arXiv subjects

Filipp N. Rybakov

Publications and source records attributed to Filipp N. Rybakov.

At least 19 recordsLinked to original sources

arXiv2026

Magnetic hopfions at room temperature

Hopfions are three-dimensional (3D) topological solitons predicted to exist in diverse magnetic systems, yet their practical utility has been largely restricted to cryogenic environments. Here, we overcome this temperature constraint by demonstrating stable magnetic hopfions in the chiral magnet Co8Zn8Mn4 at and above room temperature. Using a transmission electron microscope equipped for in situ optical excitation, we generate magnetic hopfions with femtosecond laser pulses. Long-term observations further reveal Brownian-like motion at room temperature and thermally activated collapse upon approaching the high-temperature regime. Together with micromagnetic simulations and homotopy group analysis, our experimental observations uncover the hopfion formation mechanism through the fusion of bimeron pairs. These findings establish room-temperature magnetic hopfions and provide a framework for their further studies under technologically relevant conditions.

cond-mat.mtrl-sci↗

arXiv2026

Electric-current-assisted nucleation of zero-field hopfion rings

Magnetic hopfions are three-dimensional topological solitons -- knotted, vortex-like spin configurations. In chiral magnets, hopfions can appear as isolated structures or they can be linked to skyrmion strings. Previous studies employed a sophisticated protocol and a special sample geometry to nucleate such hopfions linked to one or a few skyrmion strings. Here, we introduce an electric-current-assisted nucleation protocol that is simple and independent of the sample shape and size. The resulting hopfions exhibit extraordinary stability in the presence of both positive and negative magnetic fields, in perfect agreement with micromagnetic simulations. We also present a comprehensive framework for classifying hopfions, skyrmions, and merons by deriving the corresponding homotopy group.

cond-mat.mes-hall↗

arXiv2026

Linked skyrmions in shifted magnetic bilayer

Magnetic solitons have recently attracted significant attention due to their intricate physical properties and potential applications in information processing. The majority of the studies in this field, however, are focused on a particular type of solitons known as skyrmions, characterised by a unit topological charge. Here, we present a shifted magnetic bilayer that can demonstrate magnetic solitons with arbitrary large topological charges. These configurations, which we call linked skyrmions, consist of multiple skyrmions linked together with topological point defects. These topological point defects, termed as anti-aligned points, originate from the mutually orthogonal Dzyaloshinskii-Moriya interaction in two different layers. By tuning the interlayer exchange coupling and the external magnetic field, one can also achieve different ground states in this bilayer. Additionally, the system also demonstrates conventional skyrmion-bags and $kπ$-skyrmions. Finally we propose a suitable material candidate where these magnetic configurations can be realised. Our findings, thus, can provide a way to achieve solitons with large topological charge and realise them in realistic systems.

cond-mat.mes-hall↗

arXiv2025

Zeta expansion for long-range interactions under periodic boundary conditions with applications to micromagnetics

We address the efficient computation of power-law-based interaction potentials of homogeneous $d$-dimensional bodies with an infinite $n$-dimensional array of copies, including their higher-order derivatives. This problem forms a serious challenge in micromagnetics with periodic boundary conditions and related fields. Nowadays, it is common practice to truncate the associated infinite lattice sum to a finite number of images, introducing uncontrolled errors. We show that, for general interacting geometries, the exact infinite sum for both dipolar interactions and generalized Riesz power-law potentials can be obtained by complementing a small direct sum by a correction term that involves efficiently computable derivatives of generalized zeta functions. We show that the resulting representation converges exponentially in the derivative order, reaching machine precision at a computational cost no greater than that of truncated summation schemes. In order to compute the generalized zeta functions efficiently, we provide a superexponentially convergent algorithm for their evaluation, as well as for all required special functions, such as incomplete Bessel functions. Magnetic fields and related quantities can thus be evaluated to machine precision in arbitrary cuboidal domains periodically extended along one or two dimensions. We benchmark our method against known formulas for magnetic interactions and against direct summation for Riesz potentials with sufficiently large exponents, consistently achieving full precision. In addition, we identify new corrections to the asymptotic limit of the demagnetization field and tabulate high-precision benchmark values that can be used as a reliable reference for micromagnetic solvers. The techniques developed are broadly applicable, with direct impact in other areas such as molecular dynamics.

math.NA↗

arXiv2024

Topological invariants of vortices, merons, skyrmions, and their combinations in continuous and discrete systems

Magnetic vortices and skyrmions are typically characterized by distinct topological invariants. This work presents a unified approach for the topological classification of these textures, encompassing isolated objects and configurations where skyrmions and vortices coexist. Using homotopy group analysis, we derive topological invariants that form the free abelian group, $\mathbb{Z}\times\mathbb{Z}$. We provide an explicit method for calculating the corresponding integer indices in continuous and discrete systems. This unified classification framework extends beyond magnetism and is applicable to physical systems in general.

cond-mat.mes-hall↗

arXiv2024

Reduced theory of symmetric and antisymmetric exchange interactions in nanowires

We investigate the behavior of minimizers of perturbed Dirichlet energies supported on a wire generated by a regular simple curve $γ$ and defined in the space of $\mathbb{S}^2$-valued functions. The perturbation $K$ is represented by a matrix-valued function defined on $\mathbb{S}^2$ with values in $\mathbb{R}^{3 \times 3}$. Under natural regularity conditions on $K$, we show that the family of perturbed Dirichlet energies converges, in the sense of $Γ$-convergence, to a simplified energy functional on $γ$. The reduced energy unveils how part of the antisymmetric exchange interactions contribute to an anisotropic term whose specific shape depends on the curvature of $γ$. We also discuss the significant implications of our results for studies of ferromagnetic nanowires when Dzyaloshinskii-Moriya interaction (DMI) is present.

math.AP↗

arXiv2024

Embedded skyrmion bags in thin films of chiral magnets

Magnetic skyrmions are topologically nontrivial spin configurations that possess particle-like properties. Earlier research was mainly focused on a specific type of skyrmion with topological charge Q = -1. However, theoretical analyses of two-dimensional chiral magnets have predicted the existence of skyrmion bags -- solitons with arbitrary positive or negative topological charge. Although such spin textures are metastable states, recent experimental observations have confirmed the stability of isolated skyrmion bags in a limited range of applied magnetic fields. Here, by utilizing Lorentz transmission electron microscopy, we show the extraordinary stability of skyrmion bags in thin plates of B20-type FeGe. In particular, we show that skyrmion bags embedded within a skyrmion lattice remain stable even in zero or inverted external magnetic fields. A robust protocol for nucleating such embedded skyrmion bags is provided. Our results agree perfectly with micromagnetic simulations and establish thin plates of cubic chiral magnets as a powerful platform for exploring a broad spectrum of topological magnetic solitons.

cond-mat.mes-hall↗

arXiv2023

Magneto-Crystalline Composite Topological Defects and Half-Hopfions

We consider a new class of topological defects in chiral magnetic crystals such as FeGe and MnSi. These are composite topological defects that arise when skyrmions in the magnetic order intersect with twin boundaries in the underlying crystalline lattice. We show that the resulting stable configurations are a new type of defect that can be viewed as half-hopfions.

cond-mat.mes-hall↗

arXiv2023

Metaheuristic conditional neural network for harvesting skyrmionic metastable states

We present a metaheuristic conditional neural-network-based method aimed at identifying physically interesting metastable states in a potential energy surface of high rugosity. To demonstrate how this method works, we identify and analyze spin textures with topological charge $Q$ ranging from 1 to $-13$ (where antiskyrmions have $Q<0$) in the Pd/Fe/Ir(111) system, which we model using a classical atomistic spin Hamiltonian based on parameters computed from density functional theory. To facilitate the harvest of relevant spin textures, we make use of the newly developed Segment Anything Model (SAM). Spin textures with $Q$ ranging from $-3$ to $-6$ are further analyzed using finite-temperature spin-dynamics simulations. We observe that for temperatures up to around 20\,K, lifetimes longer than 200\,ps are predicted, and that when these textures decay, new topological spin textures are formed. We also find that the relative stability of the spin textures depend linearly on the topological charge, but only when comparing the most stable antiskyrmions for each topological charge. In general, the number of holes (i.e., non-self-intersecting curves that define closed domain walls in the structure) in the spin texture is an important predictor of stability -- the more holes, the less stable is the texture. Methods for systematic identification and characterization of complex metastable skyrmionic textures -- such as the one demonstrated here -- are highly relevant for advancements in the field of topological spintronics.

physics.comp-ph↗

arXiv2023

Heliknoton in a film of cubic chiral magnet

Cubic chiral magnets exhibit a remarkable diversity of two-dimensional topological magnetic textures, including skyrmions. However, the experimental confirmation of topological states localized in all three spatial dimensions remains challenging. In this paper, we investigate a three-dimensional topological state called a heliknoton, which is a hopfion embedded into a helix or conic background. We explore the range of parameters at which the heliknoton can be stabilized under realistic conditions using micromagnetic modeling, harmonic transition state theory, and stochastic spin dynamics simulations. We present theoretical Lorentz TEM images of the heliknoton, which can be used for experimental comparison. Additionally, we discuss the stability of the heliknoton at finite temperatures and the mechanism of its collapse. Our study offers a pathway for future experimental investigations of three-dimensional topological solitons in magnetic crystals.

cond-mat.mes-hall↗

arXiv2022

Non-Abelian Vortices in Magnets

We show that non-Abelian vortices can exist in magnetic materials. These are singularity-free textures, are described by spin-lattice and field theory models, and we demonstrate that typical magnetic materials can be quite suitable for their realization and observation. We give a topological classification of these vortices and reveal their connection with Abelian topological structures, such as usual vortices, merons and skyrmions. We also describe how non-Abelian magnetic vortices can carry topologically protected information and present reasons for the advantage of such information carriers, as compared to Abelian entities.

cond-mat.str-el↗

arXiv2022

Diversity of states in a chiral magnet nanocylinder

The diversity of three-dimensional magnetic states in a FeGe nanocylinder is studied using micromagnetic simulations and off-axis electron holography in the transmission electron microscope. In particular, we report the observation of a dipole string -- a spin texture composed of two coupled Bloch points -- which becomes stable under geometrical confinement. Quantitative agreement is obtained between experimental and theoretical phase shift images by taking into account the presence of a damaged layer on the surface of the nanocylinder. The theoretical model is based on the assumption that the damaged surface layer, which results from focused ion beam milling during sample preparation, has similar magnetic properties to those of an amorphous FeGe alloy. The results highlight the importance of considering the magnetic properties of the surface layers of such nanoscale samples, which influence their magnetic states.

cond-mat.mes-hall↗

arXiv2022

Chiral standing spin waves in skyrmion lattice

This work studies the resonance excitations of the three-dimensional skyrmions lattice in the finite thickness plate of an isotropic chiral magnet using spin dynamics simulations. We found that the absorption spectra and resonance modes differ from those predicted by the two-dimensional model and the model of the unconfined bulk crystal. The features observed on the spectra can be explained by the formation of chiral standing spin waves, which, contrary to conventional standing spin waves, are characterized by the helical profile of dynamic magnetization of fixed chirality defined by the Dzyaloshinskii-Moriya interaction. In this case, the dynamic susceptibility becomes a function of the plate thickness, which gives rise to an interesting effect that manifests itself in periodical fading of the intensity of corresponding modes and makes excitation of these modes impossible at specific thicknesses.

cond-mat.mes-hall↗

arXiv2022

Vortex nucleation barrier in superconductors beyond the Bean-Livingston approximation: A numerical approach for the sphaleron problem in a gauge theory

The knowledge of vortex nucleation barriers is crucial for applications of superconductors, such as single-photon detectors and superconductor-based qubits. Contrarily to the problem of finding energy minima and critical fields, there are no controllable methods to explore the energy landscape, identify saddle points, and compute associated barriers. Similar problems exist in high-energy physics where the saddle-point configurations are called sphalerons. Here, we present a generalization of the string method to gauge field theories, which allows the calculation of energy barriers in superconductors. We solve the problem of vortex nucleation, assessing the effects of the nonlinearity of the model, complicated geometry, surface roughness, and pinning.

cond-mat.supr-con↗

arXiv2022

Flux Qubit Based on Hybrid Ferromagnetic-Superconducting Device

We propose a realization of flux qubit based on the hybrid ferromagnetic-superconducting device where the flux bias is induced purely by vector potential of the vanishing magnetic field. We support our conclusions with theoretical analysis and self-consistent three-dimensional simulations for material specific parameters.

cond-mat.supr-con↗

arXiv2021

Magnetic particle-antiparticle creation and annihilation

A fundamental property of particles and antiparticles, such as electrons and positrons, is their ability to annihilate one another. Similar behavior is predicted for magnetic solitons -- localized spin textures that can be distinguished by their topological index $Q$. Theoretically, magnetic topological solitons with opposite values of $Q$, such as skyrmions and their antiparticles -- antiskyrmions -- are expected to be able to merge continuously and to annihilate. However, experimental verification of such particle-antiparticle pair production and annihilation processes has been lacking. Here, we report the creation and annihilation of skyrmion-antiskyrmion pairs in an exceptionally thin film of the cubic chiral magnet B20-type FeGe observed using transmission electron microscopy. Our observations are highly reproducible and are fully consistent with micromagnetic simulations. Our findings provide a new platform for fundamental studies of particles and antiparticles based on magnetic solids and open new perspectives for practical applications of thin films of isotropic chiral magnets.

cond-mat.str-el↗

arXiv2021

The absence of superconductivity in the next-to-leading order Ginzburg-Landau functional for Bardeen-Cooper-Schrieffer superconductor

Shortly after the Gor'kov microscopic derivation of the Ginzburg-Landau (GL) model via a small order parameter expansion in Bardeen-Cooper-Schrieffer theory of superconductivity, the derivation was carried to next-to-leading order in that parameter and its spatial derivatives. The aim was to obtain a generalized GL free energy that approximates the microscopic model better. Since 1960s, multiple works have claimed or implicitly assumed that this extended GL model corresponds to the free energy and has solutions in the form of local minima describing superconductivity, such as vortex solutions. In contrast to this, we prove that this extended GL functional does not represent free energy since it does not have any solutions in the form of minima. Accordingly, it cannot be used to describe superconducting states.

cond-mat.supr-con↗

arXiv2021

Geometry and Symmetry in Skyrmion Dynamics

The uniform motion of chiral magnetic skyrmions induced by a spin-transfer torque displays an intricate dependence on the skyrmions' topological charge and shape. We reveal surprising patterns in this dependence through simulations of the Landau-Lifshitz-Gilbert equation with Zhang-Li torque and explain them through a geometric analysis of Thiele's equation. In particular, we show that the velocity distribution of topologically non-trivial skyrmions depends on their symmetry: it is a single circle for skyrmions of high symmetry and a family of circles for low-symmetry configurations. We also show that the velocity of the topologically trivial skyrmions, previously believed to be the fastest objects, can be surpassed, for instance, by antiskyrmions. The generality of our approach suggests the validity of our results for exchange frustrated magnets, bubble materials, and others.

cond-mat.mes-hall↗