Modulation Instability And Gap Solitons In Periodic Ferromagnetic Films

Solitons show unique properties and high potential for applications and, hence,have been one of the most exciting topics in modern nonlinear science. Magneticsoliton is a kind of nonlinear excitation in magnetic systems. The study of magneticsoliton can be dated back to1931. And now the researches taken on great practicalsignificances have been made both in experimental and theoretical studies. In thispaper, we focus on the theoretical investigation of magnetic soliton characteristics inperiodic ferromagnetic thin films and the dynamics of magnetic soliton induced byspin-polarized currents in ferromagnetic metallic thin films. The main researchcontents and results are given below:In the first part, we introduce the properties and history of magnetic soliton, theLandau-Lifshitz-Gilbert equation (LLG), as well as the development and applicationof periodic ferromagnetic materials. Then, we discuss the nonlinear Schr dingerequation (NLSE), which is used to describe the evolution dynamics of the envelopemagnetic soliton. The multiple scale expansion is also introduced, which is typicaltheoretical tools for the analysis of the nonlinear differential equation.In the second part, by use of the multiple scale expansion, the nonlinear envelopeequations are obtained from the Landau-Lifshitz-Gilbert equation naturally. Then, inorder to illustrate above results, the case with Kronig-Penney potential is considered,which can be realized by periodically screening of the magnetic field. By analyzingthe structure of envelope equations, we find the bright and dark gap soliton solutionsfor the cases with easy-axis and easy-plane anisotropy. The emerging of gap solitonsis due to nonlinear-induced frequency shift and periodically tailoring of the spectrum.At last, the effect of spin-polarized current on local moment can be simplified asspin torque terms in a gerneralized Landau-Lifshitz-Gilbert equation. Consideringadiabatic and non-adiabatic spin torque terms, the magnetization dynamics induced byspin-polarized current is investigated. Based on multiple scale expansion, we can findthe nonlinear envelope equations induced by spin-polarized current.