arXiv subjects

Denis D. Sheka

Publications and source records attributed to Denis D. Sheka.

At least 37 records · Page 2Linked to original sources

arXiv2019

Micromagnetic Theory of Curvilinear Ferromagnetic Shells

Here, we present a micromagnetic theory of curvilinear ferromagnets, which allows discovering novel fundamental physical effects which were amiss. In spite of the firm confidence for more than 70 years, we demonstrate that there is an intimate coupling between volume and surface magnetostatic charges. Evenmore, the physics of curvilinear systems requires existence of a new fundamental magnetostatic charge determined by local characteristics of the surface. As a stark consequence, novel physical nonlocal anisotropy and chiral effects emerge in spatially corrugated magnetic thin films. Besides these fundamental discoveries, this work reassures confidence in theoretical predictions for experimental explorations and novel devices, based on curved thin films.

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arXiv2019

Spin eigen-excitations of an antiferromagnetic skyrmion

We theoretically predict and classify the localized modes of a skyrmion in a collinear uniaxial antiferromagnet and discuss how they can be excited. As a central result, we find two branches of skyrmion eigenmodes with distinct physical properties characterized by being low or high energy excitations. The frequency dependence of the low-energy modes scales as $R_0^{-2}$ for skyrmions with large radius $R_0$. Furthermore, we predict localized high-energy eigenmodes, which have no direct ferromagnetic counterpart. Except for the breathing mode, we find that all localized antiferromagnet skyrmion modes, both in the low and high-energy branch, are doubly degenerated in the absence of a magnetic field and split otherwise. We explain our numerical results for the low-energy modes within a string model representing the skyrmion boundary.

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arXiv2018

Magnetization induced shape transformations in flexible ferromagnetic rings

Flexible ferromagnetic rings are spin-chain magnets, in which the magnetic and mechanical subsystems are coupled. The coupling is achieved through the tangentially oriented anisotropy axis. The possibility to operate the mechanics of the nanomagnets by controlling their magnetization is an important issue for the nanorobotics applications. A minimal model for the deformable curved anisotropic Heisenberg ferromagnetic wire is proposed. An equilibrium phase diagram is constructed for the closed loop geometry: (i) A vortex state with vanishing total magnetic moment is typical for relatively large systems; in this case the wire has the form of a regular circle. (ii) A topologically trivial onion state with the planar magnetization distribution is realized in small enough systems; magnetic loop is elliptically deformed. By varying geometrical and elastic parameters a phase transition between the vortex and onion states takes place. The detailed analytical description of the phase diagram is well confirmed by numerical simulations.

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arXiv2018

Engineered Chiral Skyrmion and Skyrmionium States by the Gradient of Curvature

Curvilinear nanomagnets can support magnetic skyrmions stabilized at a local curvature without any intrinsic chiral interactions. Here, we propose a new mechanism to stabilize chiral Néel skyrmion states relying on the \textit{gradient} of curvature. We illustrate our approach with an example of a magnetic thin film with perpendicular magnetic anisotropy shaped as a circular indentation. We show that in addition to the topologically trivial ground state, there are two skyrmion states with winding numbers $\pm 1$ and a skyrmionium state with a winding number $0$. These chiral states are formed due to the pinning of a chiral magnetic domain wall at a bend of the nanoindentation due to spatial inhomogeneity of the curvature-induced Dzyaloshinskii--Moriya interaction. The latter emerges due to the gradient of the local curvature at a bend. While the chirality of the skyrmion is determined by the sign of the local curvature, its radius can be varied in a broad range by engineering the position of the bend with respect to the center of the nanoindentation. We propose a general method, which enables one to reduce a magnetic problem for any surface of revolution to the common planar problem by means of proper modification of constants of anisotropy and Dzyaloshinskii--Moriya interaction.

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arXiv2018

Localization of magnon modes in a curved magnetic nanowire

Spin waves in magnetic nanowires can be bound by a local bending of the wire. The eigenfrequency of a truly local magnon mode is determined by the curvature: a general analytical expression is established for any infinitesimally weak localized curvature of the wire. The interaction of the local mode with spin waves, propagating through the bend, results in scattering features, which is well confirmed by spin-lattice simulations.

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arXiv2018

Geometry-induced motion of magnetic domain walls in curved nanostripes

Dynamics of topological magnetic textures are typically induced externally by, e.g.~magnetic fields or spin/charge currents. Here, we demonstrate the effect of the internal-to-the-system geometry-induced motion of a domain wall in a curved nanostripe. Being driven by the gradient of the curvature of a biaxial stripe, transversal domain walls acquire remarkably high velocities of up to 100 m/s and do not exhibit any Walker-type speed limit. We pinpoint that the inhomogeneous distribution of the curvature-induced Dzyaloshinskii--Moriya interaction is a driving force for the motion of a domain wall. Although we showcase our approach on the specific Euler spiral geometry, the approach is general and can be applied to a wide class of geometries.

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arXiv2017

Spin eigen-excitations of the magnetic skyrmion and problem of the effective mass

Properties of magnon modes localized on a ferromagnetic skyrmion are studied. Three types of possible asymptotic behavior of the modes eigenfrequencies are found for the case of large skyrmion radius $R_s$, namely $ω_0\sim R_s^{-2}$ for the breathing mode, $ω_{-|μ|}\sim R_s^{-1}$ and $ω_{|μ|}\sim R_s^{-3}$ for modes with negative and positive azimuthal quantum numbers, respectively. A number of properties of the magnon eigenfunctions are determined. This enables us to demonstrate that the skyrmion dynamics based on the traveling wave model is described by the massless Thiele equation.

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arXiv2017

Multiplet of skyrmion states on a curvilinear defect: skyrmion lattices as a ground state

We show that the presence of a localized curvilinear defect drastically changes magnetic properties of a thin perpendicularly magnetized ferromagnetic film. For a large enough defect amplitude a discrete set of equilibrium magnetization states appears forming a ladder of energy levels. Each equilibrium state has either zero or unit topological charge, i.e. topologically trivial and skyrmion multiplets generally appear. Transitions between the levels with the same topological charge are allowed and can be utilized to encode and switch a bit of information. There is a wide range of geometrical and material parameters, where the skyrmion level has the lowest energy. As a result, periodically arranged curvilinear defects generate a skyrmion lattice as the ground state.

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arXiv2017

Magnetization in narrow ribbons: curvature effects

A ribbon is a surface swept out by a line segment turning as it moves along a central curve. For narrow magnetic ribbons, for which the length of the line segment is much less than the length of the curve, the anisotropy induced by the magnetostatic interaction is biaxial, with hard axis normal to the ribbon and easy axis along the central curve. The micromagnetic energy of a narrow ribbon reduces to that of a one-dimensional ferromagnetic wire, but with curvature, torsion and local anisotropy modified by the rate of turning. These general results are applied to two examples, namely a helicoid ribbon, for which the central curve is a straight line, and a Möbius ribbon, for which the central curve is a circle about which the line segment executes a $180^\circ$ twist. In both examples, for large positive tangential anisotropy, the ground state magnetization lies tangent to the central curve. As the tangential anisotropy is decreased, the ground state magnetization undergoes a transition, acquiring an in-surface component perpendicular to the central curve. For the helicoid ribbon, the transition occurs at vanishing anisotropy, below which the ground state is uniformly perpendicular to the central curve. The transition for the Möbius ribbon is more subtle; it occurs at a positive critical value of the anisotropy, below which the ground state is nonuniform. For the helicoid ribbon, the dispersion law for spin wave excitations about the tangential state is found to exhibit an asymmetry determined by the geometric and magnetic chiralities.

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arXiv2016

Geometry induced phase transitions in magnetic spherical shell

Equilibrium magnetization states in thin spherical shells of a magnetically soft ferromagnet are determined by the competition between two interactions: (i) The local exchange interaction favours the more homogeneous onion state with magnetization oriented in meridian directions; such a state is realized in relatively small particles. (ii) The nonlocal magnetostatic interaction prefers the double-vortex configuration with the magnetization oriented in the parallels directions, since it minimizes the volume magnetostatic charges. These sates are topologically equivalent, in contrast to the same-name states of magnetic nanoring. As a consequence, a continuous (the second order) phase transition between the vortex and onion states takes place. The detailed analytical description of the phase diagram is well confirmed by micromagnetic simulations.

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arXiv2016

Topologically stable magnetization states on a spherical shell: curvature stabilized skyrmions

Topologically stable structures include vortices in a wide variety of matter, such as skyrmions in ferro- and antiferromagnets, and hedgehog point defects in liquid crystals and ferromagnets. These are characterized by integer-valued topological quantum numbers. In this context, closed surfaces are a prominent subject of study as they form a link between fundamental mathematical theorems and real physical systems. Here we perform an analysis on the topology and stability of equilibrium magnetization states for a thin spherical shell with easy-axis anisotropy in normal directions. Skyrmion solutions are found for a range of parameters. These magnetic skyrmions on a spherical shell have two distinct differences compared to their planar counterpart: (i) they are topologically trivial, and (ii) can be stabilized by curvature effects, even when Dzyaloshinskii-Moriya interactions are absent. Due to its specific topological nature a skyrmion on a spherical shell can be simply induced by a uniform external magnetic field.

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arXiv2015

Rashba Torque Driven Domain Wall Motion in Magnetic Helices

Manipulation of the domain wall propagation in magnetic wires is a key practical task for a number of devices including racetrack memory and magnetic logic. Recently, curvilinear effects emerged as an efficient mean to impact substantially the statics and dynamics of magnetic textures. Here, we demonstrate that the curvilinear form of the exchange interaction of a magnetic helix results in an effective anisotropy term and Dzyaloshinskii--Moriya interaction with a complete set of Lifshitz invariants for a one-dimensional system. In contrast to their planar counterparts, the geometrically induced modifications of the static magnetic texture of the domain walls in magnetic helices offer unconventional means to control the wall dynamics relying on spin-orbit Rashba torque. The chiral symmetry breaking due to the Dzyaloshinskii-Moriya interaction leads to the opposite directions of the domain wall motion in left- or right-handed helices. Furthermore, for the magnetic helices, the emergent effective anisotropy term and Dzyaloshinskii-Moriya interaction can be attributed to the clear geometrical parameters like curvature and torsion offering intuitive understanding of the complex curvilinear effects in magnetism.

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arXiv2015

Curvature and torsion effects in the spin-current driven domain wall motion

The domain wall motion along a helix-shaped nanowire is studied for the case of spin-current driving via Bazaliy-Zhang-Li mechanism. The analysis is based on collective variable approach. Two new effects are ascertained: (i) the curvature results in appearance of the Walker limit for a uniaxial wire, (ii) the torsion results in effective shift of the nonadiabatic spin torque parameter $β$. The latter effect changes considerably the domain wall velocity and can result in negative domain wall mobility. This effect can be also used for an experimental determination of the nonadiabatic parameter $β$ and damping coefficient $α$.

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arXiv2015

Torsion induced effects in magnetic nanowires

Magnetic helix wire is one of the most simple magnetic systems which manifest properties of both curvature and torsion. There exist two equilibrium states in the helix wire with easy-tangential anisotropy: a quasi-tangential magnetization distribution in case of relatively small curvatures and torsions, and an onion state in opposite case. In the last case the magnetization is close to tangential one, deviations are caused by the torsion and curvature. Possible equilibrium magnetization states in the helix magnet with different anisotropy directions are studied theoretically. The torsion also essentially influences the spin-wave dynamics, acting as an effective magnetic field. Originated from the curvature induced effective Dzyaloshinskii interaction, this magnetic field leads to the coupling between the helix chirality and the magnetochirality, it breaks mirror symmetry in spin-wave spectrum. All analytical predictions on magnetization statics an dynamics are well confirmed by the direct spin lattice simulations.

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arXiv2015

Curvature induced domain wall pinning

It is shown that a local bend of a nanowire is a source of pinning potential for a transversal head-to-head (tail-to-tail) domain wall. Eigenfrequency of the domain wall free oscillations at the pinning potential and the effective friction are determined as functions of the curvature and domain wall width. The pinning potential originates from the effective curvature induced Dzyaloshinsky-like term in the exchange energy. The theoretical results are verified by means of micromagnetic simulations for the case of parabolic shape of the wire bend.

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arXiv2015

Resonantly exited precession motion of three-dimensional vortex core in magnetic nanospheres

We found resonantly excited precession motions of a three-dimensional vortex core in soft magnetic nanospheres and controllable precession frequency with the sphere diameter 2R, as studied by micromagnetic numerical and analytical calculations. The precession angular frequency for an applied static field $H_{DC}$ is given as $ω_{MV}= γ_{eff} H_{DC}$, where $γ_{eff} = γ $ is the effective gyromagnetic ratio in collective vortex dynamics, with the gyromagnetic ratio $γ$ and the average magnetization component $ $ of the ground-state vortex in the core direction. Fitting to the micromagnetic simulation data for $ $ yields a simple explicit form of $ = (73.6 \pm 3.4)(l_{ex}/2R)^{2.20 \pm 0.14}$, where $l_{ex}$ is the exchange length of a given material. This dynamic behavior might serve as a foundation for potential bio-applications of size-specific resonant excitation of magnetic vortex-state nanoparticles, for example, magnetic particle resonance imaging.

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arXiv2015

Magnetization patterning induced by electrical spin-polarized current in nanostripes

The combined action of a transverse spin-polarized current and the current-induced Ørsted field on long ferromagnetic nanostripes is studied numerically and analytically. The magnetization behavior is analyzed for stripes with various widths and for all range of the applied current density. It is established that Ørsted field does not destroy periodical magnetization structures induced by the spin-torque, e.g. vortex-antivortex crystal and cross-tie domain walls. However, the action of the Ørsted field disables the saturation state for the strong currents: a stationary state with a single longitudinal domain wall appears instead. Shape of this wall remains constant with the current increasing. The latter phenomenon is studied both numerically and analytically.

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arXiv2015

Curvature effects in statics and dynamics of low dimensional magnets

We develop an approach to treat magnetic energy of a ferromagnet for arbitrary curved wires and shells on the assumption that the anisotropy contribution much exceeds the dipolar and other weak interactions. We show that the curvature induces two effective magnetic interactions: effective magnetic anisotropy and effective Dzyaloshinskii-like interaction. We derive an equation of magnetisation dynamics and propose a general static solution for the limit case of strong anisotropy. To illustrate our approach we consider the magnetisation structure in a ring wire and a cone surface: ground states in both systems essentially depend on the curvature excluding strictly tangential solutions even in the case of strong anisotropy. We derive also the spectrum of spin waves in such systems.

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