Shot noise of spin current and spin transfer torque

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

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