Chiral Bobber Research Articles

Micromagnetic study of the dynamics of toron chains

This work analyzes the nucleation and stabilization of torons in cylindrical nanopillars with bulk DMI and easy-plane anisotropy. A micromagnetic study reveals the dependence of toron chains on the nanopillar length and the different behaviors when nucleating an even or odd number of torons in a magnetic nanopillar. Spin wave resonant modes in these systems are explored, evidencing differences according to the number of torons. The interplay between torons, chiral bobbers, and their associated spin wave modes is analyzed, which is relevant for applications demanding dynamical modes in the range of gigahertz.

Spin-wave-driven tornado-like dynamics of three-dimensional topological magnetic textures

The abundant topological magnetic textures in three-dimensional systems provide opportunities to investigate the fundamental spin dynamics and realize spintronic applications. The dynamics of such magnetic textures have however rarely been studied, especially for those driven by spin waves, which allow applications with ultralow energy consumption and ease of implementation even in insulating systems. Here, we report our micromagnetic simulations on the spin-wave-driven dynamics of a skyrmion tube (SkT) and chiral bobber (ChB) in a thick magnetic film. We predict tornado-like dynamics in both SkT and ChB, where the topological centers present a lateral rotation with the rotation centers forming a distorted profile in the thickness direction. While the velocity of SkT scales with the driving power, the ChB motion presents a threshold in the driving field, which is found to depend linearly on its penetration length. This distinct behavior could be useful to differentiate ChB from SkT and estimate its penetration length experimentally.

Seeding and Emergence of Composite Skyrmions in a van der Waals Magnet.

Topological charge plays a significant role in a range of physical systems. In particular, observations of real-space topological objects in magnetic materials have been largely limited to skyrmions - states with a unitary topological charge. Recently, more exotic states with varying topology, such as antiskyrmions, merons, or bimerons and 3D states such as skyrmion strings, chiral bobbers, and hopfions, have been experimentally reported. Along these lines, the realization of states with higher-order topology has the potential to open new avenues of research in topological magnetism and its spintronic applications. Here, real-space imaging of such spin textures, including skyrmion, skyrmionium, skyrmion bag, and skyrmion sack states, observed in exfoliated flakes of the van der Waals magnet Fe3-x GeTe2 (FGT) is reported. These composite skyrmions may emerge from seeded, loop-like states condensed into the stripe domain structure, demonstrating the possibility to realize spin textures with arbitrary integer topological charge within exfoliated flakes of 2D magnets. The general nature of the formation mechanism motivates the search for composite skyrmion states in both well-known and new magnetic materials, which may yet reveal an even richer spectrum of higher-order topologicalobjects.

Microscopic origin of the electric Dzyaloshinskii-Moriya interaction

The microscopic origin of the electric Dzyaloshinskii-Moriya interaction (eDMI) is unveiled and discussed by analytical analysis and first-principles based calculations. As similar to the magnetic Dzyaloshinskii-Moriya interaction (mDMI), eDMI also originates from the electron-mediated effect and more specifically from certain electron hoppings that are being activated due to certain local inversion-symmetry breaking. However, the eDMI energy is found to be at least a third-order interaction in atomic displacements instead of bilinear in magnetic dipole moments for mDMI. Furthermore, the eDMI energy form is presented, and we find that novel electrical topological defects (namely, chiral electric bobbers) can arise from this eDMI. Thus unraveling the microscopic origin of eDMI has the potential to lead to, and explain, the discovery of novel polar topological phases.

Real-Space Observations of Three-Dimensional Antiskyrmions and Skyrmion Strings.

Nanometric topological spin textures, such as skyrmions (Sks) and antiskyrmions (antiSks), have attracted much attention recently. However, most studies have focused on two-dimensional spin textures in films with inherent or synthetic antisymmetric spin-exchange interaction, termed Dzyaloshinskii-Moriya interaction, although three-dimensional (3D) topological spin textures, such as antiSks composed of alternating Bloch- and Néel-type spin spirals, chiral bobbers carrying emergent magnetic monopoles, and deformed Sk strings, are ubiquitous. To elucidate these textures, we have developed a 3D nanometric magnetic imaging technique, tomographic Lorentz transmission electron microscopy (TEM). The approach enables the visualization of the 3D shape of magnetic objects and their 3D vector field mapping. Here we report 3D vector field maps of deformed Sk-strings and antiSk using the technique. This research approach will lead to discoveries and understanding of fertile 3D magnetic structures in a broad class of magnets, providing insight into 3D topological magnetism.

Breathing mode dynamics of coupled three-dimensional chiral bobbers

Recently, three-dimensional (3D) magnetic textures have moved into the focus of spintronics as both technologically relevant and physically intriguing on a fundamental level. A rich variety of 3D textures is currently being investigated; however, their unambiguous experimental detection and detailed study remains challenging. In this work, a new type of chiral 3D spin-texture, consisting of two antiferromagnetically coupled Néel bobbers, is explored. The static properties of this structure depend on the chirality of the individual bobbers. Different chirality combinations are studied with regard to their phase stability regions by micromagnetic simulations and compared to antiferromagnetically coupled skyrmion tubes. Furthermore, the coupled internal breathing modes are investigated by application of a periodically alternating external magnetic field. The breathing modes of each studied system possess a unique fingerprint, which might allow for the identification of the resonating spin textures via their dispersion curves.

Bloch point dynamics in exchange-spring heterostructures

Magnetization textures that are stabilized by topological constraints, such as skyrmions and chiral bobbers, as well as the emergent electrodynamics associated with their motion, provide a promising avenue toward novel energy-efficient nanomagnetic devices. Here, it is shown that exchange-spring-type heterostructures, where soft ferromagnets with azimuthal symmetry are exchange-coupled to a ferromagnetic layer with perpendicular magnetic anisotropy, can be used for the creation and control of skyrmion tubes and Bloch points during magnetization reversal of the soft ferromagnet, where the rapid motion of the Bloch points induces an emergent electric field with a magnitude of the order of megavolts per meter. The exchange coupling to the hard ferromagnet restores the system to its original configuration, making the process fully reversible and repeatable, and the duration of the magnetization processes and the motion of the Bloch points can be tuned by adjusting the size of the ferromagnet. Based on these numerical predictions, it is proposed that exchange-spring heterostructures could be used to generate picosecond electromagnetic pulses.

Current-induced dynamics and tunable spectra of a magnetic chiral bobber

Chiral bobber (ChB) is an exotic three-dimensional topological texture in chiral magnets. It is composed of a Bloch-point singularity and a skyrmion tube; the incommensurate characteristic length scales of these two components would thus lead to novel dynamics of a ChB. Here, we report the current-induced motion and the accompanying Hall effect of a ChB. Surprisingly, we find that the Hall angle of a ChB can be tuned in a wide range from \ensuremath{-}90 \ifmmode^\circ\else\textdegree\fi{} to positive angles. A further study of spin-wave excitations identified high-frequency resonant modes, which are related to the velocity of ChB and lattice constants. The excited frequency can be two orders of magnitude higher than that of skyrmions. The broad ranges of Hall angles and frequency spectra could boost the development of spintronic devices using topological textures.

Chiral polarization textures induced by the flexoelectric effect in ferroelectric nanocylinders

Polar chiral structures have recently attracted much interest within the scientific community, as they pave the way towards innovative device concepts similar to the developments achieved in nanomagnetism. Despite the growing interest, many fundamental questions related to the mechanisms controlling the appearance and stability of ferroelectric topological structures remain open. In this context, ferroelectric nanoparticles provide a flexible playground for such investigations. Here, we present a theoretical study of ferroelectric polar textures in a cylindrical core-shell nanoparticle. The calculations reveal a chiral polarization structure containing two oppositely oriented diffuse axial domains located near the cylinder ends, separated by a region with a zero-axial polarization. We name this polarization configuration "flexon" to underline the flexoelectric nature of its axial polarization. Analytical calculations and numerical simulation results show that the flexon's chirality can be switched by reversing the sign of the flexoelectric coefficient. Furthermore, the anisotropy of the flexoelectric coupling is found to critically influence the polarization texture and domain morphology. The flexon rounded shape, combined with its distinct chiral properties and the localization nature near the surface, are reminiscent of Chiral Bobber structures in magnetism. In the azimuthal plane, the flexon displays the polarization state of a vortex with an axially polarized core region, i.e., a meron. The flexoelectric effect, which couples the electric polarization and elastic strain gradients, plays a determining role in the stabilization of these chiral states. We discuss similarities between this interaction and the recently predicted ferroelectric Dyzaloshinskii-Moriya interaction leading to chiral polarization states.

Creation of a Chiral Bobber Lattice in Helimagnet-Multilayer Heterostructures.

A chiral bobber is a localized three-dimensional magnetization configuration, terminated by a singularity. Chiral bobbers coexist with magnetic skyrmions in chiral magnets, lending themselves to new types of skyrmion-complementary bits of information. However, the on-demand creation of bobbers, as well as their direct observation remained elusive. Here, we introduce a new mechanism for creating a stable chiral bobber lattice state via the proximity of two skyrmion species with comparable size. This effect is experimentally demonstrated in a Cu_{2}OSeO_{3}/[Ta/CoFeB/MgO]_{4} heterostructure in which an exotic bobber lattice state emerges in the phase diagram of Cu_{2}OSeO_{3}. To unambiguously reveal the existence of the chiral bobber lattice state, we have developed a novel characterization technique, magnetic truncation rod analysis, which is based on resonant elastic x-ray scattering.

Coexistence of distinct skyrmion phases observed in hybrid ferromagnetic/ferrimagnetic multilayers

Materials hosting magnetic skyrmions at room temperature could enable compact and energetically-efficient storage such as racetrack memories, where information is coded by the presence/absence of skyrmions forming a moving chain through the device. The skyrmion Hall effect leading to their annihilation at the racetrack edges can be suppressed, for example, by antiferromagnetically-coupled skyrmions. However, avoiding modifications of the inter-skyrmion distances remains challenging. As a solution, a chain of bits could also be encoded by two different solitons, such as a skyrmion and a chiral bobber, with the limitation that it has solely been realized in B20-type materials at low temperatures. Here, we demonstrate that a hybrid ferro/ferri/ferromagnetic multilayer system can host two distinct skyrmion phases at room temperature, namely tubular and partial skyrmions. Furthermore, the tubular skyrmion can be converted into a partial skyrmion. Such systems may serve as a platform for designing memory applications using distinct skyrmion types.

Prediction of confined and controllable Bloch points in nanocubes of chiral magnets

This work predicts that individual Bloch points can be created and stabilized by magnetostatic and chiral interactions in nanocuboids, confined in between two chiral bobbers of opposing polarity. The Bloch point can be moved by an external magnetic field of moderate strength but only if the field strength is enough to overcome a pinning potential that results from intrinsic exchange forces and extrinsic surface effects. The Bloch point can be driven by the external field reversibly, in a direction opposing the field, and it remains stable up to moderate field strengths. At a critical field strength the Bloch point escapes through one of the surfaces, leaving behind a collinear magnetization configuration, and upon removing the field a new Bloch point is formed. These findings highlight the topological diversity in nanostructures and show that a Bloch point, despite its zero-dimensionality, couples to external fields via a substantial magnetic volume around it. The control of topological point defects has technological implications with regards to reversibly movable nanomagnetic textures and their associated emergent electrodynamics.

Efficient optimization method for finding minimum energy paths of magnetic transitions

Efficient algorithms for the calculation of minimum energy paths of magnetic transitions are implemented within the geodesic nudged elastic band (GNEB) approach. While an objective function is not available for GNEB and a traditional line search can, therefore, not be performed, the use of limited memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) and conjugate gradient algorithms in conjunction with orthogonal spin optimization (OSO) approach is shown to greatly outperform the previously used velocity projection and dissipative Landau–Lifschitz dynamics optimization methods. The implementation makes use of energy weighted springs for the distribution of the discretization points along the path and this is found to improve performance significantly. The various methods are applied to several test problems using a Heisenberg-type Hamiltonian, extended in some cases to include Dzyaloshinskii–Moriya and exchange interactions beyond nearest neighbours. Minimum energy paths are found for magnetization reversals in a nano-island, collapse of skyrmions in two-dimensional layers and annihilation of a chiral bobber near the surface of a three-dimensional magnet. The LBFGS-OSO method is found to outperform the dynamics based approaches by up to a factor of 8 in some cases.

Localized structures in magnetic systems without the center of inversion

The main theoretical and experimental results of the study of magnetic skyrmions in films of isotropic chiral magnets are considered. A significant part of the paper presents new results that were not included in previous monographs and reviews. Skyrmions are formations characterized by a quantized topological number. They attract considerable attention of researchers due to their dynamics in external fields, which has promising features in terms of applications in spintronics. Special attention is given to the structure and interaction of 3D skyrmions, and a new magnetic structure — the chiral bobber — is considered.

ЭКСПЕРИМЕНТАЛЬНОЕ ОБНАРУЖЕНИЕ БОББЕРОВ И НОВАЯ КОНЦЕПЦИЯ МАГНИТНОЙ ТВЕРДОТЕЛЬНОЙ ПАМЯТИ

Chiral magnetic skyrmions are nanoscale vortex-like spin textures that form in the presence of an applied magnetic field in ferromagnets that support the DzyaloshinskiiMoriya interaction (DMI) because of strong spin-orbit coupling and broken inversion symmetry of the crystal. Recently, a new type of localized particle-like object – the chiral bobber (ChB) – was predicted theoretically (Rybakov et al., 2015) in such materials. Here, we report the direct observation of ChBs (Zheng et al., 2018) in thin films of B20-type FeGe by means of quantitative off-axis electron holography. Furthermore, we show that ChBs are able to coexist with skyrmions over a wide range of parameters, which suggests their possible practical applications in novel magnetic solid-state memory devices, in which a stream of binary data bits can be encoded by a sequence of skyrmions and bobbers. Work was performed within the state task of FANO Russia (subject “Quantum,” No. g.r. 01201463332) (АААА-А18-118020190095-4)).

Distinct magnetotransport and orbital fingerprints of chiral bobbers

While chiral magnetic skyrmions have been attracting significant attention in the past years, recently, a new type of a chiral particle emerging in thin films $-$ a chiral bobber $-$ has been theoretically predicted and experimentally observed. Here, based on theoretical arguments, we provide a clear pathway to utilizing chiral bobbers for the purposes of future spintronics by uncovering that these novel chiral states possess inherent transport fingerprints that allow for their unambiguous electrical detection in systems comprising several types of chiral states. We reveal that unique transport and orbital characteristics of bobbers root in the non-trivial magnetization distribution in the vicinity of the Bloch points, and demonstrate that tuning the details of the Bloch point topology can be used to drastically alter the emergent response properties of chiral bobbers to external fields, which bears great potential for engineering chiral dynamics and cognitive computing.

Homogeneous and heterogeneous nucleation of skyrmions in thin layers of cubic helimagnets

Formation of isolated chiral skyrmions by homogeneous and heterogeneous nucleation has been studied in thin layers of cubic helimagnets via elongation of torons and chiral bobbers, correspondingly. Both torons and bobbers are localized in three dimensions, contain singularities, and according to the theoretical analysis within the standard phenomenological models can exist as metastable states in saturated and modulated phases of noncentrosymmetric ferromagnets. Their elongation into the defect-free skyrmion filament is facilitated by small anisotropic contributions making skyrmion cores negative with respect to the surrounding parental state. We show that isolated magnetic torons pose the same problem of compatibility with a surrounding phase as the torons in confinement-frustrated chiral nematics [I. Smalyukh et al., Nature Mater 9, 139-145 (2010)]. We underline the distinct features of magnetic and liquid-crystals torons and calculate phase diagrams indicating their stability regions.

Chiral bobbers and skyrmions in epitaxial FeGe/Si(111) films

We report experimental and theoretical evidence for the formation of chiral bobbers - an interfacial topological spin texture - in FeGe films grown by molecular beam epitaxy (MBE). After establishing the presence of skyrmions in FeGe/Si(111) thin film samples through Lorentz transmission electron microscopy and topological Hall effect, we perform magnetization measurements that reveal an inverse relationship between film thickness and the slope of the susceptibility (d\c{hi}/dH). We present evidence for the evolution as a function of film thickness, L, from a skyrmion phase for L < LD/2 to a cone phase with chiral bobbers at the interface for L > LD/2, where LD ~ 70 nm is the FeGe pitch length. We show using micromagnetic simulations that chiral bobbers, earlier predicted to be metastable, are in fact the stable ground state in the presence of an additional interfacial Rashba Dzyaloshinskii-Moriya interaction (DMI).

Experimental observation of chiral magnetic bobbers in B20-type FeGe.

Chiral magnetic skyrmions1,2 are nanoscale vortex-like spin textures that form in the presence of an applied magnetic field in ferromagnets that support the Dzyaloshinskii-Moriya interaction (DMI) because of strong spin-orbit coupling and broken inversion symmetry of the crystal3,4. In sharp contrast to other systems5,6 that allow for the formation of a variety of two-dimensional (2D) skyrmions, in chiral magnets the presence of the DMI commonly prevents the stability and coexistence of topological excitations of different types 7 . Recently, a new type of localized particle-like object-the chiral bobber (ChB)-was predicted theoretically in such materials 8 . However, its existence has not yet been verified experimentally. Here, we report the direct observation of ChBs in thin films of B20-type FeGe by means of quantitative off-axis electron holography (EH). We identify the part of the temperature-magnetic field phase diagram in which ChBs exist and distinguish two mechanisms for their nucleation. Furthermore, we show that ChBs are able to coexist with skyrmions over a wide range of parameters, which suggests their possible practical applications in novel magnetic solid-state memory devices, in which a stream of binary data bits can be encoded by a sequence of skyrmions and bobbers.