arXiv subjects

Konstantin L. Metlov

Publications and source records attributed to Konstantin L. Metlov.

At least 19 recordsLinked to original sources

arXiv2026

Exact solution for stationary states of a closed memristor with mobile charged vacancies

A nonlinear model of a memristor based on charged mobile vacancies is considered taking into account the electrostatic interaction between them. This interaction significantly affects the stationary (limiting) vacancy distributions formed under the action of the electric current flowing through the memristor, for which analytical expressions are obtained in this work. Between the regions with reduced and increased vacancy concentrations, an intermediate electrically neutral region is formed due to the electrostatic interaction. Interestingly, the limiting resistances in the ``on'' and ``off'' states of such a memristor do not depend on the strength of the electrostatic interaction, at least in the leading first order in the vacancy concentration.

cond-mat.mes-hall↗

arXiv2026

Three-dimensional magnetization textures as quaternionic functions

Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic applications. Compared to 1D domain walls or 2D magnetic vortices/skyrmions, they are a much harder challenge to represent, analyze and reason about. Here we build analytical representation for such a textures (with arbitrary number of singularity-free hopfions and singular Bloch point pairs) as products of simple quaternionic functions. It can serve as a language for expressing theoretical models of 3D magnetization textures and specifying a variety of topologically non-trivial initial conditions for micromagnetic simulations. It also follows from the quaternion algebra properties that three dimensional magnetic states can potentially be useful for implementing topological quantum computation.

cond-mat.mes-hall↗

arXiv2026

Spatial decay of isolated magnetic hopfions in chiral helimagnets

Magnetic hopfions in chiral magnets are topological solitons, localized in three dimensions. But is their localization strong? To address this question we derive an asymptotic expansion for the isolated hopfion's spatial profile. It becomes starting point for a simple analytical model, which is asymptotically correct both near the hopfion center and far away from it. Region of equilibrium hopfions on the phase diagram of a helimagnet is computed and material requirements for supporting movable isolated magnetic hopfions on uniform background are discussed.

cond-mat.mes-hall↗

arXiv2026

Magnetic small-angle neutron scattering by a nanocrystalline ferromagnet with anisotropic exchange interaction

A micromagnetic framework for magnetic small-angle neutron scattering (SANS) is presented that accounts for weak symmetric anisotropic exchange in centrosymmetric nanocrystalline ferromagnets. The exchange interaction is expressed via a general fourth-rank tensor decomposed into isotropic and deviatoric parts. We start with the exchange energy and effective field, assuming weakly fluctuating in space saturation magnetization, solve micromagnetic problem to find spatial distribution of local magnetization vector and compute the averaged (over random orientations of nanocrystals) SANS cross sections. The isotropic part reproduces the classical Heisenberg-type SANS response, while non-zero deviatoric part of the exchange tensor gives rise to new angular harmonics in the magnetic SANS cross section. As a specific example, analytical response functions for an exchange tensor with hexagonal symmetry in perpendicular and parallel scattering geometries are derived. The results provide a basis for identifying and quantifying symmetric exchange anisotropy in magnetic SANS experiments.

cond-mat.mes-hall↗

arXiv2025

Switching of a closed mobile vacancy based memristor, whose specific resistance linearly depends on local vacancy concentration

The linear (proportional to local vacancy concentration) term in specific resistance of the material does not directly contribute to the change of memristor's total resistance when the vacancies are redistributed inside while keeping their total number constant. But it still changes kinetics of the vacancy drift under the influence of a passing electric current. These changes are especially significant in the presence of metal-insulator phase transition in the memristor's material. In this paper, kinetic equation for local vacancy concentration is obtained, and exact solutions for its steady states are analyzed. It is shown that not only in the weakly nonlinear case (when the dependence of the specific resistance on the vacancy concentration can be neglected), but also in a strongly non-linear memristor with phase transition, its kinetics can be reduced to the classical exactly solvable Burgers equation.

cond-mat.mes-hall↗

arXiv2025

Elliptical stability of hopfions in bulk helimagnets

Magnetic hopfions are three-dimensional topological solitons with non-zero Hopf index ${\cal H}$ in the vector field of material's local magnetization. In this Letter elliptical stability of hopfions with ${\cal H}=1$ in a classical helimagnet is studied on the basis of a variational model. It is shown that, depending on their internal structure (vortex and antivortex tubes ordering), the hopfions can either be stable in a bulk magnet or unstable with respect to elongation along their central axis. It is found that the energy of stable hopfions is always below the energy of the $2π$-skyrmion lattice in the same material, suggesting the possibility to use $2π$-skyrmions as a precursor for hopfion nucleation. Stability diagram for hopfions on the magnetic anisotropy-field phase diagram is computed numerically. Explicit analytical expressions for some of its critical lines are derived.

cond-mat.mes-hall↗

arXiv2025

Control of the magnetic hopfion lattice in helimagnet with the external field and anisotropy

A generalized micromagnetic model of hopfions in a helimagnet with a two-dimensional (allowing both radial and azimuthal dependence) profile function is considered. Calculations confirm the elliptical stability of hopfions and the previously obtained analytical expression for the upper critical field of their lattice. Dependencies of the hopfion lattice periods on the magnitude of the applied external magnetic field and the uniaxial anisotropy constant of the material are obtained. It is shown that in an anisotropic helimagnet, the hopfion lattice expands in the direction of the anisotropy axis, and the expansion can be controlled by the external field and the uniaxial anisotropy constant.

cond-mat.mes-hall↗

arXiv2024

Magnetostatic bounds on stability of hopfions in bulk helimagnets

Magnetic hopfions are three-dimensional localized topological solitons in the volume of a magnet. In this work, starting with a classical free energy density of a helimagnet, an approximate variational model of hopfions is studied. The hopfion stability regions on the uniaxial anisotropy-external magnetic field phase diagram are computed and their evolution with increasing magnetostatic interaction strength is considered. It is found that magnetostatic interaction destabilizes the hopfions and, above the certain strength (relative to Dzyaloshinskii-Moriya interaction), destroys their stability completely. Numerical estimates for this bound are provided. They can help focus the search for materials, supporting bulk magnetic hopfions.

cond-mat.mes-hall↗

arXiv2024

Small-angle neutron scattering signatures of magnetic hopfions

Magnetic hopfions are three-dimensional localized magnetic topological solitons which can exist in the bulk of magnetic materials. Based on a Ritz model for magnetic hopfions in a chiral magnet, the unpolarized magnetic small-angle neutron scattering (SANS) cross section, the spin-flip scattering cross section, and the chiral function (characterizing the imbalance between the two spin-flip scattering amplitudes) are computed here analytically; while the real-space correlation function is obtained numerically. Features of these functions, specific to magnetic hopfions, are discussed. Our results enable the SANS method to be used for the detection of magnetic hopfions.

cond-mat.mes-hall↗

arXiv2023

Fingerprint of vortex-like flux closure in isotropic Nd-Fe-B bulk magnet

Taking advantage of recent progress in neutron instrumentation and in the understanding of magnetic-field-dependent small-angle neutron scattering, here, we study the three-dimensional magnetization distribution within an isotropic Nd-Fe-B bulk magnet. The magnetic neutron scattering cross section of this system features the so-called spike anisotropy, which points towards the presence of a strong magnetodipolar interaction. This experimental result combined with a damped oscillatory behavior of the corresponding correlation function and recent micromagnetic simulation results on spherical nanoparticles suggest an interpretation of the neutron data in terms of vortex-like flux-closure patterns. The field-dependent correlation length Lc is well reproduced by a phenomenological power-law model. While the experimental neutron data for Lc are described by an exponent close to unity (p = 0.86), the simulation results yield p = 1.70, posing a challenge to theory to include vortex-vortex interaction effects.

cond-mat.mes-hall↗

arXiv2023

Topological magnetic memory with multiply-connected planar magnetic nanoelements

A coding scheme is introduced, allowing to store a set of linked bit strings in planar magnetic nanoelements with holes. Analytical expressions for the corresponding magnetization distributions are developed up to a homotopy and the specific examples are given for doubly- and triply-connected cases. The energy barriers, protecting the information-bearing states, are discussed. Compared to a set of disparate simply-connected nanoelements of the same total connectivity, the nanoelements with holes can hold much more information due to the possibility of linking the individual bits.

cond-mat.mes-hall↗

arXiv2022

Two types of metastable magnetic hopfions

Localized magnetic topological solitons with Hopf index of 1 in an unbounded bulk magnet are studied theoretically, starting with the classical micromagnetic Hamiltonian. It is shown analytically that (like Bloch and Néel walls in classical magnetism) there are two possible stable configurations of these solitons, which are equivalent topologically. Their stability regions are plotted on a phase diagram in the magnetic field -- uniaxial anisotropy space for different normalized magnetostatic interaction strengths. For some parameters both types of hopfions can be stable.

cond-mat.mes-hall↗

arXiv2021

Role of higher-order effects in spin-misalignment small-angle neutron scattering of high-pressure torsion nickel

Magnetic-field-dependent unpolarized small-angle neutron scattering (SANS) experiments demonstrate that high-pressure torsion (HPT) straining induces spin misalignments in pure Ni, which persist in magnetic fields up to 4 T. The spin-misalignment scattering patterns are elongated perpendicular to the applied magnetic field due to an unusual predominant longitudinal $sin^2(θ)$-type angular anisotropy. Such a contribution cannot be explained by the conventional second order (in spin misalignment amplitude) micromagnetic SANS theory in the approach-to-saturation regime, nor can its magnitude relative to the other features of the cross sections by the third order micromagnetic SANS theory. This indicates that the high-density of crystal defects induced via HPT straining in Ni makes such higher-order effects in the micromagnetic SANS cross sections observable.

cond-mat.mtrl-sci↗

arXiv2020

Nonlinear effects in memristors with mobile vacancies

Because the local concentration of vacancies in any material is bounded, their motion must be accompanied by nonlinear effects. Here we look for such effects in a simple model for electric field driven vacancy motion in memristors, solving the corresponding nonlinear Burgers' equation with impermeable nonlinear boundary conditions analytically. We find non-monotonous relaxation of the resistance while switching between the stable (``on''/``off'') states of the memristor; and qualitatively different film thickness dependencies of switching time (under applied current) and relaxation time (under no current). Our exact solution can serve as a useful benchmark for simulations of more complex memristor models.

cond-mat.mes-hall↗

arXiv2020

Experimental Observation of Vortex Rings in a Bulk Magnet

Vortex rings are remarkably stable structures occurring in numerous systems: for example in turbulent gases, where they are at the origin of weather phenomena [1]; in fluids with implications for biology [2]; in electromagnetic discharges [3]; and in plasmas [4]. While vortex rings have also been predicted to exist in ferromagnets [5], they have not yet been observed. Using X-ray magnetic nanotomography [6], we imaged three-dimensional structures forming closed loops in a bulk micromagnet, each composed of a vortex-antivortex pair. Based on the magnetic vorticity, a quantity analogous to hydrodynamic vorticity, we identify these configurations as magnetic vortex rings. While such structures have been predicted to exist as transient states in exchange ferromagnets [5], the vortex rings we observe exist as stable, static configurations, whose stability we attribute to the dipolar interaction. In addition, we observe stable vortex loops intersected by magnetic singularities [7], at which the magnetisation within the vortex and antivortex cores reverses. We gain insight into the stability of these states through field and thermal equilibration protocols. These measurements pave the way for the observation of complex three-dimensional solitons in bulk magnets, as well as for the development of applications based on three-dimensional magnetic structures.

cond-mat.mes-hall↗

arXiv2020

Experimental observation of third-order effect in magnetic small-angle neutron scattering

A recent theory [Metlov and Michels, Phys. Rev. B 91, 054404 (2015)] predicts a qualitatively new effect in the magnetic small-angle neutron scattering (SANS) cross section of statistically-isotropic disordered ferromagnetic media. The effect is due to the third-order terms in the amplitude of the inhomogeneities. Here, its existence is demonstrated both numerically via large-scale micromagnetic simulations and analyzed experimentally in a two-phase iron-based nanocomposite. The previous model is extended to an arbitrary spatial defect profile, which allows us to describe the experimental field dependence of the third-order SANS effect quantitatively.

cond-mat.mtrl-sci↗

arXiv2018

Metastable states of sub-micron scale ferromagnetic periodic antidot arrays

The magnetic textures on nanoscale possess topological features due to the continuity of the magnetization vector field and its boundary conditions. In thin planar nanoelements, where the dependence of the magnetization across the thickness is inessential, the textures can be represented as a soup of 2-d topological solitons, corresponding to magnetic vortices and antivortices, which are the solutions of Skyrme's model. Topology of the element (of the boundary conditions) then imposes the restrictions on properties and locations of these objects. Periodic arrays of magnetic antidots have topology with infinite connectivity. In this work we classify and build an approximate analytical representation of metastable magnetization textures in such arrays and prove the conservation of their topological charge.

cond-mat.mes-hall↗

arXiv2018

Microstructural-defect-induced Dzyaloshinskii-Moriya interaction

The antisymmetric Dzyaloshinskii-Moriya interaction (DMI) plays a decisive role for the stabilization and control of chirality of skyrmion textures in various magnetic systems exhibiting a noncentrosymmetric crystal structure. A less studied aspect of the DMI is that this interaction is believed to be operative in the vicinity of lattice imperfections in crystalline magnetic materials, due to the local structural inversion symmetry breaking. If this scenario leads to an effect of sizable magnitude, it implies that the DMI introduces chirality into a very large class of magnetic materials---defect-rich systems such as polycrystalline magnets. Here, we show experimentally that the microstructural-defect-induced DMI gives rise to a polarization-dependent asymmetric term in the small-angle neutron scattering (SANS) cross section of polycrystalline ferromagnets with a centrosymmetric crystal structure. The results are supported by theoretical predictions using the continuum theory of micromagnetics. This effect, conjectured already by Arrott in 1963, is demonstrated for nanocrystalline terbium and holmium (with a large grain-boundary density), and for mechanically-deformed microcrystalline cobalt (with a large dislocation density). Analysis of the scattering asymmetry allows one to determine the defect-induced DMI constant, $D = 0.45 \pm 0.07 \, \mathrm{mJ/m^2}$ for Tb at $100 \, \mathrm{K}$. Our study proves the generic relevance of the DMI for the magnetic microstructure of defect-rich ferromagnets with vanishing intrinsic DMI. Polarized SANS is decisive for disclosing the signature of the defect-induced DMI, which is related to the unique dependence of the polarized SANS cross section on the chiral interactions. The findings open up the way to study defect-induced skyrmionic magnetization textures in disordered materials.

cond-mat.mtrl-sci↗