Coupling of spin-transfer torque to microwave magnetic field: A micromagnetic modal analysis

Micromagnetic computational spectral mapping technique is applied to analyze the magnetic oscillation modes excited by either a microwave circularly polarized magnetic field or a spin polarized current flowing through Permalloy (Py) spin valves. A complete study has been carried out on multilayers Py(10 nm)/Cu(5 nm)/Py(2.5 nm) with rectangular cross section (60x20 nm(2)). The magnetic normal modes obtained agree with recent analytical spin wave models in patterned nanostructures. When both excitations, microwave field and spin polarized current, are applied at the same time a complex coupling process is observed. The detailed micromagnetic analysis of the coupling shows three different stages: (i) The initial stage in which the magnetic normal modes are dominant, (ii) an intermediate stage showing an incoherent behavior, and (iii) the final stage where a persistent domain wall oscillation is present. Micromagnetic spectral mapping technique is shown to be an adequate tool for describing the temporal evolution of the magnetization spatial patterns in nanostructures.