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We theoretically examine the spin-transfer torque in the presence of spin-orbit interaction (SOI) at impurities in a ferromagnetic metal on the basis of linear response theory. We obtained, in addition to the usual spin-transfer torque, a new contributioin $sim {bm j}_{rm SH}^{phantom{dagger}} cdot abla {bm n}$ in the first order in SOI, where ${bm j}_{rm SH}^{phantom{dagger}}$ is the spin Hall current driven by an external electric field. This is a reaction to inverse spin Hall effect driven by spin motive force in a ferromagnet.
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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 Greens 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 $sintheta$ 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 $2pi$. 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.
We have proposed a method to synchronize multiple spin-transfer torque oscillators based on spin pumping, inverse spin Hall, and spin Hall effects. The proposed oscillator system consists of a series of nano-magnets in junction with a normal metal with high spin-orbit coupling, and an accumulative feedback loop. We conduct simulations to demonstrate the effect of modulated charge currents in the normal metal due to spin pumping from each nano-magnet. We show that the interplay between the spin Hall effect and inverse spin Hall effect results in synchronization of the nano-magnets.
We investigate an interfacial spin-transfer torque and $beta$-term torque with alternating current (AC) parallel to a magnetic interface. We find that both torques are resonantly enhanced as the AC frequency approaches to the exchange splitting energy. We show that this resonance allows us to estimate directly the interfacial exchange interaction strength from the domain wall motion. We also find that the $beta$-term includes an unconventional contribution which is proportional to the time derivative of the current and exists even in absence of any spin relaxation processes.
We demonstrate that the spin Hall effect in a thin film with strong spin-orbit scattering can excite magnetic precession in an adjacent ferromagnetic film. The flow of alternating current through a Pt/NiFe bilayer generates an oscillating transverse spin current in the Pt, and the resultant transfer of spin angular momentum to the NiFe induces ferromagnetic resonance (FMR) dynamics. The Oersted field from the current also generates an FMR signal but with a different symmetry. The ratio of these two signals allows a quantitative determination of the spin current and the spin Hall angle.
We investigate the dynamics of a magnetic vortex driven by spin-transfer torque due to spin current in the adiabatic case. The vortex core represented by collective coordinate experiences a transverse force proportional to the product of spin current and gyrovector, which can be interpreted as the geometric force determined by topological charges. We show that this force is just a reaction force of Lorentz-type force from the spin current of conduction electrons. Based on our analyses, we propose analytically and numerically a possible experiment to check the vortex displacement by spin current in the case of single magnetic nanodot.
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