Two-dimensional magnetic solitons and thermodynamics of quasi-two-dimensional magnets

Иванов, Б. А.; Sheka, Denis D.

doi:10.1016/0960-0779(94)e0117-8

Cited by 3 publications

(1 citation statement)

References 35 publications

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“…Therefore, the generalized force-balance equation (10a) taking into account singular force F sing should be used for the description of the gyroscopic dynamics for systems with singular topological solitons. Note that usage of the standard force balance in the form (7) leads to the discrepancy in the definition of the gyroscopic force between the soliton perturbation theory [5] and direct integration of the field equations [1,17,18].…”

Section: Energy and Force-balance Equationsmentioning

confidence: 99%

Field momentum and gyroscopic dynamics of classical systems with topological defects

Sheka¹

2006

J. Phys. A: Math. Gen.

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The standard relation between the field momentum and the force is generalized for the system with a field singularity: in addition to the regular force, there appears the singular one. This approach is applied to the description of the gyroscopic dynamics of the classical field with topological defects. The collectivevariable Lagrangian description is considered for gyroscopical systems taking into account singularities. Using this method we describe the dynamics of twodimensional magnetic solitons. We establish a relation between the gyroscopic force and the singular one. An effective Lagrangian description is discussed for the magnetic soliton dynamics.

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Section: Energy and Force-balance Equationsmentioning

confidence: 99%

Field momentum and gyroscopic dynamics of classical systems with topological defects

Sheka¹

2006

J. Phys. A: Math. Gen.

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Chiral fermion dynamics in 2d magnetic vortices: Manifestation of momentum-spin-locking

Pötz

Hammer

2016

Journal of Applied Physics

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The electronic surface-states of a topological insulator in the presence of an in-plane magnetization vortex M(ϕ)=M(cos(Φ+νϕ), sin(Φ+νϕ)) are investigated theoretically. For a general angle of magnetization Φ∈[0,2π) and topological charge ν = 1, the modifications to the zero-mass single Dirac cone dispersion are treated exactly and the spectrum of bound eigenstates which forms in the energy window ±M cos(Φ) is derived. The space-time resolved dynamics of Dirac fermions in the presence of such vortices is studied numerically using a single-cone (2 + 1)D finite-difference scheme. In the continuous spectral region, Φ-dependent scattering of Dirac fermions at the vortex is observed. Depending on the type of vortex (Φ, ν) and the impact parameter, the propagation direction of the Dirac fermion is changed: the magnetization of the vortex exerts a torque onto the fermion spin which, by momentum-spin locking associated with the helical Dirac states, results in an in-plane rotation of the propagation direction of the scattered Dirac fermion. In head-on collisions of a Gaussian wave-packet with ν = 1 vortices a Φ-dependent lensing effect is seen in our simulations. Depending on the direction of incidence, the vortex Φ=−π/2, ν = 2 is identified as a coherent particle-beam splitter or “condenser” in head-on collisions.

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Soliton-magnon scattering in a two-dimensional isotropic magnetic material

Иванов

Muravev

Sheka

1999

J. Exp. Theor. Phys.

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It is studied the scattering of magnons by the 2d topological Belavin-Polyakov soliton in isotropic ferromagnet. Analytical solutions of the scattering problem are constructed: (i) exactly for any magnon wave vectors for the partial wave with the azimuthal number m = 1 (translational mode), and (ii) in the long-and short-wave limits for the rest modes. The magnon mode frequencies are found for the finite size magnets. An effective equation of the soliton motion is constructed. The magnon density of states, connected with the soliton-magnon interaction, is found in a long-wave approximation. 75.10.Hk, 75.30.Ds, 75.50.Ee Nonlinear topologically nontrivial excitations (solitons) are well-known to play a special role in a lowdimensional magnetic systems. For example, the presence of vortices in 2d easy-plane (EP) magnets gives rise to Berezinskiȋ-Kosterlitz-Thouless phase transition [1]. Kinks in 1d magnets and localized Belavin-Polyakov solitons (BP-solitons [2]) in 2d isotropic magnets are responsible for the destruction of the long-range order at finite temperature. This can be explained within the scope of so-called soliton phenomenology, where the magnet can be described as a two-component gas of elementary excitations: solitons and magnons. Such approach was developed for 1d magnets [3], see also Refs. [4,5]. The soliton signature in dynamical response functions can be observed experimentally. Translational motion of solitons leads to the so-called soliton central peak. Another possibility to detect the soliton signature is to look for magnon modes, localized on the soliton (local modes, LM), observed in [6]. For 1d magnets such scattering causes the change of the magnon density of states which is necessary for self-consistent calculation of temperature dependence of the soliton density [3].For 2d the concept of soliton-magnon gas has been extended, e.g. to describe EP magnets [7], and to explain the EPR line-width in easy-axial magnets [8,9]. However the general behaviour of the 2d soliton dynamics is not clear at present. In particular, the form of inertial terms in the dynamical equations for the soliton centre is unknown; the soliton density have not been calculated, but been used as input parameter.The problem of the soliton dynamics or the problem of LM existing are intimately connected with the solitonmagnon scattering. For example, using numerical data for the scattering amplitude the non-Newtonian effective equation of motion of the magnetic vortex was constructed [10]. For the 2d EP antiferromagnet (AFM), finite-frequency truly localized internal mode was predicted [11]. For all mentioned papers, an analysis of 2d solitons was carried out numerically. It becomes espe-cially important to analyze models for which analytical results can be obtained. We are aware of only the exact solution for BP-soliton [2], which describes a topological soliton in isotropic magnets.In this Letter we have investigated the soliton-magnon scattering for the BP-soliton in the isotropic ferromagnet (FM). An exact analytic...

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Two-dimensional magnetic solitons and thermodynamics of quasi-two-dimensional magnets

Cited by 3 publications

References 35 publications

Field momentum and gyroscopic dynamics of classical systems with topological defects

Field momentum and gyroscopic dynamics of classical systems with topological defects

Chiral fermion dynamics in 2d magnetic vortices: Manifestation of momentum-spin-locking

Soliton-magnon scattering in a two-dimensional isotropic magnetic material

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