arXiv subjects

Andrey O. Leonov

Publications and source records attributed to Andrey O. Leonov.

18 recordsLinked to original sources

arXiv2026

Attractive Hopfions and Bimerons in Thin Films of Chiral Magnets: Cluster Formation and Lattice Instability in the Conical Phase

We investigate the energetics, interactions, and ordering tendencies of bimerons (cholesteric fingers of the second type, CF--2) and hopfions in thin films of chiral magnets and chiral liquid crystals hosting a conical background state. Although isolated bimerons possess positive eigen-energy with respect to the conical phase, they develop an attractive interaction mediated by the restructuring and partial overlap of their positive-energy shells, i.e., intermediate regions formed relative to the conical state. This attraction promotes the formation of bound pairs and extended bimeron chains, even in parameter regimes where a periodic bimeron lattice is no longer thermodynamically stable. Extending the analysis to three dimensions, we show that circularization of bimerons into hopfions renders their energy finite and gives rise to a well-defined metastability window closely linked to the stability range of cholesteric fingers. Isolated hopfions likewise exhibit an attractive interaction within the conical phase, leading to the formation of hexagonally ordered clusters. The attraction originates from the competition between favorable and unfavorable twist regions and from the energetic cost of the shell structures imposed by the conical background. Despite the presence of attractive pair potentials and cluster formation, we demonstrate that hexagonal hopfion lattices do not exhibit an equilibrium lattice period. Instead, the system evolves toward states in which the conical spiral or the CF--1 phase (cholesteric fingers of the first type) progressively invade the inter-soliton regions, thereby preventing crystallization. Our results reveal a regime of attraction without stable long-range order and clarify the interplay between topology, confinement, and conical-phase frustration in chiral magnet and liquid-crystal thin films.

cond-mat.soft↗

arXiv2026

Current-Induced Dynamics and Instability Pathways of Skyrmioniums in Chiral Magnets

We present a comprehensive study of current-driven dynamics, transformations, and instabilities of skyrmioniums in chiral magnetic films, considering both isolated objects and collective states forming skyrmionium-based meta-matter. Using micromagnetic simulations combined with an analytical description based on the generalized Thiele equation, we clarify how the internal structure of skyrmioniums governs their nonequilibrium response to electric currents. Despite having zero total topological charge, skyrmioniums exhibit a finite transverse velocity under applied currents. We show that this skyrmionium Hall effect originates from an imbalance between positive and negative topological contributions of the inner skyrmion and surrounding ring, which typically occupy different areas. Current-induced deformations further enhance this imbalance, yielding Hall angles comparable to those of skyrmions. At higher current densities, skyrmioniums undergo distinct instabilities depending on magnetic field and uniaxial anisotropy, including elongation, collapse into a skyrmion, transformation into a topologically trivial droplet, and expansion into stripe textures. We map these regimes in current--field and current--anisotropy phase diagrams and resolve their microscopic pathways via the evolution of topological charge and local rotational measures. Beyond isolated textures, mixed skyrmion--skyrmionium lattices display rich collective dynamics, including elastic transport, polymorphic transitions, soliton exchange, and stripe formation. Pulsed currents provide additional control, enabling access to regimes beyond continuous driving. Our results establish skyrmioniums and their meta-matter as tunable nonequilibrium systems probing the topological energy landscape far from equilibrium.

cond-mat.mes-hall↗

arXiv2026

Cholesteric Fingers from a Magnetic Perspective: Topology, Energetics, and Interactions

Chiral liquid crystals and chiral magnets host a wide variety of topological solitons described by closely related continuum theories, namely the Frank-Oseen and Dzyaloshinskii models. Exploiting this correspondence, we develop a unified description of cholesteric fingers in confined liquid crystals and their magnetic counterparts. Within a continuum framework including bulk and surface anisotropies, we analyze the topology, structure, interactions, and collective states of the two main finger types, CF-1 and CF-2. We show that cholesteric fingers are composite chiral solitons built from merons. CF-2 corresponds to a bimeron with unit topological charge, while CF-1 is a topologically trivial composite of two merons with identical vorticities. From a homotopic viewpoint these textures correspond to skyrmions and droplets. Strong homeotropic anchoring induces confinement effects that reshape the meron structure and redistribute topological charge across the film thickness. Isolated fingers in the homogeneous state interact repulsively and behave as particle-like objects. Periodic phases emerge when the energy of an isolated finger becomes negative, leading to nucleation-type transitions with a diverging lattice period. Degenerate finger types allow mixed periodic sequences, analogous to stacking polytypes. In a conical background, interactions become attractive due to overlap of distortion regions. Film thickness controls stability and structure: at small thickness solitons collapse, while at large thickness bimerons exhibit bistability between surface-stabilized and bulk-like states.

cond-mat.soft↗

arXiv2025

Confinement-Induced Metastability and Structural Diversity of Hopfions in Chiral Magnetic Films

Topological particle-like excitations such as skyrmions and hopfions offer rich opportunities for spintronic and photonic applications. While skyrmions have been extensively studied, the stabilization mechanisms and phase behavior of three-dimensional hopfions remain largely unexplored. Here, we investigate the formation, stability, and interactions of hopfions in thin chiral magnetic films with surface anchoring, using three-dimensional micromagnetic simulations within a material-independent framework applicable to both magnetic and liquid crystalline systems. We identify four distinct types of isolated hopfions, generated by rotating bimeron and finger-like solitons around a central axis. The metastability regions of these precursor textures closely follow the boundaries of modulated finger phases, enabling their size to be continuously tuned through anisotropydriven inflation and collapse. Remarkably, we demonstrate that hopfions near their inflation threshold possess energies comparable with the homogeneous state, allowing them to enclose regions of modulated phases or other solitons, forming higher-order, bag-like domains. In contrast, periodic hopfion lattices remain intrinsically unstable under confinement, spontaneously relaxing into finger phases. These findings establish general principles for stabilizing, tuning, and assembling three-dimensional topological solitons in confined chiral systems, suggesting experimentally accessible routes for texture engineering in liquid crystals via electric-field control.

cond-mat.mes-hall↗

arXiv2025

Skyrmionium meta-matter: a topologically heterogeneous magnetic crystal with emergent hybrid dynamics

We introduce and systematically investigate a new class of topological magnetic textures, skyrmionium meta-matter, composed of skyrmioniums (Skm, $Q=0$) and skyrmions (Sk, $Q=-1$) arranged in periodic lattices mimicking the richness of atomic materials. Pure skyrmionium lattices are unstable against elongation distortions and relax into the spiral phase, but even a small fraction of skyrmions acts as topological "pins" that stabilize diverse mixed Skm--Sk crystals. We classify these states by topological stoichiometry (Skm$_n$Sk$_m$) and show that each composition hosts multiple metastable polymorphs with distinct plane-group symmetries. Structural transformations between polymorphs are achieved by varying the lattice spacing, suggesting experimental control via pressure or strain. The collective spin dynamics is explored for both in-plane and out-of-plane AC magnetic fields. The resulting absorption spectra show resonant modes beyond the two rotational and one breathing mode of conventional skyrmion lattices. We identify hybrid excitations unique to Skm--Sk crystals, including (i) deformation-assisted rotations, where skyrmions acquire polygonal shapes and rotate, and (ii) orbital modes, where breathing skyrmioniums induce circular motion of confined skyrmions without changing their size. Mode frequencies span sub-GHz to above 10 GHz, consistent with exchange and DMI energy scales. Our results establish skyrmionium-based meta-matter as a versatile platform for tunable, topologically heterogeneous magnetic lattices with rich structural and dynamical properties, paving the way for reconfigurable magnonic and spintronic applications.

cond-mat.mes-hall↗

arXiv2024

Meron-mediated phase transitions in quasi-two-dimensional chiral magnets with easy-plane anisotropy: successive transformation of the hexagonal skyrmion lattice into the square lattice and into the tilted FM state

I revisit the well-known structural transition between hexagonal and square skyrmion lattices induced by increasing easy-plane anisotropy in quasi-two-dimensional chiral magnets. I show that the hexagonal skyrmion order, by the first-order phase transition, transforms into a distorted (rhombic) skyrmion lattice. The transition is mediated by merons and anti-merons emerging within the boundaries between skyrmion cells. Since the energy density associated with anti-merons is highly positive owing to the wrong rotational sense, one anti-meron per unit cell annihilates: anti-merons are squeezed by the pairs of approaching merons at the opposite sides of the hexagonal unit cell. Further, in a narrow range of anisotropy values, the distorted skyrmion lattice gradually transforms into a perfect square order of skyrmions (alternatively called "a square meron-antimeron crystal") when two merons eventually merge into one. Thus, within the square skyrmion lattice, there is one meron and two anti-merons per unit cell, which underlie the subsequent first-order phase transition into the tilted ferromagnetic state. A pair of oppositely charged merons mutually annihilates, whereas a remaining anti-meron couples with an anti-meron occupying the center of the unit cell. As an outcome, the tilted ferromagnetic state contains bimeron clusters (chains) with the attracting inter-soliton potential. Moreover, domain-wall merons are actively involved in dynamic responses of the square skyrmion lattices. As an example, I theoretically study spin-wave modes and their excitations by ac magnetic fields. Two found resonance peaks are the result of the complex dynamics of domain-wall merons: whereas in the high-frequency mode, merons rotate counterclockwise as one might expect, in the low-frequency mode, merons are created and annihilated consistently with the rotational motion of the domain boundaries.

cond-mat.mes-hall↗

arXiv2024

Reorientation transition between square and hexagonal skyrmion lattices near the saturation into the homogeneous state in quasi-two-dimensional chiral magnets

I revisit the well-known phase transition between the hexagonal skyrmion lattice and the homogeneous state within the phenomenological Dzyaloshinskii theory for chiral magnets which includes only the exchange, Dzyaloshinskii-Moriya and Zeeman energy contributions. I show that, in a narrow field range near the saturation field, the hexagonal skyrmion order gradually transforms into a square arrangement of skyrmions. Then, by the second-order phase transition during which the lattice period diverges, the square skyrmion lattice releases a set of repulsive isolated skyrmions. On decreasing magnetic field, isolated skyrmions re-condense into the square lattice at the same critical field as soon as their eigen-energy becomes negative with respect to the field-aligned state. The underlying reason of the reorientation transition between two skyrmion orders can be deduced from the energy density distribution within isolated skyrmions surrounded by the homogeneous state. When the negative energy within the ring-shaped area at the skyrmion outskirt outweighs the positive energy amount around the skyrmion axis, skyrmions tend to form the square lattice, in which the overlap of skyrmion profiles results in smaller energy losses as compared with the hexagonal crystal. With the further decreasing field, the hexagonal lattice achieves smaller energy density in comparison with the square one due to the denser packing of individual skyrmions.

cond-mat.mes-hall↗

arXiv2024

Communicating skyrmions as the main mechanism underlying skyrmionium (meta)stability in quasi-two-dimensional chiral magnets

We re-examine the internal structure of skyrmioniums stabilized in quasi-two-dimensional chiral magnets with easy-axis uniaxial anisotropy. Skyrmioniums are particle-like states of two nested skyrmions with opposite polarities contributing to zero topological charge. The physical principles of skyrmionium stability are drawn from both the analytical analysis with a trial function and from numerical simulations within the framework of micromagnetism. We deduce that the radii of the internal skyrmion with the positive polarity and the ring-shaped external skyrmion with the negative polarity are mutually dependent, which constitutes the paradigm of communicating skyrmions. For large central skyrmions, the skyrmionium transforms into a narrow circular domain wall, whereas for small internal radii, the ring expands, which occurs at the verge of collapsing into an ordinary isolated skyrmion. We show that skyrmioniums may form lattices of two varieties depending on the polarity of the internal skyrmion. At the phase diagram (magnetic field)-(uniaxial anisotropy), both skyrmionium lattices share the same area with one-dimensional spiral states and remain metastable solutions for the whole range of control parameters. By expanding at the critical line, skyrmionium lattices do not release isolated skyrmioniums. Isolated skyrmioniums of just one type exist apart from the corresponding lattice in a narrow field region restricted by the critical line of expansion from below and by the line of collapse above.

cond-mat.mes-hall↗

arXiv2021

Field-driven metamorphoses of isolated skyrmions within the conical state of cubic helimagnets

Topologically stable field configurations appear in many fields of physics, from elementary particles to condensed matter and cosmology. During the last decade, chiral liquid crystals and chiral magnets took on the role of model objects for experimental investigation of topological solitons and understanding of their nonsingular field configurations. Here we introduce a paradigm of facile skyrmionic networks with mutually-orthogonal orientations of constituent isolated skyrmions. Such networks are envisioned as a novel concept of spintronic devices and are presumably responsible for precursor phenomena near the ordering temperatures of bulk cubic helimagnets. In particular, we demonstrate an interconversion between mutually orthogonal skyrmions: horizontal skyrmions swirl into an intermediate spring-like states and subsequently squeeze into vertical skyrmions with both polarities. Skyrmion tubes are also considered as building blocks for particle-like states with more involved internal structure. A family of target-skyrmions, which includes an overlooked so far type with a multiple topological charge, is formed owing to the tendency to minimize the interaction energy between vertical and horizontal skyrmions. The conical phase serves as a suitable background for considered skyrmion evolution. It substantializes the attracting skyrmion-skyrmion interaction in the skyrmionic networks, shapes their internal structure and guides the nucleation processes. Alternatively, intricate textural changes of isolated skyrmions result not only in the structural deformations of a host conical state, but may lead to the formation of an exotic skyrmion order with pairs of merons being the core of the game. Generically, the fundamental insights provided by this work emphasize a three-dimensional character of skyrmion metamorphoses and can also be extended to three-dimensional solitons, such as hopfions.

cond-mat.mes-hall↗

arXiv2020

Evolution of Helimagnetic Correlations when approaching the Quantum Critical Point of Mn$_{1-x}$Fe$_x$Si

We present a comprehensive investigation of the evolution of helimagnetic correlations in Mn$_{1-x}$Fe$_x$Si with increasing doping. By combining polarised neutron scattering and high resolution Neutron Spin Echo spectroscopy we investigate three samples with $x$=0.09, 0.11 and 0.14, i.e. with compositions on both sides of the concentration $x^* \sim 0.11$ where the helimagnetic Bragg peaks disappear and between $x^*$ and the quantum critical concentration $x_C \sim 0.17$, where $T_C$ vanishes. We find that the abrupt disappearance of the long range helical periodicity at $x^*$, does not affect the precursor fluctuating correlations. These build up with decreasing temperature in a similar way as for the parent compound MnSi. Also the dynamics bears strong similarities to MnSi. The analysis of our results indicates that frustration, possibly due to achiral RKKY interactions, increases with increasing Fe doping. We argue that this effect explains both the expansion of the precursor phase with increasing $x$ and the abrupt disappearance of long range helimagnetic periodicity at $x^*$.

cond-mat.str-el↗

arXiv2020

Field and anisotropy driven transformations of spin spirals in cubic skyrmion hosts

We discuss distinctive features of spiral states in bulk chiral magnets such as MnSi and Cu$_2$OSeO$_3$ that stem from the effect of the cubic magneto-crystalline anisotropy. First of all, at both the helical-to-conical and the conical-to-ferromagnetic transitions, taking place at H$_{c1}$ and H$_{c2}$, respectively, the cubic anisotropy leads to reversible or irreversible jump-like reorientations of the spiral wavevectors. The subtle interplay between the easy and hard anisotropy axes gives rise to a phase transition between elliptically distorted conical states almost without any detectable change in the period. We show that the competition between on-site cubic and exchange anisotropy terms can also lead to oblique spiral states. Our work gives clear directions for further experimental studies to reveal theoretically predicted spiral states in cubic helimagnets beyond the aforementioned well-established states thus, can help to understand the magnetic phase diagram of these archetypal skyrmion hosts. In addition, we show that properties of isolated skyrmions such as inter-skyrmion attraction, orientation and/or nucleation are also rooted in the properties of host spirals states, in which skyrmions are stabilized.

cond-mat.mes-hall↗

arXiv2020

Stability of in-plane and out-of-plane chiral skyrmions in epitaxial MnSi(111)/Si(111) thin films: surface twists versus easy-plane anisotropy

The revisited theoretical phase diagrams for thin films of cubic helimagnets with the easy-plane anisotropy are shown to have different topology as previously reported [Phys. Rev. B 85, 094429 (2012)]. For both in-plane and out-of-plane directions of an applied magnetic field, the phase diagrams exhibit extensive areas of stable skyrmions, which overlap for a wide range of anisotropy parameters. Although the existence of the out-of-plane skyrmions was contradicted within the previous theoretical models, we prove that additional surface twists lead to their stability, while the moderate easy-plane anisotropy increases the stability range of in-plane skyrmions. Moreover, the interplay between the anisotropy and the surface twists gives rise to a stable spiral state canted with respect to the surfaces. Being absent in bulk helimagnets, this oblique spiral occupies vast areas at the phase diagrams in thin-film nanosystems and serves as a connecting-link between cones and helicoids. Our theory gives clear directions for renewed experimental studies of in-plane and out-of-plane skyrmions in epitaxial MnSi(111)/Si(111) thin films.

cond-mat.mes-hall↗

arXiv2019

Skyrmions and spirals in MnSi under hydrostatic pressure

The archetype cubic chiral magnet MnSi is home to some of the most fascinating states in condensed matter such as skyrmions and a non-Fermi liquid behavior in conjunction with a topological Hall effect under hydrostatic pressure. Using small angle neutron scattering, we study the evolution of the helimagnetic, conical and skyrmionic correlations with increasing hydrostatic pressure. We show that the helical propagation vector smoothly reorients from $\langle 111 \rangle$ to $\langle100\rangle$ at intermediate pressures. At higher pressures, above the critical pressure, the long-range helimagnetic order disappears at zero magnetic field. Nevertheless, skyrmion lattices and conical spirals form under magnetic fields, in a part of the phase diagram where a topological Hall effect and a non-Fermi liquid behavior have been reported. These unexpected results shed light on the puzzling behavior of MnSi at high pressures and the mechanisms that destabilize the helimagnetic long-range order at the critical pressure.

cond-mat.mtrl-sci↗

arXiv2019

Real-space observation of skyrmion clusters with mutually orthogonal skyrmion tubes

We report the discovery and direct visualization of skyrmion clusters with mutually-orthogonal orientations of constituent isolated skyrmions in chiral liquid crystals and ferromagnets. We show that the nascent conical state underlies attracting inter-skyrmion potential, whereas an encompassing homogeneous state leads to the repulsive skyrmion-skyrmion interaction. The crossover between different regimes of skyrmion interaction could be identified upon changing layer thickness and/or the surface anchoring. We develop a phenomenological theory describing two types of skyrmions and the underlying mechanisms of their interaction. We show that isolated horizontal skyrmions with the same polarity may approach a vertical isolated skyrmion from both sides and thus constitute two energetically-different configurations which are also observed experimentally. In an extreme regime of mutual attraction, the skyrmions wind around each other forming compact superstructures with undulations. We also indicate that our numerical simulations on skyrmion clusters are valid in a parameter range corresponding to the A-phase region of cubic helimagnets.

cond-mat.mes-hall↗

arXiv2019

Skyrmion instabilities and distorted spiral states in a frustrated chiral magnet

Magnetic skyrmions are particle-like topological excitations that recently generated much interest as candidates for future spintronic devices based on skyrmion small size, enhanced topological stability, and/or mutual interaction. Here we examine the properties of isolated skyrmions in a frustrated chiral magnet with competing Dzyaloshinskii-Moriya and frustrated exchange interactions. We show that the skyrmion size drastically decreases even for small values of competing stabilization mechanisms. Skyrmion mutual interaction remains attracting as is inherent for frustrated skyrmions, but the value of the Dzyaloshinskii constant regulates the number of minima in the interaction potentials. Moreover, the constructed phase diagrams for a chiral helimagnet contain a distorted spiral state that can be considered as a buffer between the helicoidal and conical one-dimensional modulations. The formulated concepts may further enhance the functionalities of spintronic devices. In particular, the controlled instability of skyrmions with respect to the conical state allows to obtain bimeron-like structures. Moreover, our results provide physical insight into the chiral states in the magnetic systems, e.g., in MnSi$_{1-x}$Ge$_x$.

cond-mat.mes-hall↗

arXiv2018

Current-induced shuttlecock-like movement of non-axisymmetric chiral skyrmions

Current-induced motion of non-axisymmetric skyrmions within angular phases of polar helimagnetis with the easy plane anisotropy is studied by micromagnetic simulations.Such non-axisymmetric skyrmions consist of a circular core and a crescent-shaped domain-wall region formed with respect to the tilted surrounding state. A current-driven motion of non-axisymmetric skyrmions exhibits two distinct time regimes: initially the skyrmions rotate towards the current flow direction and subsequently move along the current with the skyrmionic crescent first. According to the Thiele equation, the asymmetric distribution of the topological charge and the dissipative force tensor play an important role for giving the different velocities for the circular and the crescent-shaped constituent parts of the skyrmion what underlies such a shuttlecock-like movement. Moreover, the current-velocity relation depends on the tilt angle of the surrounding angular phase what makes in particular the transverse velocity of skyrmions sensitive to their field-driven configurational transformation.

cond-mat.mtrl-sci↗

arXiv2018

Toggle-switch-like crossover between two types of isolated skyrmions within the conical phase of cubic helimagnets

We investigate the field-induced crossover between two types of isolated skyrmions that exist within the conical phase of cubic helimagnets and orient themselves either along or perpendicular to the field. Such a crossover takes place for the same value of the field, at which the closely packed skyrmion lattice was predicted to stabilize in the A-phase region. The clusters and a skyrmion lattice comprised by the skyrmions perpendicular to the field, however, are unfavorable and lose their stability as compared with the skyrmions parallel to the field. We also followed transformation of perpendicular skyrmions into pairs of merons that rupture the helical state. An attractive interactions between different types of isolated skyrmions make it feasible to construct complex cluster states with the cubic arrangement of skyrmions.

cond-mat.mes-hall↗

arXiv2018

Crossover of skyrmion and helical modulations in noncentrosymmetric ferromagnets

The coupling between angular (twisting) and longitudinal modulations arising near the ordering temperature of noncentrosymmetric ferromagnets strongly influences the structure of skyrmion states and their evolution in an applied magnetic field. In the precursor states of cubic helimagnets, a continuous transformation of skyrmion lattices into the saturated state is replaced by the first-order processes accompanied by the formation of multidomain states. Recently the effects imposed by dominant longitudinal modulations have been reported in bulk MnSi and FeGe. Similar phenomena can be observed in the precursor regions of cubic helimagnet epilayers and in easy-plane chiral ferromagnets (e.g. in the hexagonal helimagnet CrNb3S6).

cond-mat.mes-hall↗