Current-Induced Magnetization Dynamics in 1-D Bicomponent Magnonic Crystal

Nonlinear localized magnetic excitations in 1-D bicomponent magnonic crystal are investigated under periodic magnetic field of spatially varying strength with spin current. The governing modified Landau-Lifshitz equation with spin current is transformed into the variable coefficient nonlinear Schrödinger (VCNLS) equation using a stereographic projection. In general, the VCNLS equation is nonintegrable and by using similarity transformation technique, the VCNLS equation is reduced into the standard NLS equation with certain integrability conditions. A systematic connection between the solution of VCNLS and NLS equations is established. The solution of VCNLS equation is obtained using the solution of the NLS equation. The excitation of magnetization is in the form of solitons on the oscillatory background with structure similar to the form of spin Bloch waves, and in addition, the spin current controls the soliton velocity. The velocity of soliton is directly proportional to the strength of current density and inversely proportional to the average saturation magnetization value, which is the value of saturation magnetization of the composite material at the interface of the two ferromagnetic materials, which are used to form the bicomponent magnonic crystal.