Magnetization dynamics induced by spin-polarized currents in magnetic nanodevices have been numerically simulated using a single-domain model proposed by Slonczewski extended to include temperature effects. For currents with a spin polarization antiparallel to the device easy axis and for fields above the magnetostatic anisotropy field, transfer of spin momentum from one layer to an adjacent layer can cause the layers to undergo sustained oscillations. Here we numerically calculate the expected excitation spectra and linewidths of spin-transfer oscillators and explain observed variations in excitation linewidths. The linewidth arises from thermal excitations that give rise to disorder in the orbits and, in certain regimes, hopping between nearly degenerate orbits. The excitation spectra for a 2.5 nm X 50 nm X 100 nm device show transitions from thermally activated elliptical motion, at zero and low currents, to a bent elliptical motion at intermediate currents, and finally to tilted out-of-plane orbits. At the transition between in-plane and out-of-plane orbits, there is a region of low-frequency noise due to thermal hopping between degenerate orbits and a shift in the spectral behavior. The linewidth arising from thermal interactions is a sensitive function of the device volume and varies from 1 to 2 GHz for 2.5 nm X 50 nm X 100 nm devices to 20 to 40 MHz for 10 nm X 200 nm X 400 nm devices. The modeling explains the difference in linewidths observed for nanopillar and point-contact geometries as a natural consequence of inherent thermal fluctuations and the difference in excitation volumes.
Physical Review B (Condensed Matter and Materials Physics)
magnetic nanodevices, magnetodynamics, spin momentum, spin valve, transfer