Instabilities of spin torque driven auto-oscillations of a ferromagnetic disk magnetized in plane

Abstract

The stability of the magnetization auto-oscillations of the ferromagnetic free layer of a cylindrical nanopillar structure is studied theoretically using a classical Hamiltonian formalism for weakly interacting nonlinear waves, in a weakly dissipative system. The free layer corresponds to a very thin circular disk, made of a soft ferromagnetic material like Permalloy, and it is magnetized in plane by an externally applied magnetic field. There is a dc electric current that traverses the structure, becomes spin polarized by a fixed layer, and excites the modes of the free layer through the transfer of spin angular momentum. If this current exceeds a critical value, it is possible to generate a large amplitude periodic auto-oscillation of a dynamic mode of the magnetization. We separate our theoretical study into two parts. First, we consider an approximate expression for the demagnetizing field in the disk, i.e., (H) over bar (D) = -4 pi M-z(z) over cap or a very thin film approximation, and secondly we consider the effect of the full demagnetizing field, where one sees important effects due to the edges of the disk. In both cases, as the applied current density is increased, we determine the modes that will first auto-oscillate and when these become unstable to the growth of other modes, i.e., their ranges of "isolated" auto-oscillation.