Simple Model of Nonlinear Spin Waves in Graphene Structures

Kulyabov, Dmitry S.; Сергеевич, Кулябов Дмитрий; Lovetskiy, Konstantin P.; Петрович, Ловецкий Константин; Севастьянов, Л А; Ньат, Ле Ань

doi:10.22363/2312-9735-2018-26-3-244-251

Cited by 2 publications

(3 citation statements)

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“…We also find it interesting to further consider the interaction of breathers with each other and with other physical fields, as well as the dynamics of spinons on graphene (fullerene, nanotube) nonplanar surfaces of various topologies. This work is devoted to a numerical study of the model 4 [15], [16]. Within the framework of the proposed model, the problems of approximate calculation of potential fields, approximate solution of the Schrödinger equations and simulation of control of the external field of population levels [8] are solved.…”

Section: Introductionmentioning

confidence: 99%

Numerical modeling of stationary pseudospin waves on a graphene monoatomic films

Nhat

Ань²,

Lovetskiy

et al. 2019

Discrete and Continuous Models

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For the first time, the theoretical model of the spin-electron structure of a singlelayer graphene film was proposed by Wallace. The literature also describes ferromagnetism generated by none of the three common causes: impurities, defects, boundaries. We believe that the source of ferromagnetism is the spontaneous breaking of spin symmetry in a graphene film. The classical field model describing spontaneously broken symmetry is necessarily non-linear. Among non-linear models, the simplest is the well-known 4 model. We believe that, as a first approximation, we can describe with its help all the characteristics of spin waves that interest us, their spectra, and the domain structure of ferromagnetism in graphene. The model admits kink and anti-kink exact solutions and a quasiparticle breather, which we modeled numerically. We use the kink-anti-kink interaction energy obtained numerically to solve the Schrödinger equation, which simulates the quantum dynamics of breathers, which underlies the description of spin waves. The solution of the Schrödinger equation by the Ritz method leads to a generalized problem of eigenvalues and eigenvectors, the solution of which is mainly devoted to this work.

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Section: Introductionmentioning

confidence: 99%

Numerical modeling of stationary pseudospin waves on a graphene monoatomic films

Nhat

Ань²,

Lovetskiy

et al. 2019

Discrete and Continuous Models

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“…The authors proposed in two articles [1,7] the desirability of a nonlinear model that describes a possible mechanism of ferromagnetism in graphene structures, resulting from electron-electron interaction and spontaneous breaking of spin symmetry of valence electrons. We investigated such spatially localized nonlinear spin of the valence electron density on the graphene surface such as kinks, and their interactions, as well as quasibound metastable states of the interacting kinks and antikinks, that are breathers [8].…”

Section: Introductionmentioning

confidence: 99%

“…Evidently, in the articles [1,[4][5][6][7][8], it is shown that the density of spin symmetry was broken by the spontaneous breaking, which obeyed a nonlinear equation, and the offered nonlinear models with the limits will exist exact and approximate solutions for the distribution of the spin density and magnetization on the surface of the graphene structures, as the method of the scattering matrix [5]; the finite element method (FEM) and the Ritz method [1,7]; the Ritz method using Hermitian functions as coordinate functions [8].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for the Schrödinger equation with potential in graphene structures

Nhat¹

2019

Nanosystems: Phys. Chem. Math.

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This paper presents a different numerical solution to compute eigenvalues of the Schrödinger equation with the potentials in graphene structures [1]. The research subjects include the Schrödinger equation and the exchange-correlation energy of the graphene structures in Grachev's article. Specifically, we used the pseudospectral method basing on the Chebyshev-Gauss-Lobatto grid to determine the approximate numerical results of the problem. The results are the discrete energy spectra and the corresponding eigenfunctions of the nonlinear spin waves in the graphene structure. Additionally, these results can be applied to create the nonlinear spin waves in the graphene structures.

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Simple Model of Nonlinear Spin Waves in Graphene Structures

Cited by 2 publications

References 0 publications

Numerical modeling of stationary pseudospin waves on a graphene monoatomic films

Numerical modeling of stationary pseudospin waves on a graphene monoatomic films

Numerical solution for the Schrödinger equation with potential in graphene structures

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