Shot noise of spin current and spin transfer torque

We report the theoretical investigation of the shot noise of the spin current (S(σ)) and the spin transfer torque (S(τ)) for non-collinear spin polarized transport in a spin-valve device which consists of a normal scattering region connected by two ferromagnetic electrodes (MNM system). Our theory was developed using the non-equilibrium Green's function method, and general nonlinear S(σ) - V and S(τ) - V relations were derived as a function of the angle θ between the magnetizations of two leads. We have applied our theory to a quantum dot system with a resonant level coupled with two ferromagnetic electrodes. It was found that, for the MNM system, the auto-correlation of the spin current is enough to characterize the fluctuation of the spin current. For a system with three ferromagnetic layers, however, both auto-correlation and cross-correlation of the spin current are needed to characterize the noise of the spin current. For a quantum dot with a resonant level, the derivative of spin torque with respect to bias voltage is proportional to sinθ when the system is far away from resonance. When the system is near resonance, the spin transfer torque becomes a non-sinusoidal function of θ. The derivative of the noise of the spin transfer torque with respect to the bias voltage Nτ behaves differently when the system is near or far away from resonance. Specifically, the differential shot noise of the spin transfer torque Nτ is a concave function of θ near resonance while it becomes a convex function of θ far away from resonance. For certain bias voltages, the period Nτ(θ) becomes π instead of 2π. For small θ, it was found that the differential shot noise of the spin transfer torque is very sensitive to the bias voltage and the other system parameters.