  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.
