arXiv subjects

Dmitry A. Garanin

Publications and source records attributed to Dmitry A. Garanin.

At least 19 recordsLinked to original sources

arXiv2026

Oscillation modes of skyrmion strings in a ferromagnetic film

It is shown that a skyrmion string in a ferromagnetic film consisting of $N$ atomic layers exhibits flexural oscillations at eigenfrequencies $|ω_{m}|=(4J'S/\hbar)\sin^{2}[πm/(2N)]$, where $J'$ is the interlayer exchange coupling, $S$ is the length of the atomic spin, and $m=1,...,N-1$. This result is confirmed numerically for individual skyrmion strings in a discrete microscopic spin-lattice model of up to ten atomic layers, as well as for skyrmion-string lattices at finite temperature.

cond-mat.mtrl-sci↗

arXiv2026

Massive dynamics of skyrmions in ferrimagnetic films

Deformations of skyrmions arising from the presence of more than one magnetic sublattice lead to their massive dynamics in ferrimagnets as compared to the massless dynamics in 2D ferromagnets. This results in the gyroscopic motion of skyrmions, which manifests as skyrmion cyclotron resonance that can be excited by microwaves or spin currents. We investigate analytically and numerically the motion and resonant oscillations of individual skyrmions and skyrmion lattices in the presence of dissipation in a two-sublattice transition-metal -- rare-earth (TM/RE) system. The focus is on the dependence of the skyrmion dynamics on the RE concentration. Parameters of the CoGd ferrimagnet are utilized in the numerical work. The massive dynamics of skyrmions in ferrimagnets, as well as the spectrum of their excitations, undergo significant changes near the angular momentum compensation point, which should not be difficult to detect in experiments.

cond-mat.mes-hall↗

arXiv2026

Skyrmion Cyclotron Resonance in Ferrimagnets

We show that a resonance due to gyroscopic motion of skyrmions, conceptually similar to the electron cyclotron resonance in metals, can be excited in a ferrimagnetic film by a spin current or microwaves. It must permit unambiguous measurement of the skyrmion mass for which a universal expression depending solely on the exchange interaction between spins belonging to two different ferrimagnetic sublattices is derived. The dependence of the skyrmion cyclotron frequency on parameters is computed for a TM/RE ferrimagnet, using CoGd as an example. The cyclotron frequency exhibits a dip near the angular momentum compensation point, where it hybridizes with the ferromagnetic resonance. The skyrmion cyclotron mode is studied for individual skyrmions and for skyrmion lattices, where the effect must be strong enough to be observed in microwave and spin-current experiments.

cond-mat.other↗

arXiv2024

Static and Microwave Properties of Amorphous Magnets Near Saturation

Static and dynamic properties of magnetically soft amorphous ferromagnets have been studied analytically and numerically within random-field and random-anisotropy models. External field and coherent anisotropy that are weak compared to their random counterparts are sufficient to bring the magnet close to saturation. The scaling of spin-spin correlations in this regime is computed, and its dependence on parameters is confirmed by Monte Carlo simulation. We show that near the ferromagnetic resonance, the spin excitations are damped and spatially localized due to randomness even close to saturation. On increasing the strength of randomness, the localization length goes down in accordance with theoretical expectations, while the damping of spin excitations goes up.

cond-mat.mtrl-sci↗

arXiv2024

Scaling of Static and Dynamical Properties of Random Anisotropy Magnets

Recently observed scaling in the random-anisotropy model of amorphous or sintered ferromagnets is derived by an alternative method and extended for studying the dynamical properties in terms of the Landau-Lifshitz equations for spin blocks. Switching to the rescaled exchange and anisotropy constants allows one to investigate the dynamics by using a reduced number of variables, which greatly speeds up computations. The proposed dynamical scaling is applied to the problem of microwave absorption by a random anisotropy magnet. The equivalence of the rescaled model to the original atomic model is confirmed numerically. The method is proposed as a powerful tool in studying static and dynamic properties of systems with quenched randomness.

cond-mat.dis-nn↗

arXiv2024

Melting and Freezing of a Skyrmion Lattice

We report comprehensive Monte-Carlo studies of the melting of skyrmion lattices in systems of small, medium, and large sizes with the number of skyrmions ranging from $10^{3}$ to over $10^{5}$. Large systems exhibit hysteresis similar to that observed in real experiments on the melting of skyrmion lattices. For sufficiently small systems which achieve thermal equilibrium, a fully reversible sharp solid-liquid transition on temperature with no intermediate hexatic phase is observed. A similar behavior is found on changing the magnetic field that provides the control of pressure in the skyrmion lattice. We find that on heating the melting transition occurs via a formation of grains with different orientations of hexagonal axes. On cooling, the fluctuating grains coalesce into larger clusters until a uniform orientation of hexagonal axes is slowly established. The observed scenario is caused by collective effects involving defects and is more complex than a simple picture of a transition driven by the unbinding and annihilation of dislocation and disclination pairs.

cond-mat.mes-hall↗

arXiv2024

Solid-Liquid Transition in a Skyrmion Matter

We report Monte-Carlo studies of the orientational order and melting of a 2D skyrmion lattice containing more than one million spins. Two models have been investigated, a microscopic model of lattice spins with Dzyaloshinskii-Moryia interaction that possesses skyrmions, and the model in which skyrmions are treated as point particles with repulsive interaction derived from a spin model. They produce similar results. The skyrmion lattice exhibits a sharp one-step transition between solid and liquid phases on temperature and the magnetic field. This solid-liquid transition is characterized by the kink in the magnetization. The field-temperature phase diagram is computed. We show that the application of the field gradient to a 2D system of skyrmions produces a solid-liquid interface that must be possible to observe in experiments.

cond-mat.mtrl-sci↗

arXiv2023

Scaling Theory of Magnetic Order and Microwave Absorption in Amorphous and Granular Ferromagnets

Magnetic order and microwave absorption in amorphous ferromagnets and materials sintered from nanoscale ferromagnetic grains are investigated analytically and numerically within the random-anisotropy model. We show that a scaling argument specific to static randomness allows one to make conclusions about the behavior of a large system with a weak disorder by studying a smaller system with a strong disorder. The breakdown of the scaling on increasing the strength of the magnetic anisotropy and/or the size of the grain separates two distinct regimes in magnetic ordering and frequency dependence of the absorbed microwave power. Analytical results are confirmed by numerical experiments on spin lattices containing up to ten million spins. Our findings should help design materials with desired magnetic and microwave properties. The method can be extended to other systems with quenched randomness.

cond-mat.dis-nn↗

arXiv2022

Polyhexatic and Polycrystalline States of Skyrmion Lattices

Abstract We report Monte Carlo studies of lattices of up to $10^{5}$ skyrmions treated as particles with negative core energy and repulsive interaction obtained from a microscopic spin model. Temperature dependence of translational and orientational correlations has been investigated for different experimental protocols and initial conditions. Cooling the skyrmion liquid from fully disordered high-temperature state results in the formation of a skyrmion polycrystal. A perfect skyrmion lattice prepared at $T=0$, on raising temperature undergoes a first-order melting transition into a polyhexatic state that consists of large orientationally ordered domains of fluctuating shape. On the further increasing temperature, these domains decrease in size, leading to a fully disordered liquid of skyrmions.

cond-mat.stat-mech↗

arXiv2021

Random Anisotropy Magnet at Finite Temperature

Abstract We present finite-temperature Monte Carlo studies of a 2D random-anisotropy magnet on lattices containing one million spins. The correlated spin-glass state predicted by analytical theories is reproduced in simulations, as are the field-cooled and zero-field-cooled magnetization curves observed in experiments. The orientations of lattice spins begin to freeze when the temperature is lowered. The freezing transition is due to the energy barriers generated by the random anisotropy rather than due to random interactions in conventional spin-glasses. We describe freezing by introducing the time-dependent spin-glass order parameter $q$ and the spin-melting time $τ_{M}$ defined via $q=τ_{M}/t$ above freezing, where t is the time of the experiment represented by the number of Monte Carlo steps.

cond-mat.mtrl-sci↗

arXiv2021

Energy balance and energy correction in dynamics of classical spin systems

Energy-correction method is proposed as an addition to mainstream integrators for equations of motion of systems of classical spins. This solves the problem of non-conservation of energy in long computations and makes mainstream integrators competitive with symplectic integrators for spin systems that for different-site interactions conserve the energy explicitly. The proposed method is promising for spin systems with single-site interactions for which symplectic integrators do not conserve energy and thus have no edge against mainstream integrators. From the energy balance in the spin system with a phenomenological damping and Langevin fields, a formula for the dynamical spin temperature in the presence of single-site anisotropy is obtained.

physics.comp-ph↗

arXiv2021

Conservation of Angular Momentum in the Elastic Medium with Spins

Exact conservation of the angular momentum is worked out for an elastic medium with spins. The intrinsic anharmonicity of the elastic theory is shown to be crucial for conserving the total momentum. As a result, any spin-lattice dynamics inevitably involves multiphonon processes and interaction between phonons. This makes transitions between spin states in a solid fundamentally different from transitions between atomic states in vacuum governed by linear electrodynamics. Consequences for using solid-state spins as qubits are discussed.

cond-mat.mes-hall↗

arXiv2020

Skyrmions in an oblique field: A path to novel binary and quaternary memory

We propose a novel binary and quaternary memory device based upon skyrmion states induced by the oblique field in a square magnetic island. To describe stable states and dynamics of the skyrmion, we employ the lattice model that uses the parameters of a real material and accounts for all relevant interactions. Depending on the orientation of the field, two or four spatially separated energy minima emerge in the oblique field. The energy barriers between the minima can be controlled by the strength and orientation of the magnetic field. We study the dynamics of the skyrmion and show that it can be moved between any two states by application of the field gradient. Islands of thickness of a few tens of atomic layers permit room-temperature manipulation of the proposed device.

cond-mat.mtrl-sci↗

arXiv2019

Biskyrmions Lattices in Centrosymmetric Magnetic Films

Abstract Theoretical framework is developed that explains biskyrmion lattices observed in non-chiral magnetic films. We study films of finite thickness containing up to $1000\times1000\times100$ spins. Hexatic biskyrmion lattices in a pure 2D exchange model are naturally described by the Weierstrass $\wp$ and $ζ$ elliptic functions. Starting with such a lattice as an initial state we investigate how it evolves towards the minimum-energy state in the presence of perpendicular magnetic anisotropy and dipole-dipole interaction. In accordance with experiments, we find that the final state is a triangular lattice of biskyrmion bubbles containing Bloch lines.

cond-mat.mes-hall↗

arXiv2019

Thermal Collapse of a Skyrmion

Thermal collapse of an isolated skyrmion on a two-dimensional spin lattice has been investigated. The method is based upon solution of the system of stochastic Landau-Lifshitz-Gilbert equations for up $10^4$ spins. Recently developed pulse-noise algorithm has been used for the stochastic component of the equations. The collapse rate follows the Arrhenius law. Analytical formulas derived within a continuous spin-field model support numerically-obtained values of the energy barrier and the pre-exponential factor, and their dependence on the magnetic field. Our findings agree with experiments, as well as with recent numerical results obtained by other methods.

cond-mat.mes-hall↗

arXiv2019

Stability of Biskyrmions in Centrosymmetric Magnetic Films

Motivated by the observation of biskyrmions in centrosymmetric magnetic films (Yu et al. Nature Communications 2014, Wang et al. Advanced Materials 2016), we investigate analytically and numerically the stability of biskyrmions in films of finite thickness, taking into account the nearest-neighbor exchange interaction, perpendicular magnetic anisotropy (PMA), dipole-dipole interaction (DDI), and the discreteness of the atomic lattice. The biskyrmion is characterized by the topological charge $Q=2$, the spatial scale $λ$, and another independent length $d$ that can be interpreted as a separation of two $Q=1$ skyrmions inside a $Q=2$ topological defect in the background of uniform magnetization. We find that biskyrmions with $d$ of order $λ$ can be stabilized by the magnetic field within a certain range of the ratio of PMA to DDI in a film having a sufficient number of atomic layers $N_{z}$. The shape of biskyrmions has been obtained by the numerical minimization of the energy of interacting spins in a $1000\times1000\times N_{z}$ atomic lattice. It is close to the exact solution of Belavin-Polyakov model when $d$ is below the width of the ferromagnetic domain wall. We compute the magnetic moment of a biskyrmion and discuss ways of creating biskyrmions in experiment.

cond-mat.mes-hall↗

arXiv2019

Breathing Mode of a Skyrmion on a Lattice

The breathing mode of a skyrmion, corresponding to coupled oscillations of its size and chirality angle is studied numerically for a conservative classical-spin system on a $500\times500$ lattice. The dependence of the oscillation frequency on the magnetic field is computed. It is linear at small fields, reaches maximum on increasing the field, then sharply tends to zero as the field approaches the threshold above which the skyrmion loses stability and collapses. Physically transparent analytical model is developed that explains the results qualitatively and provides the field dependence of the oscillation frequency that is close to the one computed numerically. It is shown that a large-amplitude breathing motion in which the skyrmion chirality angle $γ$ is rotating in one direction is strongly damped and quickly ends by the skyrmion collapse. To the contrary, smaller-amplitude breathing motion in which $γ$ oscillates is undamped.

cond-mat.mes-hall↗

arXiv2019

Thermal Creation of Skyrmions in Ferromagnetic Films with Perpendicular Anisotropy and Dzyaloshinskii-Moriya Interaction

We study theoretically, via Monte Carlo simulations on lattices containing up to 1000 x 1000 spins, thermal creation of skyrmion lattices in a 2D ferromagnetic film with perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction. At zero temperature, skyrmions only appear in the magnetization process in the presence of static disorder. Thermal fluctuations violate conservation of the topological charge and reduce the effective magnetic anisotropy that tends to suppress skyrmions. In accordance with recent experiments, we find that elevated temperatures assist the formation of skyrmion structures. Once such a structure is formed, it can be frozen into a regular skyrmion lattice by reducing the temperature. We investigate topological properties of skyrmion structures and find the average skyrmion size. Energies of domain and skyrmion states are computed. It is shown that skyrmion lattices have lower energy than labyrinth domains within a narrow field range.

cond-mat.mtrl-sci↗