Nonlinear phenomenological model of magnetic dissipation for large precession angles: Generalization of the Gilbert model

A nonlinear phenomenological model of magnetic dissipation is proposed. This model is a generalization of a standard Gilbert model, where the constant Gilbert damping parameter αG is replaced by a function αG(ξ) of the dimensionless scalar quantity ξ proportional to the square of the time rate of change of the magnetization vector (∂M∕∂t)². The proposed model is illustrated for the example of magnetization precession excited by spin-polarized current in an in-plane magnetized nanopillar---the case where the standard Gilbert model leads to qualitatively incorrect results that contradict experiments.