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 $S^\sigma-V$ and $S^\tau-V$ relations were derived as a function of angle $\theta$ 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 $\sin\theta$ 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 $\theta$. The derivative of noise spectrum of spin transfer torque with respect to the bias voltage $N_\tau$ behaves differently when the system is near or far away from the resonance. Specifically, the differential shot noise of spin transfer torque $N_\tau$ is a concave function of $\theta$ near the resonance while it becomes convex function of $\theta$ far away from resonance. For certain bias voltages, the period $N_\tau(\theta)$ becomes $\pi$ instead of $2\pi$. For small $\theta$, it was found that the differential shot noise of spin transfer torque is very sensitive to the bias voltage and the other system parameters. 
Yunjin Yu, Hongxin Zhan, Langhui Wan, Bin Wang, Yadong Wei, Qingfeng   Sun and Jian Wang
cond-mat.mes-hall cond-mat.mtrl-sci