fractional statistics in gapped quantum spin liquids.

Realistic model Hamiltonians for quantum spin liquids frequently exhibit a large separation of energy scales between their elementary excitations. At intermediate, experimentally relevant temperatures, some excitations are sparse and hop coherently, whereas others are thermally incoherent and dense. Here, we study the interplay of two such species of quasiparticle, dubbed spinons and visons, which are subject to nontrivial mutual statistics - one of the hallmarks of quantum spin liquid behaviour. Our results for [Formula: see text] quantum spin liquids show an intriguing feedback mechanism, akin to the Nagaoka effect, whereby spinons become localised on temperature-dependent patches of expelled visons. This phenomenon has important consequences for the thermodynamic and transport properties of the system, as well as for its response to quenches in temperature. We argue that these effects can be measured in experiments and may provide viable avenues for obtaining signatures of quantum spin liquid behaviour.

Correlated Quantum Tunneling of Monopoles in Spin Ice.

The spin ice materials Ho_{2}Ti_{2}O_{7} and Dy_{2}Ti_{2}O_{7} are by now perhaps the best-studied classical frustrated magnets. A crucial step towards the understanding of their low temperature behavior-both regarding their unusual dynamical properties and the possibility of observing their quantum coherent time evolution-is a quantitative understanding of the spin-flip processes which underpin the hopping of magnetic monopoles. We attack this problem in the framework of a quantum treatment of a single-ion subject to the crystal, exchange, and dipolar fields from neighboring ions. By studying the fundamental quantum mechanical mechanisms, we discover a bimodal distribution of hopping rates that depends on the local spin configuration, in broad agreement with rates extracted from experiment. Applying the same analysis to Pr_{2}Sn_{2}O_{7} and Pr_{2}Zr_{2}O_{7}, we find an even more pronounced separation of timescales signaling the likelihood of coherent many-body dynamics.

Emergent order in the kagome Ising magnet Dy3Mg2Sb3O14.

The Ising model-in which degrees of freedom (spins) are binary valued (up/down)-is a cornerstone of statistical physics that shows rich behaviour when spins occupy a highly frustrated lattice such as kagome. Here we show that the layered Ising magnet Dy3Mg2Sb3O14 hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scattering and bulk thermomagnetic measurements reveal a phase transition at ∼0.3 K from a disordered spin-ice-like regime to an emergent charge ordered state, in which emergent magnetic charge degrees of freedom exhibit three-dimensional order while spins remain partially disordered. Monte Carlo simulations show that an interplay of inter-layer interactions, spin canting and chemical disorder stabilizes this state. Our results establish Dy3Mg2Sb3O14 as a tuneable system to study interacting emergent charges arising from kagome Ising frustration.

Tunable nonequilibrium dynamics of field quenches in spin ice.

We present nonequilibrium physics in spin ice as a unique setting that combines kinematic constraints, emergent topological defects, and magnetic long-range Coulomb interactions. In spin ice, magnetic frustration leads to highly degenerate yet locally constrained ground states. Together, they form a highly unusual magnetic state--a "Coulomb phase"--whose excitations are point-like defects--magnetic monopoles--in the absence of which effectively no dynamics is possible. Hence, when they are sparse at low temperature, dynamics becomes very sluggish. When quenching the system from a monopole-rich to a monopole-poor state, a wealth of dynamical phenomena occur, the exposition of which is the subject of this article. Most notably, we find reaction diffusion behavior, slow dynamics owing to kinematic constraints, as well as a regime corresponding to the deposition of interacting dimers on a honeycomb lattice. We also identify potential avenues for detecting the magnetic monopoles in a regime of slow-moving monopoles. The interest in this model system is further enhanced by its large degree of tunability and the ease of probing it in experiment: With varying magnetic fields at different temperatures, geometric properties--including even the effective dimensionality of the system--can be varied. By monitoring magnetization, spin correlations or zero-field NMR, the dynamical properties of the system can be extracted in considerable detail. This establishes spin ice as a laboratory of choice for the study of tunable, slow dynamics.