Nonlinear spin dynamics of a ferromagnetic ring in the vortex state and its application as a spin-transfer nano-oscillator

We study a nonlinear spin dynamics of a ferromagnetic ring in a vortex state induced by the spin -polarized current. We also suggest using the ferromagnetic ring as a free layer of a coreless vortex spin -transfer nanooscillator. The calculated working frequency is about several GHz, which is much higher than the gyromode frequency of the disk -based vortex oscillator. The response of the vortex -state ring to the spin -polarized current has hysteretic behavior with the reasonable values of the thresholds' current densities: ignition threshold is about 10 8 A cm - 2 and elimination current to maintain the oscillations has much lower values of about 10 6 A cm - 2 . The output signal can be extracted with the help of the inverse spin -Hall effect or by the giant magnetoresistance. The output electromotive force averaged over all sample vanishes and we suggest using a ferromagnetic ring or disk in a vortex state as a giant magnetoresistance analyzer. For an inverse spin -Hall analyzer we advise using two heavy metals with different signs of spin -Hall angle. The ring -based spin -transfer nano -oscillator (STNO) is supposed to increase the areas of practical application of the STNOs.