Search

The Notebook validation tool nbval allows to load and execute Python code from a Jupyter notebook file. While computing outputs from the cells in the notebook, these outputs are compared with the outputs saved in the notebook file, treating each cell as a test. Deviations are reported as test failures, with various configuration options available to control the behaviour. Application use cases include the validation of notebook-based documentation, tutorials and textbooks, as well as the use of notebooks as additional unit, integration and system tests for the libraries that are used in the notebook. Nbval is implemented as a plugin for the pytest testing software., Comment: 12 pages, 3 figures

We use mobile phone call detail records to estimate the resettlement times of a subset of individuals that have been previously identified to be internally displaced persons (IDPs) following a sudden-onset disaster. Four different mobility metrics - two versions of radius of gyration and two versions of entropy - are used to study the behaviour of populations during three disasters - the 2010 earthquake in Haiti, the 2015 Gorkha earthquake in Nepal, and Hurricane Matthew in Haiti in 2016. We characterise the rate at which a disrupted population resettles by the fraction of individuals who remain disrupted each week after the disaster. We find that this rate can be modelled very well as the sum of two exponential decays and observe that the resettling rate for all three disasters is similar, with half the original number of displaced persons having resettled within four to five weeks of the disaster. If the study of further disasters leads to the observation of similar exponential decay rates, then it would imply that the number of IDPs at any time can be inferred from an estimate of the initial number of IDPs immediately following the disaster. Alternatively, the method provides a way to monitor disaster resilience and compare recovery rates across disasters. The method has the advantage that no assumptions need to be made regarding the location or time of resettlement. Our results indicate that CDRs can significantly contribute to measuring and predicting displacement durations, distances, and locations of IDPs in post-disaster scenarios. We believe that information and estimates provided by specifically developed CDR analytics, coupled with field data collection and traditional survey methods, can assist the humanitarian response to natural disasters and the subsequent resettlement efforts., Comment: 31 pages, 12 figures

Recent studies have demonstrated that skyrmionic states can be the ground state in thin-film FeGe disk nanostructures in the absence of a stabilising applied magnetic field. In this work, we advance this understanding by investigating to what extent this stabilisation of skyrmionic structures through confinement exists in geometries that do not match the cylindrical symmetry of the skyrmion -- such as as squares and triangles. Using simulation, we show that skyrmionic states can form the ground state for a range of system sizes in both triangular and square-shaped FeGe nanostructures of $10\,\text{nm}$ thickness in the absence of an applied field. We further provide data to assist in the experimental verification of our prediction; to imitate an experiment where the system is saturated with a strong applied field before the field is removed, we compute the time evolution and show the final equilibrium configuration of magnetization fields, starting from a uniform alignment., Comment: 7 pages, 7 figures

Computational micromagnetics requires numerical solution of partial differential equations to resolve complex interactions in magnetic nanomaterials. The Virtual Micromagnetics project described here provides virtual machine simulation environments to run open-source micromagnetic simulation packages. These environments allow easy access to simulation packages that are often difficult to compile and install, and enable simulations and their data to be shared and stored in a single virtual hard disk file, which encourages reproducible research. Virtual Micromagnetics can be extended to automate the installation of micromagnetic simulation packages on non-virtual machines, and to support closed-source and new open-source simulation packages, including packages from disciplines other than micromagnetics, encouraging reuse. Virtual Micromagnetics is stored in a public GitHub repository under a three-clause Berkeley Software Distribution (BSD) license., Comment: 12 pages, 1 figure

The potential for application of magnetic skyrmions in high density storage devices provides a strong drive to investigate and exploit their stability and manipulability. Through a three-dimensional micromagnetic hysteresis study, we investigate the question of existence of skyrmions in cylindrical nanostructures of variable thickness. We quantify the applied field and thickness dependence of skyrmion states, and show that these states can be accessed through relevant practical hysteresis loop measurement protocols. As skyrmionic states have yet to be observed experimentally in confined helimagnetic geometries, our work opens prospects for developing viable hysteresis process-based methodologies to access and observe skyrmionic states., Comment: 4 pages, 2 figures

In confined helimagnetic nanostructures, skyrmionic states in the form of incomplete and isolated skyrmion states can emerge as the ground state in absence of both external magnetic field and magnetocrystalline anisotropy. In this work, we study the dynamic properties (resonance frequencies and corresponding eigenmodes) of skyrmionic states in thin film FeGe disk samples. We employ two different methods in finite-element based micromagnetic simulation: eigenvalue and ringdown method. The eigenvalue method allows us to identify all resonance frequencies and corresponding eigenmodes that can exist in the simulated system. However, using a particular experimentally feasible excitation can excite only a limited set of eigenmodes. Because of that, we perform ringdown simulations that resemble the experimental setup using both in-plane and out-of-plane excitations. In addition, we report the nonlinear dependence of resonance frequencies on the external magnetic bias field and disk sample diameter and discuss the possible reversal mode of skyrmionic states. We compare the power spectral densities of incomplete skyrmion and isolated skyrmion states and observe several key differences that can contribute to the experimental identification of the state present in the sample. We measure the FeGe Gilbert damping, and using its value we determine what eigenmodes can be expected to be observed in experiments. Finally, we show that neglecting the demagnetisation energy contribution or ignoring the magnetisation variation in the out-of-film direction - although not changing the eigenmode's magnetisation dynamics significantly - changes their resonance frequencies substantially. Apart from contributing to the understanding of skyrmionic states physics, this systematic work can be used as a guide for the experimental identification of skyrmionic states in confined helimagnetic nanostructures., Comment: manuscript: 17 pages, 9 figures; supplementary information: 10 pages, 8 figures

Using finite element micromagnetic simulations, we study how resonant magnetisation dynamics in thin magnetic discs with perpendicular anisotropy are influenced by magnetostatic coupling to a magnetic nanoparticle. We identify resonant modes within the disc using direct magnetic eigenmode calculations and study how their frequencies and profiles are changed by the nanoparticle's stray magnetic field. We demonstrate that particles can generate shifts in the resonant frequency of the disc's fundamental mode which exceed resonance linewidths in recently studied spin torque oscillator devices. Importantly, it is shown that the simulated shifts can be maintained over large field ranges (here up to 1T). This is because the resonant dynamics (the basis of nanoparticle detection here) respond directly to the nanoparticle stray field, i.e. detection does not rely on nanoparticle-induced changes to the magnetic ground state of the disk. A consequence of this is that in the case of small disc-particle separations, sensitivities to the particle are highly mode- and particle-position-dependent, with frequency shifts being maximised when the intense stray field localised directly beneath the particle can act on a large proportion of the disc's spins that are undergoing high amplitude precession., Comment: 9 pages, 9 figures. Updated version from 31.7.2016 includes minor changes in introduction and sections III.C and III.D (additional information linking the results to real-world bio-sensing devices)

Nowadays, micromagnetic simulations are a common tool for studying a wide range of different magnetic phenomena, including the ferromagnetic resonance. A technique for evaluating reliability and validity of different micromagnetic simulation tools is the simulation of proposed standard problems. We propose a new standard problem by providing a detailed specification and analysis of a sufficiently simple problem. By analyzing the magnetization dynamics in a thin permalloy square sample, triggered by a well defined excitation, we obtain the ferromagnetic resonance spectrum and identify the resonance modes via Fourier transform. Simulations are performed using both finite difference and finite element numerical methods, with \textsf{OOMMF} and \textsf{Nmag} simulators, respectively. We report the effects of initial conditions and simulation parameters on the character of the observed resonance modes for this standard problem. We provide detailed instructions and code to assist in using the results for evaluation of new simulator tools, and to help with numerical calculation of ferromagnetic resonance spectra and modes in general.

We demonstrate that chiral skyrmionic magnetization configurations can be found as the minimum energy state in B20 thin film materials with easy-plane magnetocrystalline anisotropy with an applied magnetic field perpendicular to the film plane. Our observations contradict results from prior analytical work, but are compatible with recent experimental investigations. The size of the observed skyrmions increases with the easy-plane magnetocrystalline anisotropy. We use a full micromagnetic model including demagnetization and a three-dimensional geometry to find local energy minimum (metastable) magnetization configurations using numerical damped time integration. We explore the phase space of the system and start simulations from a variety of initial magnetization configurations to present a systematic overview of anisotropy and magnetic field parameters for which skyrmions are metastable and global energy minimum (stable) states., Comment: 5 pages, 3 figures

We review design and development decisions and their impact for the open source code Nmag from a software engineering in computational science point of view. We summarise lessons learned and recommendations for future computational science projects. Key lessons include that encapsulating the simulation functionality in a library of a general purpose language, here Python, provides great flexibility in using the software. The choice of Python for the top-level user interface was very well received by users from the science and engineering community. The from-source installation in which required external libraries and dependencies are compiled from a tarball was remarkably robust. In places, the code is a lot more ambitious than necessary, which introduces unnecessary complexity and reduces main- tainability. Tests distributed with the package are useful, although more unit tests and continuous integration would have been desirable. The detailed documentation, together with a tutorial for the usage of the system, was perceived as one of its main strengths by the community., Comment: 7 pages, 5 figures, Software Engineering for Science, ICSE2016

A phenomenological equation called Landau-Lifshitz-Baryakhtar (LLBar) equation, which could be viewed as the combination of Landau-Lifshitz (LL) equation and an extra "exchange damping" term, was derived by Baryakhtar using Onsager's relations. We interpret the origin of this "exchange damping" as nonlocal damping by linking it to the spin current pumping. The LLBar equation is investigated numerically and analytically for the spin wave decay and domain wall motion. Our results show that the lifetime and propagation length of short-wavelength magnons in the presence of nonlocal damping could be much smaller than those given by LL equation. Furthermore, we find that both the domain wall mobility and the Walker breakdown field are strongly influenced by the nonlocal damping., Comment: 10 pages, 6 figures

We demonstrate the use of the magnetic-field-dependence of highly spatially confined, GHz-frequency ferromagnetic resonances in a ferromagnetic nanostructure for the detection of adsorbed magnetic nanoparticles. This is achieved in a large area magnonic crystal consisting of a thin ferromagnetic film containing a periodic array of closely spaced, nano-scale anti-dots. Stray fields from nanoparticles within the anti-dots modify resonant dynamic magnetisation modes in the surrounding magnonic crystal, generating easily measurable resonance peak shifts. The shifts are comparable to the resonance linewidths for high anti-dot filling fractions with their signs and magnitudes dependent upon the modes' localisations (in agreement with micromagnetic simulation results). This is a highly encouraging result for the development of frequency-based nanoparticle detectors for high speed nano-scale biosensing., Comment: 7 pages, 5 figures

We study translational, breathing and twisting resonant modes of transverse magnetic domain walls pinned at notches in ferromagnetic nanostrips. We demonstrate that a mode's sensitivity to notches depends strongly on the characteristics of that particular resonance. For example, the frequencies of modes involving lateral motion of the wall are the ones which are most sensitive to changes in the notch intrusion depth (especially at the narrower, more strongly confined end of the domain wall). In contrast, the breathing mode, whose dynamics are concentrated away from the notches is relatively insensitive to changes in the notches' sizes. We also demonstrate a sharp drop in the translational mode's frequency towards zero when approaching depinning which is found, using a harmonic oscillator model, to be consistent with a reduction in the local slope of the notch-induced confining potential at its edge., Comment: 11 pages, 10 figures, additional data and analysis

We study domain wall (DW) motion induced by spin waves (magnons) in the presence of Dzyaloshinskii-Moriya interaction (DMI). The DMI exerts a torque on the DW when spin waves pass through the DW, and this torque represents a linear momentum exchange between the spin wave and the DW. Unlike angular momentum exchange between the DW and spin waves, linear momentum exchange leads to a rotation of the DW plane rather than a linear motion. In the presence of an effective easy plane anisotropy, this DMI induced linear momentum transfer mechanism is significantly more efficient than angular momentum transfer in moving the DW.

Magnetic skyrmions have the potential to provide solutions for low-power, high-density data storage and processing. One of the major challenges in developing skyrmion-based devices is the skyrmions' magnetic stability in confined helimagnetic nanostructures. Through a systematic study of equilibrium states, using a full three-dimensional micromagnetic model including demagnetisation effects, we demonstrate that skyrmionic textures are the lowest energy states in helimagnetic thin film nanostructures at zero external magnetic field and in absence of magnetocrystalline anisotropy. We also report the regions of metastability for non-ground state equilibrium configurations. We show that bistable skyrmionic textures undergo hysteretic behaviour between two energetically equivalent skyrmionic states with different core orientation, even in absence of both magnetocrystalline and demagnetisation-based shape anisotropies, suggesting the existence of Dzyaloshinskii-Moriya-based shape anisotropy. Finally, we show that the skyrmionic texture core reversal dynamics is facilitated by the Bloch point occurrence and propagation., Comment: manuscript: 14 pages, 7 figures; supplementary information: 8 pages, 7 figures

Recent studies have predicted extraordinary properties for transverse domain walls in cylindrical nanowires: zero depinning current, the absence of the Walker breakdown, and applications as domain wall oscillators. In order to reliably control the domain wall motion, it is important to understand how they interact with energy barriers. In this paper, we study the motion and depinning of transverse domain walls through potential barriers in ferromagnetic cylindrical nanowires. We use magnetic fields and spin-polarized currents to drive the domain walls along the wire. Using magnetic fields, we find that the minimum and the maximum fields required to push the domain wall through the barrier differ by 30 %. On the contrary, using spin-polarized currents, we find variations of a factor 130 between the minimum value of the depinning current density and the maximum value. We study the depinning current density as a function of the height of the energy barrier using numerical and analytical methods. We find that, for a barrier of 40 k_B T, a depinning current density of about 5 uA is sufficient to depin the domain wall. We reveal and explain the mechanism that leads to these unusually low depinning currents. One requirement for this new depinning mechanism is for the domain wall to be able to rotate around its own axis. With the right barrier design, the spin torque transfer term is acting exactly against the damping in the micromagnetic system, and thus the low current density is sufficient to accumulate enough energy quickly. These key insights may be crucial in furthering the development of novel memory technologies, such as the racetrack memory, that can be controlled through low current densities., Comment: 9 pages, 10 figures

This paper provides a realization of all classical and most exceptional finite groups of Lie type as Galois groups over function fields over F_q and derives explicit additive polynomials for the extensions. Our unified approach is based on results of Matzat which give bounds for Galois groups of Frobenius modules and uses the structure and representation theory of the corresponding connected linear algebraic groups., Comment: 59 pages; v2: added reference, slightly restructured section 6.1, few small rewordings; v3: completed realization of Steinberg's triality groups (thanks to P. Mueller for solving the remaining open question); clarified argument how to use Thm. 3.4