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In this Letter, we present a design of a helimagnet-based emerging memory device that is capable of storing multiple bits of information per device. The device consists of a helimagnet layer placed between two ferromagnetic layers, which allows us to lock-in specific spin configurations. The bottom pinned layer has high anisotropy energy or stays exchange biased, which keeps its spin configuration fixed on a specific direction, while the top layer is free to rotate under the influence of in-plane magnetic fields. We begin by finding the relaxed spin structure, which is the result of the competition between the Dzyaloshinskii–Moriya interaction (DMI) and exchange energy and is referred to as the equilibrium state (“0”). The writing of a memory state is simulated by applying an in-plane field that rotates and transforms the spin configurations of the memory device. Our results indicate that stable configurations can be achieved at rotations of an integer multiple of 180° (corresponding to states “−2,” “−1,” “1,” “2,” etc.), where the anisotropy stabilizes the free layer and, thus, the exchange coupled helimagnet. These states are separated by magnetic energy barriers and intermediate, unstable spin configurations tend to revert to their adjacent states. By simply changing the direction of the field, we can achieve multi-bit data storage per unit memory cell. The maximum number of bits is reached when the anisotropy energy barriers cannot withstand the strong DMI energy. Reading can be done by evaluating the different resistance states due to the twisted spin texture.

Computational micromagnetics has become an essential tool in academia and industry to support fundamental research and the design and development of devices. Consequently, computational micromagnetics is widely used in the community, and the fraction of time researchers spend performing computational studies is growing. We focus on reducing this time by improving the interface between the numerical simulation and the researcher. We have designed and developed a human-centred research environment called Ubermag. With Ubermag, scientists can control an existing micromagnetic simulation package, such as OOMMF, from Jupyter notebooks. The complete simulation workflow, including definition, execution, and data analysis of simulation runs, can be performed within the same notebook environment. Numerical libraries, co-developed by the computational and data science community, can immediately be used for micromagnetic data analysis within this Python-based environment. By design, it is possible to extend Ubermag to drive other micromagnetic packages from the same environment., Comment: 5 pages, 2 figures

Literate computing has emerged as an important tool for computational studies and open science, with growing folklore of best practices. In this work, we report two case studies - one in computational magnetism and another in computational mathematics - where domain-specific software was exposed to the Jupyter environment. This enables high-level control of simulations and computation, interactive exploration of computational results, batch processing on HPC resources, and reproducible workflow documentation in Jupyter notebooks. In the first study, Ubermag drives existing computational micromagnetics software through a domain-specific language embedded in Python. In the second study, a dedicated Jupyter kernel interfaces with the GAP system for computational discrete algebra and its dedicated programming language. In light of these case studies, we discuss the benefits of this approach, including progress toward more reproducible and reusable research results and outputs, notably through the use of infrastructure such as JupyterHub and Binder., Comment: 11 pages, 3 figures

The intense research effort investigating magnetic skyrmions and their applications for spintronics has yielded reports of more exotic objects including the biskyrmion, which consists of a bound pair of counter-rotating vortices of magnetization. Biskyrmions have been identified only from transmission electron microscopy images and have not been observed by other techniques, nor seen in simulations carried out under realistic conditions. Here, quantitative Lorentz transmission electron microscopy, X-ray holography, and micromagnetic simulations are combined to search for biskyrmions in MnNiGa, a material in which they have been reported. Only type-I and type-II magnetic bubbles are found and images purported to show biskyrmions can be explained as type-II bubbles viewed at an angle to their axes. It is not the magnetization but the magnetic flux density resulting from this object that forms the counter-rotating vortices.

Research on magnetic systems with broken inversion symmetry has been stimulated by the experimental proof of particle-like configurations known as skyrmions, whose non-trivial topological properties make them ideal candidates for spintronic technology. This class of materials enables Dzyaloshinskii-Moriya interactions (DMI) which favor the stabilization of chiral configurations. Recent advances in material engineering have shown that in confined geometries it is possible to stabilize skyrmionic configurations at zero field. Moreover, it has been shown that in systems based on Pd/Fe bilayers on top of Ir(111) surfaces skyrmions can be as small as a few nanometres in diameter. In this work we present scanning tunneling microscopy measurements of small Pd/Fe and Pd$_2$/Fe islands on Ir(111) that exhibit a variety of different spin textures, which can be reproduced using discrete spin simulations. These configurations include skyrmions and skyrmion-like states with extra spin rotations such as the target state, which have been of interest due to their promising dynamic properties. Furthermore, using simulations we analyze the stability of these skyrmionic textures as a function of island size, applied field and boundary conditions of the system. An understanding of the parameters and conditions affecting the stability of these magnetic structures in confined geometries is crucial for the development of energetically efficient and optimally sized skyrmion-based devices., 20 pages, 13 figures, Supplemental Material 16 pages

Journal of synchrotron radiation 26(5), 1448 - 1461 (2019). doi:10.1107/S1600577519006696, The Karabo distributed control system has been developed to address the challenging requirements of the European X-ray Free Electron Laser facility, including complex and custom-made hardware, high data rates and volumes, and close integration of data analysis for distributed processing and rapid feedback. Karabo is a pluggable, distributed application management system forming a supervisory control and data acquisition environment as part of a distributed control system. Karabo provides integrated control of hardware, monitoring, data acquisition and data analysis on distributed hardware, allowing rapid control feedback based on complex algorithms. Services exist for access control, data logging, configuration management and situational awareness through alarm indicators. The flexible framework enables quick response to the changing requirements in control and analysis, and provides an efficient environment for development, and a single interface to make all changes immediately available to operators and experimentalists., Published by Wiley-Blackwell, [S.l.]

Understanding the role of the Dzyaloshinskii–Moriya interaction (DMI) for the formation of helimagnetic order, as well as the emergence of skyrmions in magnetic systems that lack inversion symmetry, has found increasing interest due to the significant potential for novel spin based technologies. Candidate materials to host skyrmions include those belonging to the B20 group such as FeGe, known for stabilising Bloch-like skyrmions, interfacial systems such as cobalt multilayers or Pd/Fe bilayers on top of Ir(111), known for stabilising Néel-like skyrmions, and, recently, alloys with a crystallographic symmetry where anti-skyrmions are stabilised. Micromagnetic simulations have become a standard approach to aid the design and optimisation of spintronic and magnetic nanodevices and are also applied to the modelling of device applications which make use of skyrmions. Several public domain micromagnetic simulation packages such as OOMMF, MuMax3 and Fidimag already offer implementations of different DMI terms. It is therefore highly desirable to propose a so-called micromagnetic standard problem that would allow one to benchmark and test the different software packages in a similar way as is done for ferromagnetic materials without the DMI. Here, we provide a sequence of well-defined and increasingly complex computational problems for magnetic materials with DMI. Our test problems include 1D, 2D and 3D domains, spin wave dynamics in the presence of DMI, and validation of the analytical and numerical solutions including uniform magnetisation, edge tilting, spin waves and skyrmion formation. This set of problems can be used by developers and users of new micromagnetic simulation codes for testing and validation and hence establishing scientific credibility.

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

The prediction of magnetic skyrmions being used to change the way we store and process data has led to materials with Dzyaloshinskii-Moriya interaction coming into the focus of intensive research. So far, studies have looked mostly at magnetic systems composed of materials with single chirality. In a search for potential future spintronic devices, combination of materials with different chirality into a single system may represent an important new avenue for research. Using finite element micromagnetic simulations, we study an FeGe disk with two layers of different chirality. We show that for particular thicknesses of layers, a stable Bloch point emerges at the interface between two layers. In addition, we demonstrate that the system undergoes hysteretic behaviour and that two different types of Bloch point exist. These `head-to-head' and `tail-to-tail' Bloch point configurations can, with the application of an external magnetic field, be switched between. Finally, by investigating the time evolution of the magnetisation field, we reveal the creation mechanism of the Bloch point. Our results introduce a stable and manipulable Bloch point to the collection of particle-like state candidates for the development of future spintronic devices., Comment: 8 pages, 4 figures

Confined nanogeometries have proved interesting research arenas in magnetism in recent years, with bit-patterned media being one prospective method for increasing storage densities of future hard drives [1].

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.

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., 4 pages, 2 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., 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)

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., 5 pages, 3 figures

Fidimag is an open-source scientific code for the study of magnetic materials at the nano- or micro-scale using either atomistic or finite difference micromagnetic simulations, which are based on solving the Landau-Lifshitz-Gilbert equation. In addition, it implements simple procedures for calculating energy barriers in the magnetisation through variants of the nudged elastic band method. This computer software has been developed with the aim of creating a simple code structure that can be readily installed, tested, and extended. An agile development approach was adopted, with a strong emphasis on automated builds and tests, and reproducibility of results. The main code and interface to specify simulations are written in Python, which allows simple and readable simulation and analysis configuration scripts. Computationally costly calculations are written in C and exposed to the Python interface as Cython extensions. Docker containers are shipped for a convenient setup experience. The code is freely available on GitHub and includes documentation and examples in the form of Jupyter notebooks., Comment: 11 pages, 4 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

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

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 show theoretically by numerically solving the Landau-Lifshitz-Gilbert equation with a classical spin model on a two-dimensional system that both magnetic skyrmions and skyrmion lattices can be moved with microwave magnetic fields. The mechanism is enabled by breaking the axial symmetry of the skyrmion, for example, through application of a static in-plane external field. The net velocity of the skyrmion depends on the frequency and amplitude of the microwave fields as well as the strength of the in-plane field. The maximum velocity is found where the frequency of the microwave coincides with the resonance frequency of the breathing mode of the skyrmions.

We study domain-wall (DW) motion induced by spin waves (magnons) in the presence of the 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.

The nonlinear dynamic behavior of a magnetic skyrmion in circular nanodots was studied numerically by solving the Landau-Lifshitz-Gilbert equation with a classical spin model. We show that a skyrmion core reversal can be achieved within nanoseconds using a perpendicular oscillating magnetic field. Two symmetric switching processes that correspond to excitations of the breathing mode and the mixed mode (combination of the breathing mode and a radial spin- wave mode) are identified. For excitation of the breathing mode, the skyrmion core switches through nucleation of a new core from a transient uniform state. In the mixed mode, the skyrmion core reverses with the help of spins excited both at the edge and core regions. Unlike the magnetic vortex core reversal, the excitation of radial spin waves does not dominate the skyrmion core reversal process.

High coercivity magnets are an important resource for renewable energy, electric vehicles and memory technologies. Most hard magnetic materials incorporate rare-earths such as neodymium and samarium, but the concerns about the environmental impact and supply stability of these materials is prompting research into alternatives. Here, we present a hybrid bilayer of cobalt and the nano-carbon molecule C60 which exhibits significantly enhanced coercivity with minimal reduction in magnetisation. We demonstrate how this anisotropy enhancing effect cannot be described by existing models of molecule-metal magnetic interfaces. We outline a new form of magnetic anisotropy, arising from asymmetric magneto-electric coupling in the metal-molecule interface. Because this phenomenon arises from pi-d hybrid orbitals, we propose calling this effect pi-anisotropy. While the critical temperature of this effect is currently limited by the rotational degree of freedom of the chosen molecule, C60, we describe how surface functionalisation would allow for the design of room-temperature, carbon based hard magnetic films., 16 pages, 4 figures