arXiv subjects

Konstantin L. Metlov

Publications and source records attributed to Konstantin L. Metlov.

At least 37 records · Page 2Linked to original sources

arXiv2018

What makes magnetic skyrmions different from magnetic bubbles ?

A large enough piece of ferromagnet is usually not magnetized uniformly, but develops a magnetization texture. In thin films these textures can be doubly-periodic. Such are the well known magnetic bubble domains and the recently observed "skyrmion" magnetization textures in MnSi. In this paper we develop a theory of periodic magnetization textures, based on complex calculus to answer the question -- is there a difference between those two textures even if they seem to carry the same topological winding number (or topological charge) ? We find that such difference exists, facilitated by a different role played by the magnetization vector's in-plane phase. We separate classical-like and quantum-like features of magnetization textures and highlight the role of magnetic anisotropy in favouring either of these cases.

cond-mat.mes-hall↗

arXiv2016

Topological constraints on positions of magnetic solitons in multiply-connected planar magnetic nano-elements

Here we consider an interplay between the topology of the magnetization texture (which is a topological soliton, or Skyrmion) in a planar magnetic nano-element and the topology of the element itself (its connectivity). We establish the existence of a set of constraints, coupling these topologies, which are specific for multiply connected elements and are absent in simply-connected case. As an example, a specific constraint is derived for a case of planar ring magnet, relating the angular positions of magnetic vortices and antivortices inside. We analyze the recent experimental data on the vortex magnetic domain walls in the ring to validate our findings.

cond-mat.mes-hall↗

arXiv2016

Effect of Dzyaloshinski-Moriya interaction on spin-polarized neutron scattering

For magnetic materials containing many lattice imperfections (e.g., nanocrystalline magnets), the relativistic Dzyaloshinski-Moriya (DM) interaction may result in nonuniform spin textures due to the lack of inversion symmetry at interfaces. Within the framework of the continuum theory of micromagnetics, we explore the impact of the DM interaction on the elastic magnetic small-angle neutron scattering (SANS) cross section of bulk ferromagnets. It is shown that the DM interaction gives rise to a polarization-dependent asymmetric term in the spin-flip SANS cross section. Analysis of this feature may provide a means to determine the DM constant.

cond-mat.mes-hall↗

arXiv2015

Magnetic neutron scattering by magnetic vortices in thin submicron-sized soft ferromagnetic cylinders

Using analytical expressions for the magnetization textures of thin submicron-sized magnetic cylinders in vortex state, we derive closed-form algebraic expressions for the ensuing small-angle neutron scattering (SANS) cross sections. Specifically, for the perpendicular and parallel scattering geometries, we have computed the magnetic SANS cross sections for the case of small vortex-center displacements without formation of magnetic charges on the side faces of the cylinder. The results represent a significant qualitative and quantitative step forward in SANS-data analysis on isolated magnetic nanoparticle systems, which are commonly assumed to be homogeneously or stepwise-homogeneously magnetized. We suggest a way to extract the fine details of the magnetic vortex structure during the magnetization process from the SANS measurements in order to help resolving the long standing question of the magnetic vortex displacement mode.

cond-mat.mes-hall↗

arXiv2015

Magnetic states in multiply-connected flat nano-elements

Flat magnetic nano-elements are an essential component of current and future spintronic devices. By shaping an element it is possible to select and stabilize chosen metastable magnetic states, control its magnetization dynamics. Here, using a recent significant development in mathematics of conformal mapping, complex variable based approach to the description of magnetic states in planar nano-elements is extended to the case when elements are multiply-connected (that is, contain holes or magnetic anti-dots). We show that presence of holes implies a certain restriction on the set of magnetic states of nano-element.

cond-mat.mes-hall↗

arXiv2014

Third-order effect in magnetic small-angle neutron scattering by a spatially inhomogeneous medium

Magnetic small-angle neutron scattering (SANS) is a powerful tool for investigating nonuniform magnetization structures inside magnetic materials. Here, considering a ferromagnetic medium with weakly inhomogeneous uniaxial magnetic anisotropy, saturation magnetization, and exchange stiffness, we derive the second-order (in the amplitude of the inhomogeneities) micromagnetic solutions for the equilibrium magnetization textures and compute the corresponding magnetic SANS cross sections up to the next, third order. We find that in the case of perpendicular scattering (the incident neutron beam is perpendicular to the applied magnetic field) if twice the cross section along the direction orthogonal to both the field and the neutron beam is subtracted from the cross section along the field direction, the result has only a third-order contribution (the lower-order terms are canceled). This difference does not depend on the amplitude of the exchange inhomogeneities and provides a separate gateway for a deeper analysis of the sample's magnetic structure. We derive and analyze analytical expressions for the dependence of this combination on the scattering-vector magnitude for the case of spherical Gaussian inhomogeneities.

cond-mat.mtrl-sci↗

arXiv2013

Vortex precession frequency and its amplitude-dependent shift in cylindrical nanomagnets

Frequency of free magnetic vortex precession in circular soft ferromagnetic nano-cylinders (magnetic dots) of various sizes is an important parameter, used in design of spintronic devices (such as spin-torque microwave nano-oscillators) and characterization of magnetic nanostructures. Here, using a recently developed collective-variable approach to non-linear dynamics of magnetic textures in planar nano-magnets, this frequency and its amplitude-dependent shift are computed analytically and plotted for the full range of cylinder geometries. The frequency shift is positive in large planar dots, but becomes negative in smaller and more elongated ones. At certain dot dimensions a zero frequency shift is realized, which can be important for enhancing frequency stability of magnetic nano-oscillators.

cond-mat.mes-hall↗

arXiv2013

Vortex mechanics in planar nano-magnets

A collective-variable approach for the study of non-linear dynamics of magnetic textures in planar nano-magnets is proposed. The variables are just arbitrary parameters (complex or real) in the specified analytical function of a complex variable, describing the texture in motion. Starting with such a function, a formal procedure is outlined, allowing a (non-linear) system of differential equations of motion to be obtained for the variables. The resulting equations are equivalent to Landau-Lifshitz-Gilbert dynamics as far as the definition of collective variables allows it. Apart from the collective-variable specification, the procedure does not involve any additional assumptions (such as translational invariance or steady-state motion). As an example, the equations of weakly non-linear motion of a magnetic vortex are derived and solved analytically. A simple formula for the dependence of the vortex precession frequency on its amplitude is derived. The results are verified against special cases from the literature and agree quantitatively with experiments and simulations.

cond-mat.mes-hall↗

arXiv2013

Analytical approximations to the core radius and energy of magnetic vortex in thin ferromagnetic disks

The energy of magnetic vortex core and its equilibrium radius in thin circular cylinder were first presented by N.A. Usov and S.E. Peschany in 1994. Yet, the magnetostatic function, entering the energy expression, is hard to evaluate and approximate. In this communication precise and explicit analytical approximations to this function (as well as equilibrium vortex core radius and energy) are derived in terms of elementary functions. Also, several simplifying approximations to the magnetic Hamiltonian and their impact on theoretical stability of magnetic vortex state are discussed.

cond-mat.mes-hall↗

arXiv2012

Large vortex state in ferromagnetic disks

Magnetic vortices in soft ferromagnetic nano-disks have been extensively studied for at least several decades both for their fundamental (as a "live" macroscopic realization of a field theory model of an elementary particle) as well as applied value for high-speed high-density power-independent information storage. Here it is shown that there is another stable vortex state with large thickness-dependent core profile in nano-scale ferromagnetic disks of several exchange lengths in size. Its energy is computed numerically (in the framework of Magnetism@home distributed computing project) and its stability is studied analytically, which allows to plot it on magnetic phase diagram. In cylinders of certain geometries large vortices exist on par with classical ones, while being separated by an energy barrier, controllable by tuning the geometry and material of ferromagnetic disk. They can be an excellent candidate for magnetic information storage not only because the resulting disk sizes are among the smallest, able to support magnetic vortices, but also because it is the closest to the classical vortex state of all other known metastable states of magnetic nano-cylinder. It means that memory, based on switching between these two types of magnetic vortices, may, potentially, achieve the highest possible rate of switching.

cond-mat.mes-hall↗

arXiv2010

Magnetization patterns in ferromagnetic nano-elements as functions of complex variable

Assumption of certain hierarchy of soft ferromagnet energy terms, realized in small enough flat nano-elements, allows to obtain explicit expressions for their magnetization distributions. By minimising the energy terms sequentially, from most to the least important, magnetization distributions are expressed as solutions of Riemann-Hilbert boundary value problem for a function of complex variable. A number of free parameters, corresponding to positions of vortices and anti-vortices, still remain in the expression. These parameters can be found by computing and minimizing the total magnetic energy of the particle with no approximations. Thus, the presented approach is a factory of realistic Ritz functions for analytical micromagnetic calculations. These functions are so versatile, that they may even find applications on their own (e.g. for fitting magnetic microscopy images). Examples are given for multi-vortex magnetization distributions in circular cylinder, and for 2-dimensional domain walls in thin magnetic strips.

cond-mat.mes-hall↗

arXiv2010

A model for flexural phonon dispersion in graphite and graphene

A simple model for flexural phonons in graphite (and graphene, corresponding to the limiting case of infinite distance between carbon planes) is proposed, in which the local dipolar moment is assumed to be proportional to the curvature of the carbon sheets. Explicit expressions for dispersion curves with full account for the long-range dipolar interaction forces are given and fitted to the experimental data using a single adjustable parameter of the theory. This parameter is expected to depend on the ground state configuration of molecular $π$-orbitals, the same both for graphite and for graphene. At decreasing carbon sheet separation (high pressures) the phonon spectrum displays instability, corresponding to the graphite to diamond transition. Being explicitly based on the local dipolar moments, the proposed simple model could prove useful for considering electron-phonon interaction.

cond-mat.mes-hall↗

arXiv2008

Map of metastable states for thin circular magnetic nano-cylinders

Nano-magnetic systems of artificially shaped ferromagnetic islands, recently became a popular subject due to their current and potential applications in spintronics, magneto-photonics and superconductivity. When the island size is close to the exchange length of magnetic material (around 15 nm), its magnetic structure becomes markedly different. It determines both static and dynamic magnetic properties of elements, but strongly depends on their shape and size. Here we map this dependence for circular cylindrical islands of a few exchange lengths in size. We outline the region of metastability of "C"-type magnetic states, proving that they are indeed genuine and not a result of pinning on particle imperfections. A way to create the smallest particles with guaranteed magnetic vortex state at zero field becomes evident. It is expected that the map will help focus the efforts in planning of experiments and devices.

cond-mat.mes-hall↗

arXiv2006

Quasi-uniform in plane magnetization state of thin cylindrical dots in a square array and related anisotropy

The energy (magnetostatic, exchange and Zeeman terms) of a square array of cylindrical sub-micron dots made of soft ferromagnetic material is calculated analytically and minimized, taking into account quasi-uniformity of dots magnetization. The dependence of the equilibrium energy of the array on the direction of the externally applied magnetic field in the array plane is recovered, exhibiting the four-fold anisotropy. The anisotropy constant is calculated. Its values for different array geometries are in excellent agreement to the recent independent experiments. New eight-fold anisotropy effect is predicted. Theory involves no adjustable parameters.

cond-mat.mes-hall↗

arXiv2001

Stability of magnetic vortex in soft magnetic nano-sized circular cylinder

Stability of magnetic vortex with respect to displacement of its center in a nano-scale circular cylinder made of soft ferromagnetic material is studied theoretically. The mode of vortex displacement producing no magnetic charges on the cylinder side is proposed and the corresponding absolute single-domain radius of the cylinder is calculated as a function of its thickness and the exchange length of the material. In cylinders with the radii less than the single-domain radius the vortex state is unstable and is absolutely prohibited (except if pinned by material imperfections), so that the distribution of the magnetization vector in such cylinders in no applied magnetic field is uniform (or quasi-uniform). The phase diagram of nano-scale cylinders including the stability line and the metastability region obtained here is presented.

cond-mat.mes-hall↗

arXiv2001

A simple analytical description for the cross-tie domain wall structure

A closed form analytical expression for the magnetization vector distribution within the cross-tie domain wall in an isotropic ferromagnetic thin film is given. The expression minimizes the exchange energy functional exactly, and the magnetostatic energy by means of an adjustable parameter (wall width). The equilibrium value of the wall width and the film thickness corresponding to the transition between the N{é}el and the cross-tie walls are calculated. The results are compared with the recent experiments and are in good qualitative agreement.

cond-mat.mes-hall↗

arXiv2001

Two-dimensional topological solitons in soft ferromagnetic cylinders

A simple approach allowing to construct closed-form analytical zero-field magnetization distributions in cylindrical particles of a small thickness and an arbitrary shape (not necessarily circular) is presented. The approach is based on reduction of the non-linear Euler equations for magnetization vector field to the classical linear Riemann-Hilbert problem. The result contains all the distributions minimizing the exchange energy functional and the surface magnetostatic contribution exactly, except for the neighbourhood of topological singularities on the cylinder faces where the result is approximate. The completeness of the analysis permitted to find a new type of a topological soliton in the case of circular cylinder. Also, an example of magnetic vortex in a triangular cylinder is given to investigate the role of the particle corners.

cond-mat.mes-hall↗

arXiv2001

Two-dimensional topological solitons in rectangular magnetic dots

A general approach allowing to find the analytical expressions for equilibrium magnetic structures in small and flat magnetic nano-sized cylinders of arbitrary shape made of soft magnetic material is presented. The resulting magnetization distributions are two-dimensional topological solitons and have a non-zero topological charge. The approach is illustrated here on an example of a thin rectangular particle.

cond-mat.mes-hall↗