Nonlinear Spin Waves in Graphene Structures

Abstract

Basing on Dirac equation for interacting massless fermions, we propose a nonlinear model that describes a possible mechanism of ferromagnetism in graphene structures, resulting from electronelectron interaction and spontaneous breaking of spin symmetry of valence electrons. Qualitative predictions of the model are important for practical applications in spintronics. Localized kinkantikink patterns of valence electron spin density on the graphene surface are calculated, their interaction is described, and,¯nally, the formation of their quasi-bound metastable states (breathers) is investigated. The spectrum of breathers is calculated in both the analytical and the numerical form. Possible inverted population of the appropriate states may be used to generate quantum coherent nonlinear spin waves that can¯nd practical applications in nanoelectronics and spintronics.

Numerical solution for the Schrödinger equation with potential in graphene structures

“…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].…”

“…This model describes experimentally observable ferromagnetic properties of such films; prior work [6] claimed that the offered variant of the nonlinear field model, in which carriers of spin density are not fermions (electrons), but bosons (spinons), is quite adequate for describing the magnetic properties of graphene structures. 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].…”

“…Based on the density functional theory and the perturbation methods, in [1] proposed a physically reasonable nonlinear model of interacting massless Dirac fermions in graphene structures for practical applications. This model described the spin density (s) distribution of the valence electrons of the carbon atoms in graphene structures.…”

“…We can write a system of the Hamiltonian with the field function in the form (3) that satisfies the equation of the type (1) [1,7]:…”

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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.

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