Experimental Realization of the 1D Random Field Ising Model.

We have measured magnetic-field-induced avalanches in a square artificial spin ice array of interacting nanomagnets. Starting from the ground state ordered configuration, we imaged the individual nanomagnet moments after each successive application of an incrementally increasing field. The statistics of the evolution of the moment configuration show good agreement with the canonical one-dimensional random field Ising model. We extract information about the microscopic structure of the arrays from our macroscopic measurements of their collective behavior, demonstrating a process that could be applied to other systems exhibiting avalanches.

Period multiplication cascade at the order-by-disorder transition in uniaxial random field XY magnets.

Uniaxial random field disorder induces a spontaneous transverse magnetization in the XY model. Adding a rotating driving field, we find a critical point attached to the number of driving cycles needed to complete a limit cycle, the first discovery of this phenomenon in a magnetic system. Near the critical drive, time crystal behavior emerges, in which the period of the limit cycles becomes an integer n > 1 multiple of the driving period. The period n can be engineered via specific disorder patterns. Because n generically increases with system size, the resulting period multiplication cascade is reminiscent of that occurring in amorphous solids subject to oscillatory shear near the onset of plastic deformation, and of the period bifurcation cascade near the onset of chaos in nonlinear systems, suggesting it is part of a larger class of phenomena in transitions of dynamical systems. Applications include magnets, electron nematics, and quantum gases.

Scaling of domain cascades in stripe and skyrmion phases.

The origin of deterministic macroscopic properties often lies in microscopic stochastic motion. Magnetic fluctuations that manifest as domain avalanches and chaotic magnetization jumps exemplify such stochastic motion and have been studied in great detail. Here we report Fourier space studies of avalanches in a system exhibiting competing magnetic stripe and skyrmion phase using a soft X-ray speckle metrology technique. We demonstrate the existence of phase boundaries and underlying critical points in the stripe and skyrmion phases. We found that distinct scaling and universality classes are associated with these domain topologies. The magnitude and frequency of abrupt magnetic domain jumps observed in the stripe phase are dramatically reduced in the skyrmion phase. Our results provide an incisive way to probe and understand phase stability in systems exhibiting complex spin topologies.

Publisher Correction: Scaling of domain cascades in stripe and skyrmion phases.

The original version of this Article contained an error in Fig. 4d, in which the label of the region to the left of the white dashed lines incorrectly read 'Order stripes'. The correct version states 'Disorder stripes'. This has been corrected in both the PDF and HTML versions of the Article.

Erratum: Random Field Driven Spatial Complexity at the Mott Transition in VO_{2} [Phys. Rev. Lett. 116, 036401 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.036401.

Loading-rate-independent delay of catastrophic avalanches in a bulk metallic glass.

The plastic flow of bulk metallic glasses (BMGs) is characterized by intermittent bursts of avalanches, and this trend results in disastrous failures of BMGs. In the present work, a double-side-notched BMG specimen is designed, which exhibits chaotic plastic flows consisting of several catastrophic avalanches under the applied loading. The disastrous shear avalanches have, then, been delayed by forming a stable plastic-flow stage in the specimens with tailored distances between the bottoms of the notches, where the distribution of a complex stress field is acquired. Differing from the conventional compressive testing results, such a delaying process is independent of loading rate. The statistical analysis shows that in the specimens with delayed catastrophic failures, the plastic flow can evolve to a critical dynamics, making the catastrophic failure more predictable than the ones with chaotic plastic flows. The findings are of significance in understanding the plastic-flow mechanisms in BMGs and controlling the avalanches in relating solids.

Random Field Driven Spatial Complexity at the Mott Transition in VO(2).

We report the first application of critical cluster techniques to the Mott metal-insulator transition in vanadium dioxide. We show that the geometric universal properties of the metallic and insulating puddles observed by scanning near-field infrared microscopy are consistent with the system passing near criticality of the random field Ising model as temperature is varied. The resulting large barriers to equilibrium may be the source of the unusually robust hysteresis phenomena associated with the metal-insulator transition in this system.

Universality of slip avalanches in flowing granular matter.

The search for scale-bridging relations in the deformation of amorphous materials presents a current challenge with tremendous applications in material science, engineering and geology. While generic features in the flow and microscopic dynamics support the idea of a universal scaling theory of deformation, direct microscopic evidence remains poor. Here, we provide the first measurement of internal scaling relations in the deformation of granular matter. By combining macroscopic force fluctuation measurements with internal strain imaging, we demonstrate the existence of robust scaling relations from particle-scale to macroscopic flow. We identify consistent power-law relations truncated by systematic pressure-dependent cutoff, in agreement with recent mean-field theory of slip avalanches in elasto-plastic materials, revealing the existence of a mechanical critical point. These results experimentally establish scale-bridging relations in the flow of matter, paving the way to a new universal theory of deformation.

Slip statistics of dislocation avalanches under different loading modes.

Slowly compressed microcrystals deform via intermittent slip events, observed as displacement jumps or stress drops. Experiments often use one of two loading modes: an increasing applied stress (stress driven, soft), or a constant strain rate (strain driven, hard). In this work we experimentally test the influence of the deformation loading conditions on the scaling behavior of slip events. It is found that these common deformation modes strongly affect time series properties, but not the scaling behavior of the slip statistics when analyzed with a mean-field model. With increasing plastic strain, the slip events are found to be smaller and more frequent when strain driven, and the slip-size distributions obtained for both drives collapse onto the same scaling function with the same exponents. The experimental results agree with the predictions of the used mean-field model, linking the slip behavior under different loading modes.

Controlling avalanche criticality in 2D nano arrays.

Many physical systems respond to slowly changing external force through avalanches spanning broad range of sizes. Some systems crackle even without apparent external force, such as bursts of neuronal activity or charge transfer avalanches in 2D molecular layers. Advanced development of theoretical models describing disorder-induced critical phenomena calls for experiments probing the dynamics upon tuneable disorder. Here we show that isomeric structural transitions in 2D organic self-assembled monolayer (SAM) exhibit critical dynamics with experimentally tuneable disorder. The system consists of field effect transistor coupled through SAM to illuminated semiconducting nanocrystals (NCs). Charges photoinduced in NCs are transferred through SAM to the transistor surface and modulate its conductivity. Avalanches of isomeric structural transitions are revealed by measuring the current noise I(t) of the transistor. Accumulated surface traps charges reduce dipole moments of the molecules, decrease their coupling, and thus decrease the critical disorder of the SAM enabling its tuning during experiments.

Spatial complexity due to bulk electronic nematicity in a superconducting underdoped cuprate.

Surface probes such as scanning tunnelling microscopy have detected complex electronic patterns at the nanoscale in many high-temperature superconductors. In cuprates, the pattern formation is associated with the pseudogap phase, a precursor to the high-temperature superconducting state. Rotational symmetry breaking of the host crystal in the form of electronic nematicity has recently been proposed as a unifying theme of the pseudogap phase. However, the fundamental physics governing the nanoscale pattern formation has not yet been identifed. Here we introduce a new set of methods for analysing strongly correlated electronic systems, including the effects of both disorder and broken symmetry. We use universal cluster properties extracted from scanning tunnelling microscopy studies of cuprate superconductors to identify the fundamental physics controlling the complex pattern formation. Because of a delicate balance between disorder, interactions, and material anisotropy, we find that the electron nematic is fractal in nature, and that it extends throughout the bulk of the material.

Using disorder to detect locally ordered electron nematics via hysteresis.

The interplay between charge, orbital and lattice degrees of freedom in correlated electron systems has resulted in many proposals for new electronic phases of matter. An electron nematic breaks the point group symmetry of the host crystal, often from C(6) or C(4) rotational symmetry to C(2). Electron nematics have been reported in several condensed matter systems including cuprate- and iron arsenic-based high-temperature superconductors, and they have been proposed to exist in many other materials. However, the combination of reduced dimensionality and material disorder typically limits the spatial range over which electron nematic order persists, rendering its experimental detection extremely difficult. Despite the tantalizing possible connection between the phase and high-temperature superconductivity, there is surprisingly little guidance in the literature about how to detect the remaining disordered electron nematic. Here we propose two protocols for detecting disordered electron nematics in condensed matter systems using non-equilibrium methods.

Hysteresis and noise from electronic nematicity in high-temperature superconductors.

An electron nematic is a translationally invariant state which spontaneously breaks the discrete rotational symmetry of a host crystal. In a clean square lattice, the electron nematic has two preferred orientations, while dopant disorder favors one or the other orientations locally. In this way, the electron nematic in a host crystal maps to the random field Ising model. Since the electron nematic has anisotropic conductivity, we associate each Ising configuration with a resistor network and use what is known about the random field Ising model to predict new ways to test for local electronic nematic order (nematicity) using noise and hysteresis. In particular, we have uncovered a remarkably robust linear relation between the orientational order and the resistance anisotropy which holds over a wide range of circumstances.

Crackling noise.

Crackling noise arises when a system responds to changing external conditions through discrete, impulsive events spanning a broad range of sizes. A wide variety of physical systems exhibiting crackling noise have been studied, from earthquakes on faults to paper crumpling. Because these systems exhibit regular behaviour over a huge range of sizes, their behaviour is likely to be independent of microscopic and macroscopic details, and progress can be made by the use of simple models. The fact that these models and real systems can share the same behaviour on many scales is called universality. We illustrate these ideas by using results for our model of crackling noise in magnets, explaining the use of the renormalization group and scaling collapses, and we highlight some continuing challenges in this still-evolving field.