Skyrmion Lattice in Two-Dimensional Chiral Magnet

We develop a theory of the magnetic field-induced formation of Skyrmion crystal state in chiral magnets in two spatial dimensions, motivated by the recent discovery of the Skyrmionic phase of magnetization in thin film of Fe$_{0.5}$Co$_{0.5}$Si and in the A-phase of MnSi. Ginzburg-Landau functional of the chiral magnet re-written in the CP$^1$ representation is shown to be a convenient framework for the analysis of the Skyrmion states. Phase diagram of the model at zero temperature gives a sequence of ground states, helical spin $\rightarrow$ Skyrme crystal $\rightarrow$ ferromagnet, as the external field $B$ increases, in good accord with the thin-film experiment. In close analogy with Abrikosov's derivation of the vortex lattice solution in type-II superconductor, the CP$^1$ mean-field equation is solved and shown to reproduce the Skyrmion crystal state.Comment: 10 pages, 7 figure

Security feature measurement for frequent dynamic execution paths in software system

© 2018 Qian Wang et al. The scale and complexity of software systems are constantly increasing, imposing new challenges for software fault location and daily maintenance. In this paper, the Security Feature measurement algorithm of Frequent dynamic execution Paths in Software, SFFPS, is proposed to provide a basis for improving the security and reliability of software. First, the dynamic execution of a complex software system is mapped onto a complex network model and sequence model. This, combined with the invocation and dependency relationships between function nodes, fault cumulative effect, and spread effect, can be analyzed. The function node security features of the software complex network are defined and measured according to the degree distribution and global step attenuation factor. Finally, frequent software execution paths are mined and weighted, and security metrics of the frequent paths are obtained and sorted. The experimental results show that SFFPS has good time performance and scalability, and the security features of the important paths in the software can be effectively measured. This study provides a guide for the research of defect propagation, software reliability, and software integration testing

Edge-Mediated Skyrmion Chain and Its Collective Dynamics in a Confined Geometry

The emergence of a topologically nontrivial vortex-like magnetic structure, the magnetic skyrmion, has launched new concepts for memory devices. There, extensive studies have theoretically demonstrated the ability to encode information bits by using a chain of skyrmions in one-dimensional nanostripes. Here, we report the first experimental observation of the skyrmion chain in FeGe nanostripes by using high resolution Lorentz transmission electron microscopy. Under an applied field normal to the nanostripes plane, we observe that the helical ground states with distorted edge spins would evolves into individual skyrmions, which assemble in the form of chain at low field and move collectively into the center of nanostripes at elevated field. Such skyrmion chain survives even as the width of nanostripe is much larger than the single skyrmion size. These discovery demonstrates new way of skyrmion formation through the edge effect, and might, in the long term, shed light on the applications.Comment: 7 pages, 3 figure

Electrical Probing of Field-Driven Cascading Quantized Transitions of Skyrmion Cluster States in MnSi Nanowires

Magnetic skyrmions are topologically stable whirlpool-like spin textures that offer great promise as information carriers for future ultra-dense memory and logic devices1-4. To enable such applications, particular attention has been focused on the skyrmions properties in highly confined geometry such as one dimensional nanowires5-8. Hitherto it is still experimentally unclear what happens when the width of the nanowire is comparable to that of a single skyrmion. Here we report the experimental demonstration of such scheme, where magnetic field-driven skyrmion cluster (SC) states with small numbers of skyrmions were demonstrated to exist on the cross-sections of ultra-narrow single-crystal MnSi nanowires (NWs) with diameters, comparable to the skyrmion lattice constant (18 nm). In contrast to the skyrmion lattice in bulk MnSi samples, the skyrmion clusters lead to anomalous magnetoresistance (MR) behavior measured under magnetic field parallel to the NW long axis, where quantized jumps in MR are observed and directly associated with the change of the skyrmion number in the cluster, which is supported by Monte Carlo simulations. These jumps show the key difference between the clustering and crystalline states of skyrmions, and lay a solid foundation to realize skyrmion-based memory devices that the number of skyrmions can be counted via conventional electrical measurements

Disagreement and fragmentation in growing groups

The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an analytically tractable model of group formation where individuals have multidimensional binary opinions and the group grows through a noisy homophily principle, i.e., like-minded individuals attract each other with exceptions occurring with some small probability. Assuming that the level of disagreement is correlated with the number of different opinions coexisting within the group, we find analytically and numerically that in growing groups disagreement emerges spontaneously regardless of how small the noise in the system is. Moreover, for groups of infinite size, fragmentation is inevitable. We also show that the model outcomes are robust under different group growth mechanisms.Comment: 17 pages, 3 figure

Single-shot 3D coherent diffractive imaging of core-shell nanoparticles with elemental specificity.

We report 3D coherent diffractive imaging (CDI) of Au/Pd core-shell nanoparticles with 6.1 nm spatial resolution with elemental specificity. We measured single-shot diffraction patterns of the nanoparticles using intense x-ray free electron laser pulses. By exploiting the curvature of the Ewald sphere and the symmetry of the nanoparticle, we reconstructed the 3D electron density of 34 core-shell structures from these diffraction patterns. To extract 3D structural information beyond the diffraction signal, we implemented a super-resolution technique by taking advantage of CDI's quantitative reconstruction capabilities. We used high-resolution model fitting to determine the Au core size and the Pd shell thickness to be 65.0 ± 1.0 nm and 4.0 ± 0.5 nm, respectively. We also identified the 3D elemental distribution inside the nanoparticles with an accuracy of 3%. To further examine the model fitting procedure, we simulated noisy diffraction patterns from a Au/Pd core-shell model and a solid Au model and confirmed the validity of the method. We anticipate this super-resolution CDI method can be generally used for quantitative 3D imaging of symmetrical nanostructures with elemental specificity