Simulation of Magnetization Dynamics in Three-layered Ferromagnetic Structures with Pinned Boundaries
In the previous works, we had constructed the mathematical models of switching effects for magnetic valves with longitudinal and perpendicular types of magnetic anisotropy of the ferromagnetic layers. The simplifying assumption used in these models lied in uniformity of magnetization distribution through the cross-section of the active layer of the structure. This assumption allowed us to reduce the problem to the dynamical system of equations and perform the bifurcation analysis of these equations. The goal of the present work is to make a model with non-uniformity of the magnetization distribution taken into account. The model is based on the Landau-Lifshits-Gilbert equation with dissipative and current terms. The non-uniformity in the equation becomes apparent in the exchange term. To solve the resulting system of partial differential equations numerically, we used the explicit finite-difference scheme with fixed boundary conditions. The initial conditions represented the uniform perpendicular magnetization distribution through the crosssection of the layer perturbed locally in the center of the layer. The dynamics of magnetization under these conditions can be divided into three phases. The first one is spreading of the local perturbation to the boundary of the spatial domain. The second one is reflecting of these waves from the boundary and their interfering with the coming waves. The third phase is the formation of a space-periodic cellular distribution of magnetization through the cross-section of the active layer.