Session N54: Stability, Lifetime, and Nucleation of Skyrmions

Direct Demonstration of Topological Stability of Magnetic SkyrmionsviaTopology Manipulation

The topological concept, initially introduced in particle physics, brought new excitements to many other fields of physics, such as topological insulators, ultracold atoms, and topological lasers to unveil various robust states therein. In nanomagnetism, the most prominent example governed by topology is the magnetic skyrmion. Since magnetic skyrmions exhibit a nontrivial topological property, it is expected that skyrmions are robust against external perturbations. Therefore, it has sparked considerable interest due to the academic interest and the prospect of employing the skyrmions as the nanometer-scale non-volatile information carriers. Although profound the concept is, the realistic situation that magnetic moments are localized in a discrete atomic lattice raises an immediate question of whether the topological concept is still viable in the real system. Despite the fundamental importance, the thorough assessment has remained elusive due to the challenge of controlling topology and thereby directly comparing the topologically nontrivial skyrmions and trivial bubbles in a single specimen.

In this work, we first show how to manipulate magnetic topology. By tuning a magnetic field pathway, we could selectively prepare either a skyrmion state or bubble state in the same material. Based on this method, we then show how robust the magnetic skyrmion structure is compared to the stability of topologically trivial bubbles. By measuring the lifetimes of both skyrmions and bubbles in the same specimen under the same magnetic fields, we found that magnetic skyrmions exhibit far longer lifetimes with much smaller sizes, directly evidencing the topological effect in a real discrete system. Our results corroborate the physical importance of the topology in the magnetic materials and open up a versatile route towards topology manipulation, which will facilitate the implementation of ever-stable nanometer-scale magnetic devices.   

An ab-initio paradigm for exploring the stability of skyrmions

Magnetic skyrmions are topological defects in the magnetization texture. The typical sizes of skyrmions are small with diameters in the nanometer range. They behave as particles that can be created, moved, and annihilated. Topological properties strongly influence the stability and dynamics of skyrmions. Long living stable skyrmions are potential candidates for spintronic materials. Skyrmions are stabilized by Dzyaloshinskii–Moriya or asymmetric exchange interactions. Certain class of deformations and disorder influence the Dzyaloshinskii–Moriya interactions and hence the stability and dynamics of skyrmions. In this talk, we will present a multiscale paradigm to simulate skyrmions from first-principles calculations. We will talk about the role of disorder and lattice strains on the stability and dynamics of skyrmions.   

Dynamics of skyrmions driven by spin transfer and spin orbit torques

Skyrmions are topological magnetic textures with great potential for technological applications in magnetic devices. For efficient manipulation of skyrmions, it is important to understand how the motion of skyrmions can be driven by a current. We report on the motion of skyrmions in narrow channels in two different classes of materials: metallic materials with a spin transfer torque drive and ferromagnetic insulator-heavy metal bilayers with spin orbit torque from the spin Hall effect. Using numerical simulations and analytical approaches, we compare the two cases to elucidate the fastest possible speed that the skyrmions can achieve before becoming unstable.   

Dynamical Generation of Interactions and Floquet Skyrmions in Periodically Driven Spin Systems

Motivated by applications in synthetic quantum simulators, we study many-body Floquet spin systems with periodically driven two-body interactions and external fields in the high-frequency limit. We show that a hierarchy of multi-spin interactions can be generated in powers of inverse-frequency, such as Dzyaloshinskii–Moriya interaction (DMI), three- and four-spin interactions, and additional Zeeman terms. We consider different types of drives and lattice geometries in one and two dimensions to explore possible types of dynamically generated interactions. In particular, we focus on the DMI term in two-dimensional square and triangular lattices to study the dynamical generation of quantum skyrmions, controlled by drive parameters. Using exact diagonalization and hierarchical mean-field theory calculations, we characterize the energetic and topological signatures of possible skyrmion phases. This study is relevant to the experimental realization of Floquet skyrmion, for example, in recently demonstrated two-dimensional lattices of trapped ions.   

Skyrmion lattice formation and destruction mechanisms probed with SANS

A magnetic Skyrmions is a local whirl of the spin configuration in a magnetic material. These structures have promising applications in spintronic devices [1] due to their topological protection, which prevents them from being continuously created or destroyed. The formation and destruction time scales of skyrmions are important when it comes to applications. Typically, magnetic dynamics occur on the nanosecond (10-9 s) timeframe, however, the time scale of skyrmion formation may be much longer. In this work, we have measured the dynamics of skyrmion lattice formation in B20 materials MnSi, FeCoSi, Cu2OSeO3 using small-angle neutron scattering. The formation rate of skyrmions was a surprisingly slow 10's of ms. Using a stepped magnetic field, the material is moved into/out of the skyrmion stability window. Using time-domain slicing of the SANS data, the dynamics formation and destruction of the skyrmion lattice is captured in real-time. These results reveal that the formation/destruction dynamics occur between 27-40 ms. 

1.Desautels, R.D., et al., Physical Review Materials, 2019. 3(10).   

Computational Design of Long-Lifetime Room-Temperature Skyrmions

Magnetic skyrmions are spin textures that can serve as the key components in future logic devices. To retain information, long-term stability of the skyrmions at room temperature is necessary. Atomistic simulations have been developed to help identify the desirable skyrmionic materials [1-3]. We calculate the lifetimes of skyrmions at room temperature. To evaluate the activation energy for a collapsing skyrmion, the geodesic nudged elastic band (GNEB) method is employed. Additionally, the lifetime prefactor is obtained by using the harmonic approximation to the transition-state theory (HTST). Using these methods, skyrmions, with at least a year-long lifetime, are predicted in a 10 nm thick amorphous ferrimagnetic CoGd film. Additionally, we investigate the mechanism of skyrmion collapse along different reaction paths in the energy landscape. Furthermore, using machine learning, we explore several tunable parameters, including thickness, saturation magnetization, and Dzyaloshinskii-Moriya interactions (DMI), to optimize a heterostructure to host long-life room-temperature skyrmions.

[1] P. F. Bessarab et al., Phys. Rev. B 85, 184409 (2012).

[2] P. F. Bessarab et al., Comput. Phys. Commun 196, 335-347 (2015).

[3] M. Hoffmann et al., Phy. Rev. Lett. 124, 247201 (2020).   

Lifetime of metastable skyrmions in thin films of chiral magnets

Studying the lifetime of a metastable skyrmion in chiral magnetic materials is of fundamental interest and also of great importance for applications. We use a continuum field theory with exchange J, interfacial Dzyaloshinskii-Moriya interaction D, anisotropy K, and external field H, and compute the free energy barrier for the destruction for a skyrmion, using harmonic transition state theory (HTST) to take into account entropic effects. We show that the nature of the saddle point configuration changes from a Bloch point singularity in the 2D limit to a chiral bobber beyond a certain thickness in thin films. We discuss how the size and lifetime of metastable skyrmions vary across the (KJ/D², HJ/D²) phase diagram for the case of films with perpendicular magnetic anisotropy.   

Mechanism for ultrafast electric-field driven skyrmion nucleation

We show how, at ultrashort timescales, a Dzyaloshinskii-Moriya interaction can be generated in metallic thin films by an electromagnetic pulse. This interaction originates from the spin-orbit coupling between the pulse-induced electric field and the spins of the delocalized electrons of the material [1]. We perform density functional theory calculations to estimate the strength of this field-induced interaction in centrosymmetric Fe, Co, Ni, and Mn monolayers, as well as FePt and MnPt alloys. Last, using atomistic simulations, we demonstrate how an isolated antiferromagnetic skyrmion can be coherently nucleated from the collinear background by an electric field pulse at the 100-fs timescale [2]. These results provide a new handle for an ultrafast, coherent control of noncollinear magnetic states.

[1] Imamura et al., PRB 69, 121303(R) (2014) ; Hinschberger et al., PRA 93, 042117 (2016) ; Bouaziz et al., New J. Phys. 19, 023010 (2017)

[2] Desplat et al., PRB 104, L060409 (2021)   

Visually informed guesses of Chain-Of-States methods to find saddle points of the energy landscape in chiral magnetic nanodisks.

Magnetic systems with an interfacially-induced Dzyaloshinskii-Moriya Interaction (DMI) are currently the focus of active research as candidates for devices in information technologies [1-6]. A crucial figure of merit is the height of the minimum energy barrier that separates adjacent minima, since it determines stability against thermal fluctuations. It is difficult to determine analytically the transition states for thermal activated switching. This difficulty is exacerbated in the presence of DMI which roughens the energy landscape and introduces many minima. Numerically, a family of numerical algorithms relies on the evolution of chains-of-states to identify transition states [7-9]. These methods use initial guesses for transition paths that evolve downwards in energy until convergence is achieved. We highlight the importance of considering visual features of energy minima in the initial guesses for chain-of-states. Two advantages of our improved guesses are a dramatic reduction of relaxation steps, and avoidance of topological defects that correspond to singularities of the energy landscape.   

Skyrmion nucleation on a surface of topological insulators

Skyrmion nucleation induced by spin-transfer torques at an interface of a topological insulator and a ferromagnetic insulator is investigated. Due to strong spin-orbit coupling on a surface of topological insulators, which enhances the effect of spin torques, efficient manipulation of skyrmions is expected and therefore, topological insulators could provide the ideal platform to achieve high-performance skyrmionic devices.  Using micromagnetic simulations and energetics, we evaluate properties of the skyrmion nucleation on a surface of topological insulators, such as nucleation time, critical electric field, and skyrmion numbers. We show that the nucleation time is inversely proportional to the applied electric field, while the skyrmion number linearly increases with the field in the vicinity of the critical field. We also identify the Gilbert damping and temperature dependences of the critical field. Furthermore, we analytically evaluate the effect of the Dzyaloshinskii-Moriya interaction and demonstrate that the temperature dependence can be explained by the reduction of a magnon excitation gap due to the self-energy corrections.   

Optimizing skyrmion properties for technological applications: an atomistic perspective

Chiral magnetic skyrmions are not only of great scientific interest but also of potential relevance in information technology, data storage, and neuromorphic computing. Their desirable properties – such as their lifetime, mobility, and robustness with respect to external influences – depend hereby on the specific technological application. Therefore, the skyrmion properties need to be tuned accordingly to be able to compete with existing technologies or to even outperform those.

In this talk, I will present our recent works related to the optimization of skyrmion hosting materials and provide an atomistic insight into how skyrmion properties can be tuned. Our investigations are based on micromagnetic arguments as well as atomistic spin-dynamics simulations, carried out with our Spirit code [1]. To obtain static properties, we perform LLG and GNEB simulations, which provide us the energy barrier and the corresponding saddle point structure, and combine those with HTST [2] calculations to determine the lifetime prefactor. Additionally, we perform LLG simulations to investigate the dynamics of skyrmions.

In a recent publication [3], we showed that going beyond the micromagnetic limit, i.e., introducing frustration of magnetic interactions as well as considering structural aspects, provides a bright outlook for lifetime dependence on the materials properties. Additionally, I will show that the skyrmion profile, i.e., the functional dependence of the magnetization on the position relative to the skyrmion core, has a tremendous influence on skyrmion lifetime, stability, and dynamics, and I will demonstrate how the skyrmion profile can be tuned to optimize skyrmion properties.

[1] Spirit spin simulation framework, spirit-code.github.io

[2] P. F. Bessarab et al., Phys. Rev. B 85, 184409 (2012)

[3] M. Hoffmann et al., Phys. Rev. Lett. 124, 247201 (2020)