Marc-Antonio Bisotti

Ground state search, hysteretic behaviour, and reversal mechanism of skyrmionic textures in confined helimagnetic nanostructures

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.

Magnon-driven domain-wall motion with the Dzyaloshinskii-Moriya interaction

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.

Thermal stability and topological protection of skyrmions in nanotracks

Magnetic skyrmions are hailed as a potential technology for data storage and other data processing devices. However, their stability against thermal fluctuations is an open question that must be answered before skyrmion-based devices can be designed. In this work, we study paths in the energy landscape via which the transition between the skyrmion and the uniform state can occur in interfacial Dzyaloshinskii-Moriya finite-sized systems. We find three mechanisms the system can take in the process of skyrmion nucleation or destruction and identify that the transition facilitated by the boundary has a significantly lower energy barrier than the other energy paths. This clearly demonstrates the lack of the skyrmion topological protection in finite-sized magnetic systems. Overall, the energy barriers of the system under investigation are too small for storage applications at room temperature, but research into device materials, geometry and design may be able to address this.

Dynamics of skyrmionic states in confined helimagnetic nanostructures

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 eigenmodes 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.

Skyrmions in thin films with easy-plane magnetocrystalline anisotropy

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.

Phenomenological description of the nonlocal magnetization relaxation in magnonics, spintronics, and domain-wall dynamics

A phenomenological equation called the Landau-Lifshitz-Baryakhtar (LLBar) [Zh. Eksp. Teor. Fiz 87, 1501 (1984) [Sov. Phys. JETP 60, 863 (1984)]] equation, which could be viewed as the combination of the Landau-Lifshitz (LL) equation and an extra “exchange-damping” term, was derived by Baryakhtar using Onsagers 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 the LL equation. Furthermore, we find that both the domain-wall mobility and the Walker breakdown field are strongly influenced by the nonlocal damping

Hysteresis of nanocylinders with Dzyaloshinskii-Moriya interaction

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.

Proposal of a micromagnetic standard problem for ferromagnetic resonance simulations

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 OOMMF and 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.

Supplementary data: Dynamics of skyrmionic states in confined helimagnetic nanostructures

Data for the paper: Beg, Marijan, Albert, Maximilian, Bisotti, Marc-Antonio, Cortes-Ortuno, David, Wang, Weiwei, Carey, Rebecca, Vousden, Mark, Hovorka, Ondrej, Ciccarelli, Chiara, Spencer, Charles S., Marrows, Christopher H. and Fangohr, Hans (2016) Dynamics of skyrmionic states in confined helimagnetic nanostructures. Physical Review B, 1-17. File headers contain description of data.Funded by EPSRC (Spin-Torque and Spin Polarisation in Epitaxial Magnetic Silicides, EP/J007110/1, 2011 to 2014).

Virtual Micromagnetics: A Framework for Accessible and Reproducible Micromagnetic Simulation

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.