Anatomy of Spin-Transfer Torque

Spin-transfer torques occur in magnetic heterostructures because the transverse component of a spin current that flows from a non-magnet into a ferromagnet is absorbed at the interface. We demonstrate this fact explicitly using free electron models and first principles electronic structure calculations for real material interfaces. Three distinct processes contribute to the absorption: (1) spin-dependent reflection and transmission; (2) rotation of reflected and transmitted spins; and (3) spatial precession of spins in the ferromagnet. When summed over all Fermi surface electrons, these processes reduce the transverse component of the transmitted and reflected spin currents to nearly zero for most systems of interest. Therefore, to a good approximation, the torque on the magnetization is proportional to the transverse piece of the incoming spin current.Comment: 16 pages, 8 figures, submitted to Phys. Rev.

Magnetization dynamics with a spin-transfer torque

The magnetization reversal and dynamics of a spin valve pillar, whose lateral size is 64$\times$64 nm$^2$, are studied by using micromagnetic simulation in the presence of spin transfer torque. Spin torques display both characteristics of magnetic damping (or anti-damping) and of an effective magnetic field. For a steady-state current, both M-I and M-H hysteresis loops show unique features, including multiple jumps, unusual plateaus and precessional states. These states originate from the competition between the energy dissipation due to Gilbert damping and the energy accumulation due to the spin torque supplied by the spin current. The magnetic energy oscillates as a function of time even for a steady-state current. For a pulsed current, the minimum width and amplitude of the spin torque for achieving current-driven magnetization reversal are quantitatively determined. The spin torque also shows very interesting thermal activation that is fundamentally different from an ordinary damping effect.Comment: 15 figure

Current driven switching of magnetic layers

The switching of magnetic layers is studied under the action of a spin current in a ferromagnetic metal/non-magnetic metal/ferromagnetic metal spin valve. We find that the main contribution to the switching comes from the non-equilibrium exchange interaction between the ferromagnetic layers. This interaction defines the magnetic configuration of the layers with minimum energy and establishes the threshold for a critical switching current. Depending on the direction of the critical current, the interaction changes sign and a given magnetic configuration becomes unstable. To model the time dependence of the switching process, we derive a set of coupled Landau-Lifshitz equations for the ferromagnetic layers. Higher order terms in the non-equilibrium exchange coupling allow the system to evolve to its steady-state configuration.Comment: 8 pages, 2 figure. Submitted to Phys. Rev.

Thermally assisted magnetization reversal in the presence of a spin-transfer torque

We propose a generalized stochastic Landau-Lifshitz equation and its corresponding Fokker-Planck equation for the magnetization dynamics in the presence of spin transfer torques. Since the spin transfer torque can pump a magnetic energy into the magnetic system, the equilibrium temperature of the magnetic system is ill-defined. We introduce an effective temperature based on a stationary solution of the Fokker-Planck equation. In the limit of high energy barriers, the law of thermal agitation is derived. We find that the N\'{e}el-Brown relaxation formula remains valid as long as we replace the temperature by an effective one that is linearly dependent of the spin torque. We carry out the numerical integration of the stochastic Landau-Lifshitz equation to support our theory. Our results agree with existing experimental data.Comment: 5 figure

Time-Dependent Spintronic Transport and Current-Induced Spin Transfer Torque in Magnetic Tunnel Junctions

The responses of the electrical current and the current-induced spin transfer torque (CISTT) to an ac bias in addition to a dc bias in a magnetic tunnel junction are investigated by means of the time-dependent nonquilibrium Green function technique. The time-averaged current (time-averaged CISTT) is formulated in the form of a summation of dc current (dc CISTT) multiplied by products of Bessel functions with the energy levels shifted by $m\hbar \omega _{0}$. The tunneling current can be viewed as to happen between the photonic sidebands of the two ferromagnets. The electrons can pass through the barrier easily under high frequencies but difficultly under low frequencies. The tunnel magnetoresistance almost does not vary with an ac field. It is found that the spin transfer torque, still being proportional to the electrical current under an ac bias, can be changed by varying frequency. Low frequencies could yield a rapid decrease of the spin transfer torque, while a large ac signal leads to both decrease of the electrical current and the spin torque. If only an ac bias is present, the spin transfer torque is sharply enhanced at the particular amplitude and frequency of the ac bias. A nearly linear relation between such an amplitude and frequency is observed.Comment: 13 pages,8 figure

Current-Driven Magnetization Dynamics in Magnetic Multilayers

We develop a quantum analog of the classical spin-torque model for current-driven magnetic dynamics. The current-driven magnetic excitation at finite field becomes significantly incoherent. This excitation is described by an effective magnetic temperature rather than a coherent precession as in the spin-torque model. However, both the spin-torque and effective temperature approximations give qualitatively similar switching diagrams in the current-field coordinates, showing the need for detailed experiments to establish the proper physical model for current-driven dynamics.Comment: 5 pages, 2 figure

Theory of Current-Induced Magnetization Precession

We solve appropriate drift-diffusion and Landau-Lifshitz-Gilbert equations to demonstrate that unpolarized current flow from a non-magnet into a ferromagnet can produce a precession-type instability of the magnetization. The fundamental origin of the instability is the difference in conductivity between majority spins and minority spins in the ferromagnet. This leads to spin accumulation and spin currents that carry angular momentum across the interface. The component of this angular momentum perpendicular to the magnetization drives precessional motion that is opposed by Gilbert damping. Neglecting magnetic anisotropy and magnetostatics, our approximate analytic and exact numerical solutions using realistic values for the material parameters show (for both semi-infinite and thin film geometries) that a linear instability occurs when both the current density and the excitation wave vector parallel to the interface are neither too small nor too large. For many aspects of the problem, the variation of the magnetization in the direction of the current flows makes an important contribution.Comment: Submitted to Physical Review

Influence of a Uniform Current on Collective Magnetization Dynamics in a Ferromagnetic Metal

We discuss the influence of a uniform current, $\vec{j}$, on the magnetization dynamics of a ferromagnetic metal. We find that the magnon energy $\epsilon(\vec{q})$ has a current-induced contribution proportional to $\vec{q}\cdot \vec{\cal J}$, where $\vec{\cal J}$ is the spin-current, and predict that collective dynamics will be more strongly damped at finite ${\vec j}$. We obtain similar results for models with and without local moment participation in the magnetic order. For transition metal ferromagnets, we estimate that the uniform magnetic state will be destabilized for $j \gtrsim 10^{9} {\rm A} {\rm cm}^{-2}$. We discuss the relationship of this effect to the spin-torque effects that alter magnetization dynamics in inhomogeneous magnetic systems.Comment: 12 pages, 2 figure

Spin Torques in Ferromagnetic/Normal Metal Structures

Recent theories of spin-current-induced magnetization reversal are formulated in terms of a spin-mixing conductance $G^{mix}$. We evaluate $G^{mix}$ from first-principles for a number of (dis)ordered interfaces between magnetic and non-magnetic materials. In multi-terminal devices, the magnetization direction of a one side of a tunnel junction or a ferromagnetic insulator can ideally be switched with negligible charge current dissipation.Comment: 4 pages, 1 figur

Measurements of the Mass and Full-Width of the ηc\eta_c Meson

In a sample of 58 million $J/\psi$ events collected with the BES II detector, the process J/$\psi\to\gamma\eta_c$ is observed in five different decay channels: $\gamma K^+K^-\pi^+\pi^-$, $\gamma\pi^+\pi^-\pi^+\pi^-$, $\gamma K^\pm K^0_S \pi^\mp$ (with $K^0_S\to\pi^+\pi^-$), $\gamma \phi\phi$ (with $\phi\to K^+K^-$) and $\gamma p\bar{p}$. From a combined fit of all five channels, we determine the mass and full-width of $\eta_c$ to be $m_{\eta_c}=2977.5\pm1.0 ({stat.})\pm1.2 ({syst.})$ MeV/$c^2$ and $\Gamma_{\eta_c} = 17.0\pm3.7 ({stat.})\pm7.4 ({syst.})$ MeV/$c^2$.Comment: 9 pages, 2 figures and 4 table. Submitted to Phys. Lett.