Thermally induced switching in uniaxial nanomagnets subject to spin-polarized currents

In this paper, the technique is applied to the case of a uniaxial nanomagnet subject to a spin-polarized current and a constant applied field. The rotationally symmetric magnetic systems is considered where both the spin polarization and the applied field are along the symmetry axis. The main result of the paper is to provide an analytical formula for effective potential barrier separating a stable stationary point and a stable self-oscillation and thus to derive the corresponding Boltzmann factor along with the expression of the characteristic thermal relaxation time. Then, the effect of fluctuation by deriving the averaged Fokker-Planck equation in terms of the energy probability distribution function is studied. In the uniaxial case this equation has a simple structure and it is possible to derive explicit analytical solutions.