Multiple-scale derivation of the nonlinear Schrödinger equation for solitons in magnetic thin films (abstract)

Abstract

Although the nonlinear Schrödinger (NLS) equation is the theoretical starting point for the analysis of magnetostatic wave (MSW) soliton experiments in thin films,12 no first principles theory to justify its use has yet been advanced. In this work, multiple-scale asymptotics have been used in combination with Maxwell’s equations in the magnetostatic approximation and the torque equation of motion to obtain the NLS equation for a quasimonochromatic plane propagating wave in a perpendicularly magnetized thin film. A nonlinear differential equation for the magnetization amplitude envelope response with the same form as the NLS equation has been obtained when the analysis is carried out to the third-order terms in the expansion. Specific results include (1) linear terms that agree with well-established magnetostatic wave theory3 and (2) an explicit wave-number k-dependent nonlinear response parameter N. In previous work,4 N has been approximated as the MSW frequency shift with the square of the dynamic magnetization amplitude. The present results indicate that this approximation leads to errors of 20%–40%, even in the usual 100–200 rad/cm low-k range of the experiments.