arXiv subjects

Pavel A. Andreev

Publications and source records attributed to Pavel A. Andreev.

At least 19 recordsLinked to original sources

arXiv2026

Dielectric response of the antiferromagnetic multiferroics with cycloidal equilibrium for the polarization related to the noncollinear spins

Linear dynamics of the small amplitude perturbations in the antiferromagnetic multiferroics is analytically considered. Equilibrium state in the considered regime is assumed to be cycloidal structure both for the antiferromagnetic vector and the nonzero magnetization vector (presence of weak ferromagnetism in the system is included). The electric polarization of spin origin related to the "noncollinear" spins is considered and its influence on the spin dynamics is included. The dynamical electric susceptibility tensor is obtained to demonstrate response of the multiferroics on the alternating electric field. Existence of two polarization projections is found, response of each of them on two projections of the electric field perpendicular to the cycloid direction is presented. Different roles of the in plane and out of plane electric perturbations is demonstrated analytically. Essential role of the low frequency gapless spin wave in the dielectric response is described. Contributions of the spiral structure and the weak ferromagnetism in the dielectric response are specified.

cond-mat.mtrl-sci↗

arXiv2026

Spin-current model of electric polarization with the tensor gyromagnetic ratio

The spin-current model of electric polarization of spin origin is developed for a magnetic structure with anisotropic tensor gyromagnetic ratio (g-factor). Three mechanisms of the magnetoelectric effect are proposed, caused by the symmetric Heisenberg exchange interaction, the Dzyaloshinsky-Moriya interaction, and the spin-spin interaction related to the odd anisotropy of the symmetric exchange interaction of magnetic ions via nonmagnetic ion. The dependence of electric polarization on the spin density and tensor g-factor in the generalized spin-current model is derived. New solutions for macroscopic electric polarization, that arise in the cycloidal and helicoidal spin orders and are caused by the non-diagonal components of the gyromagnetic ratio, are predicted. The extended of the spin-current model to including a tensor g-factor can be important for the magnetic ferroelectrics with heavy ions which take part in the formation of magnetoelectric effect.

cond-mat.other↗

arXiv2026

Keffer-like form of the symmetric Heisenberg exchange integral: Contribution to the Landau--Lifshitz--Gilbert equation and spin wave dispersion dependence

The symmetric Heisenberg exchange interaction and antisymmetric Dzyaloshinskii-Moriya interaction are parts of the tensor potential describing effective spin-spin interaction caused by the superexchange interaction of magnetic ions via nonmagnetic ion. There is the Keffer form of the vector constant of the Dzyaloshinskii-Moriya interaction, which includes the shift of the nonmagnetic ion (ligand) from the line connecting two magnetic ions. It is suggested, in this paper, that the ligand shift can give contribution in the constant of the symmetric Heisenberg interaction in antiferromagnetic or ferrimagnetic materials. Hence, the constant of the Heisenberg interaction is composed minimum of two terms. One does not depend on the ligand shift an gives standard contribution in the energy density like term with no derivatives of the spin densities or term containing two spatial derivatives of the spin densities. It is demonstrated that additional term gives a term in the energy density containing one spatial derivative of the spin density. Corresponding contribution in the Landau--Lifshitz--Gilbert equation is found. Possibility of the noncollinear equilibrium order of spin under influence of new spin torque is discussed. Modification of the spin wave (normal modes) dispersion dependencies in the antiferromagnetic materials is found for the collinear order and for the cycloidal order of spins. Effective spin current is derived and applied for the spin-current model of the polarization origin in multiferroics.

cond-mat.mtrl-sci↗

arXiv2026

Topological charge, helicity and vorticity conservation and the reverse spin-current model in the II-nd type multifferoics

The topological charge and its density are related to the spin vorticity, while the spin vorticity is a part of full vorticity of the medium. The full vorticity is related to an integral of motion called the hydrodynamic helicity. Relation between two integrals of motion (the topological charge and the hydrodynamic helicity) is traced. The role of the spin-current model of the electric polarization formation due to the specific spin distribution in the helicity conservation is demonstrated. The reverse spin-current model is suggested to demonstrate the contribution of the polarization in the spin evolution equation, its importance for the helicity conservation is shown as well. Spin-field model of the electric polarization is the second model for the electric polarization (the deformation, firstly) formation due to the specific spin distribution, which appears from the same principles, but it has nonstationary origin. Moreover, the reverse spin-current model gives a mechanism for the spin structure formation due to the electric polarization in the system. It also appears as the requirement for the conservation of the helicity and the topological charge.

cond-mat.mtrl-sci↗

arXiv2026

Spin waves and instabilities in the collinear four component antiferromagnetic materials

The small amplitude perturbations of spins are considered in the four component antiferromagnetic materials with the equilibrium state of form up-up-down-down (uniaxial samples). Other configurations for the four component antiferromagnetic materials and two component antiferromagnetic materials are briefly considered for the comparison with main regime. Dispersion dependencies of two spin waves existing in the system are found if equilibrium spins are parallel to the anisotropy axis. Dispersion equation leading to a possibility of four spin waves is derived if equilibrium spins are perpendicular to the anisotropy axis. It is found that at least one solution has negative frequency square for all possible modules and signs of the anisotropy constants. Calculations are made for the one dimensional chain of classical spins in the approximation of the nearest neighbours interaction. Next, we also addressed the nearest neighbours interaction approximation in the limit of the continuous medium (for the Landau--Lifshitz--Gilbert equation). Mostly applied form of the Landau--Lifshitz--Gilbert equation goes beyond the nearest neighbours interaction approximation. The difference is described. Required assumptions are described.

cond-mat.mtrl-sci↗

arXiv2026

Analytical analysis of the spin wave dispersion in the cycloidal spin structures under the influence of magneto-electric coupling

Spin waves and coupling of the spin waves with electromagnetic waves are considered in the multiferroic materials with the electric dipole moment proportional to the scalar product of spins. Nature of this interaction is discussed within the spin current model. Dispersion dependence for the spin waves propagating as the perturbation of the equilibrium state described by spin cycloid is found analytically. Contribution of the wave vector of the equilibrium cycloid is traced and it is found that it decreases the contribution of the anisotropy constant, which can lead to the instability. Limit regime of the spin waves in systems of collinear spins is described to show the role of the magnetoelectric coupling for two regimes of the electric dipole moment: it proportional to the scalar product of spins or to the vector product of spins. The dielectric permeability as the response on the electromagnetic perturbations associated with the magneto-electric coupling for the same equilibrium state is calculated.

cond-mat.mtrl-sci↗

arXiv2026

On the generalized Keffer form of the Dzyaloshinskii constant: its consequences for the spin, momentum and polarization evolution

Different analytical features of the Dzyaloshinskii-Moriya interaction are related to different contributions to the Dzyaloshinskii constant in the microscopic Hamiltonian. Consequences appear in the macroscopic Landau--Lifshitz--Gilbert equation. It leads to various phenomena. Three contributions to the Dzyaloshinskii constant are reviewed and combined in the generalized Keffer form of the Dzyaloshinskii constant. The fourth possible form of the Dzyaloshinskii constant is suggested as well. Macroscopic consequences of these three mechanisms are well-known, but further possible generalizations of the Keffer form of the Dzyaloshinskii constant are suggested. Consequences for the spin evolution equations, the momentum balance equations, and polarization evolution equations are considered. Some analog of the Keffer form is suggested for the exchange integral in symmetric Heisenberg Hamiltonian demonstrating the nontrivial contribution of the ligands in this regime.

cond-mat.mtrl-sci↗

arXiv2025

Electric susceptibility of antiferromagnetic multiferroics with cycloidal spin order at magnetoelectric effect associated with collinear component of spins

The contribution of magnetoelectric effect to Landau--Lifshitz-Gilbert equation is considered in case when medium polarization is caused by parallel component of neighboring spins. The result is presented for ferromagnetic and antiferromagnetic materials. A comparison is given with the contribution of magnetoelectric effect to Landau--Lifshitz-Gilbert equation when medium polarization is caused by perpendicular component of spins. The dispersion dependence of spin waves in antiferromagnets with cycloidal equilibrium spin order is derived. The electric susceptibility and permittivity of antiferromagnetic multiferroics in which magnetoelectric effect is caused by collinear component of spins is obtained analytically.

cond-mat.mtrl-sci↗

arXiv2025

Mean-field theory of the electromagnon resonance

We present the analytical theory of the electromagnon resonance for the multiferroics of spin origin. We consider the spin density evolution under the influence of magnetoelectric coupling in the presence of the electromagnetic wave. The dielectric permeability is found for the eigen-wave perturbations accompanied by perturbations of the electric field. The imaginary part of the dielectric permeability is found as the function of the applied electric field frequency, while the frequency of the eigen-waves is found from the dispersion equation as the function of the wave vector and parameters of the system. The result shows the existence of two peaks. One sharp peak is associated with the magnon resonance, while the second wide peak at the approximately four times smaller frequency is interpreted as the electromagnon resonance in accordance with existing experimental data.

cond-mat.mtrl-sci↗

arXiv2025

Regimes of optical transparency and instabilities of collinear dielectric ferromagnetic materials in the presence of the dynamic magnetoelectric effect

The contribution of the polarization associated with the noncollinear parts of spins in the dielectric permeability tensor of multiferroic materials is considered. As the equilibrium state, we consider the systems of parallel spins, so we have zero equilibrium polarization. Dynamical polarization appears due to the spin evolution via the magnetoelectric coupling. The regime of frequencies, where the refractive index goes to 1 is found for the high (in comparison with the characteristic frequency of the anisotropic energy or the cyclotron frequency) left/right circularly polarized electromagnetic wave propagating parallel to the equilibrium spin direction. Moreover, the signs of the imaginary part of the dielectric permeability, the refractive index, and the frequency show the instability of the parallel spin configuration at the propagation of the linearly polarized electromagnetic wave due to the effective magnetoelectric interaction.

cond-mat.mtrl-sci↗

arXiv2024

Electric polarization evolution equation for antiferromagnetic multiferroics with the polarization proportional to the scalar product of the spins

The spin current model of electric polarization of multiferroics is justified via the quantum hydrodynamic method and the mean-field part of the spin-orbit interaction. The spin current model is applied to derive the electric polarization proportional to the scalar product of the spins of the near by ions, which appears to be caused by the Dzylaoshinskii-Moriya interaction. Symmetric tensor spin structure of the polarization is discussed as well. We start our derivations for the ferromagnetic multiferroic materials and present the further generalization for the antiferromagnetic multiferroic materials. We rederive the operator of the electric dipole moment, which provides the macroscopic polarization obtained via the spin current model. Finally, we use the quantum average of the found electric dipole moment operator in order to derive the polarization evolution equation for the antiferromagnetic multiferroic materials. Possibility of spiral spin structures is analyzed.

cond-mat.mtrl-sci↗

arXiv2024

Polarization evolution equation for the exchange-strictionally formed II-type multiferroic materials

The multiferroics are the materials, where single cell of a magnetically order crystal forms an electric dipole moment. We derive equation for the evolution of the macroscopic density of the electric dipole moment (polarization of the system). The derivation is made within the "quantum hydrodynamic" method, which allows to derive equations for the evolution of the macroscopic functions of the quantum systems starting with the microscopic description. In this work we do not consider the microscopic level of individual electrons and ions, but we start our analysis from the combination of ions in cells of the crystal. We present an effective Hamiltonian for the evolution of such intermediate scale objects. We also apply the equation for the electric dipole moment of the single cell, which is recontracted in the corresponding operator. Using this operator and the wave function of combination of ions in the cell, we define the macroscopic density of the electric dipole moment. Finally, we apply the nonstationary Schrodinger equation with the chosen Hamiltonian in order to derive equation evolution of the polarization. The derivation is made for the dipole formed by the exchange-striction mechanism in the II-type multiferroic materials. The interaction caused term in the polarization evolution equation is found to be proportional to the fourth space derivative of mixed product (triple scalar product) of three spin density vectors. Conditions are discussed for the regime, where interaction appears in a smaller order on the space derivatives.

cond-mat.mtrl-sci↗

arXiv2024

A new quantum hydrodynamic description of ferroelectricity in spiral magnets

The strong coupling between magnetism and ferroelectricity was found in rare earth manganites, where the electric polarization could be induced by special magnetic ordering. There is no theoretical model that would allow us to study the static and dynamic properties of electric polarization in strongly correlated magnetic dielectrics. In the presented research, we have taken the main step towards the construction of such a fundamental model, and made a direct connection between the microscopic Katsura-Nagaosa-Balatsky theory and Mostovoy's phenomenological model for magnetically induced polarization. A novel description of the ferroelectricity of spin origin is proposed within the framework of the many-particle quantum hydrodynamics method. It is applied to the study of cells of magnetic ions, where the electric dipole moment is proportional to the vector product of spins. Our approach is based on the many-particle Pauli equation, where the influence of an external magnetic field is considered. We define the electric dipole moment operator of the ion cell and introduce the macroscopic polarization as the quantum mechanical average of that operator. We formulate a model for the description of nonequilibrium polarization and derive a new polarization evolution equation. The polarization switching in ferroelectric magnets with the spiral spin-density-wave state is considered, and we demonstrate that the proposed model yields known results and can predict novel effects. The dynamic magnetoelectric effect can be investigated by employing this novel equation to study the evolution of polarization.

cond-mat.mtrl-sci↗

arXiv2024

A Mass-in-Mass Chain and the Generalization of the Dirac Equation with an Eight-Component Wave Function and with Optical and Acoustic Branches of the Dispersion Relation

The paper considers a slightly modified one-dimensional infinite mass-in-mass chain. In the case of the long-wave approximation, which corresponds to the transition to a continuous medium, we obtained a system of two equations, which is a generalization of the classical mechanics Klein-Gordon-Fock equation and has both optical and acoustic branches of the dispersion relation. Based on this classical mechanics system of equations, we have proposed a system of two relativistic quantum mechanics equations, which is a generalization of the relativistic quantum mechanics Klein-Gordon-Fock equation. Next, based on this system and following the Dirac approach, we have proposed the generalization of the Dirac equation for a free electron with an eight-component wave function in the form of a system of eight linear partial differential equations of the first order. Unlike the Dirac equation with a four-component wave function, which has only an optical branch of the dispersion relation, the generalized Dirac equation has both optical and acoustic branches of the dispersion relation, each of which has two branches with positive and negative energies, respectively. We have calculated phase and group velocities for all cases. For the positive and negative acoustic branches, the phase and group velocities are equal in modulus to the speed of light. For the positive and negative optical branches, the phase and group velocities have a structure like that of de Broglie waves. In the one-dimensional case, eight linearly independent solutions corresponding to eight combinations of two branches of dispersion, two signs of total energy, and two possible directions of spin orientation, each in the form of four plane waves, are obtained.

quant-ph↗

arXiv2022

Extended relativistic kinetic model composed of the scalar and two vector distribution functions: Application to the spin-electron-acoustic waves

Detailed deterministic derivation of the kinetic equations for the relativistic plasmas is given. Focus is made on the dynamic of one-coordinate distribution functions of various tensor dimensions, but the closed set of kinetic equations is constructed of three functions: the scalar distribution function, the vector distribution function of dipole moment, and the vector distribution function of velocity (or the dipole moment in the momentum space). All two-coordinate distributions functions are discussed as well. They are presented together with their limits existing in the self-consistent field approximation. The dynamics of the small amplitude spin-electron-acoustic waves in the dense degenerate plasmas is are studied within the kinetic model. This work presents the deterministic approach to the derivation and interpretation of the kinetic equations. So, no probability is introduced during the transition from the level of individual particles to the collective functions. Problem of thermalization is not considered, but we can see that the structure of kinetic equations is kept for the system before and after thermalization. Hence, the kinetic equations can be used to approach this item.

physics.plasm-ph↗

arXiv2022

Hydrodynamic and kinetic representation of the microscopic dynamics as the transitions on the macroscopic scale of description and meaning of the self-consistent field approximation in these models

The open problem of derivation of the relativistic Vlasov equation for the systems of charged particles moving with the velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the Maxwell equations is considered. Moreover, the method of derivation is firstly illustrated on the nonrelativistic kinetic model. Independent derivation of the relativistic hydrodynamics is also demonstrated. Key role of these derivations of the hydrodynamic and kinetic equations includes the explicit operator of averaging on the physically infinitesimal volume suggested by L.S. Kuzmenkov.

physics.plasm-ph↗

arXiv2022

Nonlinear Coupling of Electromagnetic and Spin-Electron-Acoustic Waves in Spin-polarized Degenerate Relativistic Astrophysical Plasma

Propagation of the finite amplitude electromagnetic wave through the partially spin-polarized degenerate plasmas leads to the instability. The instability happens at the interaction of the electromagnetic wave with the small frequency longitudinal spin-electron-acoustic waves. Strongest instability happens in the high density degenerate plasmas with the Fermi momentum close to $m_{e}c$, where $m_{e}$ is the mass of electron, and $c$ is the speed of light. The increase of the increment of instability with the growth of the spin polarization of plasmas is found.

physics.plasm-ph↗

arXiv2021

Waves propagating parallel to the magnetic field in relativistically hot plasmas: A hydrodynamic model

The high-frequency part of spectrum of electromagnetic waves propagating parallel to the external magnetic field is considered for the macroscopically motionless plasmas with the relativistic temperatures $T\sim m_{e}c^{2}$, where $m_{e}$ is the mass of electron, $c$ is the speed of light. The analysis is based on the novel hydrodynamic model based on four equations for the material fields which can be combined in two four vectors. These material fields are the concentration and the velocity field \emph{and} the average reverse relativistic $γ$ functor and the flux of the reverse relativistic $γ$ functor. In the nonrelativistic regime we have three waves (the ions are assumed to be motionless). Strong thermal effects lead to a coefficient in front of cyclotron frequency which decreases the effective contribution of the cyclotron frequency. At $T=0.1m_{e}c^{2}$ we have a decrease of area of existence of fast magneto-sound wave from the area of the large frequencies. While the area of existence of extraordinary waves becomes larger towards smaller frequencies. The strong magnetic field limit $\midΩ_{e}\mid > ω_{Le}$ additional wave appears with frequency below thermally decreased cyclotron frequency, where $\midΩ_{e}\mid$ is the electron cyclotron frequency, and $ω_{Le}$ is the Langmuir frequency. Further increase of temperature leads to the disappearance of fast magneto-sound wave and to the considerable increase of area of existence of extraordinary towards smaller frequencies.

physics.plasm-ph↗