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Concept: Topological defect


The flow of magnetic charge carriers (dubbed magnetic monopoles) through frustrated spin ice lattices, governed simply by Coulombic forces, represents a new direction in electromagnetism. Artificial spin ice nanoarrays realise this effect at room temperature, where the magnetic charge is carried by domain walls. Control of domain wall path is one important element of utilizing this new medium. By imaging the transit of domain walls across different connected 2D honeycomb structures we contribute an important aspect which will enable that control to be realized. Although apparently equivalent paths are presented to a domain wall as it approaches a Y-shaped vertex from a bar parallel to the field, we observe a stark non-random path distribution, which we attribute to the chirality of the magnetic charges. These observations are supported by detailed statistical modelling and micromagnetic simulations. The identification of chiral control to magnetic charge path selectivity invites analogy with spintronics.

Concepts: Electron, Electromagnetism, Electric charge, Magnetic field, Magnet, Magnetism, Magnetic monopole, Topological defect


Topological defects can markedly alter nanomaterial properties. This presents opportunities for “defect engineering,” where desired functionalities are generated through defect manipulation. However, imaging defects in working devices with nanoscale resolution remains elusive. We report three-dimensional imaging of dislocation dynamics in individual battery cathode nanoparticles under operando conditions using Bragg coherent diffractive imaging. Dislocations are static at room temperature and mobile during charge transport. During the structural phase transformation, the lithium-rich phase nucleates near the dislocation and spreads inhomogeneously. The dislocation field is a local probe of elastic properties, and we find that a region of the material exhibits a negative Poisson’s ratio at high voltage. Operando dislocation imaging thus opens a powerful avenue for facilitating improvement and rational design of nanostructured materials.

Concepts: Crystal structure, Nanotechnology, Nanomaterials, Materials science, Crystallographic defect, Dislocation, Plasticity, Topological defect


Bilayer graphene has been a subject of intense study in recent years. The interlayer registry between the layers can have dramatic effects on the electronic properties: for example, in the presence of a perpendicular electric field, a band gap appears in the electronic spectrum of so-called Bernal-stacked graphene [Oostinga JB, et al. (2007) Nature Materials 7:151-157]. This band gap is intimately tied to a structural spontaneous symmetry breaking in bilayer graphene, where one of the graphene layers shifts by an atomic spacing with respect to the other. This shift can happen in multiple directions, resulting in multiple stacking domains with soliton-like structural boundaries between them. Theorists have recently proposed that novel electronic states exist at these boundaries [Vaezi A, et al. (2013) arXiv:1301.1690; Zhang F, et al. (2013) arXiv:1301.4205], but very little is known about their structural properties. Here we use electron microscopy to measure with nanoscale and atomic resolution the widths, motion, and topological structure of soliton boundaries and related topological defects in bilayer graphene. We find that each soliton consists of an atomic-scale registry shift between the two graphene layers occurring over 6-11 nm. We infer the minimal energy barrier to interlayer translation and observe soliton motion during in situ heating above 1,000 °C. The abundance of these structures across a variety of samples, as well as their unusual properties, suggests that they will have substantial effects on the electronic and mechanical properties of bilayer graphene.

Concepts: Structure, Symmetry, Topological space, Electronic band structure, Spontaneous symmetry breaking, Higgs mechanism, Soliton, Topological defect


Topological defects in matter behave collectively to form highly non-trivial structures called topological textures that are characterised by conserved quantities such as the winding number. Here we show that an epitaxial ferroelectric square nanoplate of bismuth ferrite subjected to a large strain gradient (as much as 105 m-1) associated with misfit strain relaxation enables five discrete levels for the ferroelectric topological invariant of the entire system because of its peculiar radial quadrant domain texture and its inherent domain wall chirality. The total winding number of the topological texture can be configured from - 1 to 3 by selective non-local electric switching of the quadrant domains. By using angle-resolved piezoresponse force microscopy in conjunction with local winding number analysis, we directly identify the existence of vortices and anti-vortices, observe pair creation and annihilation and manipulate the net number of vortices. Our findings offer a useful concept for multi-level topological defect memory.

Concepts: Electron, Photon, Particle physics, Set theory, Domain wall, Topological defect, Topological quantum number, Cosmic string


Liquid crystals are widely known for their facile responses to external fields, which forms a basis of the modern information display technology. However, switching of molecular alignment field configurations typically involves topologically trivial structures, although singular line and point defects often appear as short-lived transient states. Here, we demonstrate electric and magnetic switching of nonsingular solitonic structures in chiral nematic and ferromagnetic liquid crystals. These topological soliton structures are characterized by Hopf indices, integers corresponding to the numbers of times that closed-loop-like spatial regions (dubbed “preimages”) of two different single orientations of rod-like molecules or magnetization are linked with each other. We show that both dielectric and ferromagnetic response of the studied material systems allow for stabilizing a host of topological solitons with different Hopf indices. The field transformations during such switching are continuous when Hopf indices remain unchanged, even when involving transformations of preimages, but discontinuous otherwise.

Concepts: Magnetic field, Crystal, Topology, Continuous function, Liquid crystal, Display device, Soliton, Topological defect


We report on the first demonstration of dual-wavelength square-wave pulses in a thulium-doped fiber laser. Under appropriate cavity parameters, dual-wavelength dissipative soliton resonances (DSRs) and domain wall solitons (DWSs) are successively obtained. Meanwhile, dark pulses generation is achieved at the dual-wavelength DWSs region due to the overlap of the two domain wall pulses. The fiber-based Lyot filter, conducted by inserting PMF between an in-line PBS and a PD-ISO, facilitates the generation of dual-wavelength operation. The polarization-resolved investigation suggests that the cross coupling between two orthogonal polarization components in the high nonlinear fiber plays an important role in the square-wave pulses formation. The investigation may be helpful for further understanding the square-wave pulse formation and has potential in application filed of multi-wavelength pulsed fiber lasers.

Concepts: Optical fiber, Laser, Pulse, Vector soliton, Domain wall, Fiber laser, Topological defect, Solitons


Domain walls, which are intrinsically two dimensional nano-objects exhibiting nontrivial electronic and magnetic behaviours, have been proven to play a crucial role in photovoltaic properties of ferroelectrics. Despite this recognition, the electronic properties of domain walls under illumination until now have been accessible only to macroscopic studies and their effects upon the conduction of photovoltaic current still remain elusive. The lack of understanding hinders the developing of nanoscale devices based on ferroelectric domain walls. Here, we directly characterize the local photovoltaic and photoconductive properties of 71° domain walls on BiFeO3 thin films with a nanoscale resolution. Local photovoltaic current, proven to be driven by the bulk photovoltaic effect, has been probed over the whole illuminated surface by using a specially designed photoelectric atomic force microscopy and found to be significantly enhanced at domain walls. Additionally, spatially resolved photoconductive current distribution reveals a higher density of excited carriers at domain walls in comparison with domains. Our measurements demonstrate that domain wall enhanced photovoltaic current originates from its high conduction rather than the internal electric field. This photoconduction facilitated local photovoltaic current is likely to be a universal property of topological defects in ferroelectric semiconductors.

Concepts: Electromagnetism, Magnetic field, Magnetism, Solar cell, Piezoelectricity, Domain wall, Electrical phenomena, Topological defect


Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, display rich behaviours not found elsewhere in nature. Artificial spin ice takes a materials-by-design approach to studying frustration, where lithographically patterned bar magnets mimic the frustrated interactions in real materials but are also amenable to direct characterization. Here, we introduce controlled topological defects into square artificial spin ice lattices in the form of lattice edge dislocations and directly observe the resulting spin configurations. We find the presence of a topological defect produces extended frustration within the system caused by a domain wall with indeterminate configuration. Away from the dislocation, the magnets are locally unfrustrated, but frustration of the lattice persists due to its topology. Our results demonstrate the non-trivial nature of topological defects in a new context, with implications for many real systems in which a typical density of dislocations could fully frustrate a canonically unfrustrated system.

Concepts: Magnetism, Topology, Real number, Crystallographic defect, Dislocation, Domain wall, Magnetic monopole, Topological defect


We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain.

Concepts: Fundamental physics concepts, Model theory, Vector soliton, Partial differential equation, Stability, Instability, The Band, Topological defect


Chiral magnetic interactions induce complex spin textures including helical and conical spin spirals, as well as particle-like objects such as magnetic skyrmions and merons. These spin textures are the basis for innovative device paradigms and give rise to exotic topological phenomena, thus being of interest for both applied and fundamental sciences. Present key questions address the dynamics of the spin system and emergent topological defects. Here we analyse the micromagnetic dynamics in the helimagnetic phase of FeGe. By combining magnetic force microscopy, single-spin magnetometry and Landau-Lifschitz-Gilbert simulations we show that the nanoscale dynamics are governed by the depinning and subsequent motion of magnetic edge dislocations. The motion of these topologically stable objects triggers perturbations that can propagate over mesoscopic length scales. The observation of stochastic instabilities in the micromagnetic structure provides insight to the spatio-temporal dynamics of itinerant helimagnets and topological defects, and discloses open challenges regarding their technological usage.

Concepts: Magnetic field, Mathematics, Magnetism, Topology, Force, Topological space, Open set, Topological defect