Current induced magnetization dynamics in one dimensional magnonic crystal

Nonlinear magnetic excitation in terms of solitary waves and solitons in ferromagnetic systems is well studied problem in the literature. The results reveal that the dynamics is governed by Landau - Lifshitz (LL) equation which can be mapped to Nonlinear Schrodinger (NLS) family of equations [1]. Studies with spin transfer torque in both multilayer system and single layer system has attracted much interest in the past several years [2, 3]. The result shows that spin current plays a crucial role on the dynamics of ferromagnetic system. In recent years, the study on nonlinear systems with spatial periodicity has become a great topic of interest. BEC in optical lattices, solitons in Photonic lattices and periodic magnetic systems etc., are the typical models among them [4]. Motivated by the above considerations, we investigate the nonlinear localized magnetic excitations in one dimensional magnonic crystal under periodic magnetic field with spin current. Magnonic crystal is a medium with spatially periodic variation of their magnetic properties in a definite direction. The governing modified Landau - Lifshitz (LL) equation of magnonic crystal with spin current is [5], ∂M(r, t)/ ∂t = -γ(M(r, t) x H_eff) + τ (1) where γ is the gyromagnetic ratio, M(r, t) is the magnetization of the magnonic crystal medium and H_eff is the effective field. The effective field is in general sum of several components includes the exchange field, Anisotropy field, demagnetization field and applied field which can all be space dependent.