Excitation of spin waves by spin-polarized current in magnetic nano-structures

An approximate analytic theory describing excitation of microwave spin waves by spin-polarized direct current in magnetic is presented. The theory is based on the classical Hamiltonian formalism for spin waves in magnetic films, and uses the idea that spin-polarized current passing through the free layer of a magnetic nano-structure creates in this layer an effective negative damping for spin wave modes. The developed theory in the macrospin approximation describes current-induced uniform magnetization precession both near the minimum and maximum of magnetic energy of the free layer. The same theory, also, provides a framework for the description of excitation of supercritically unstable spatially nonuniform and propagating spin wave modes.