Current-induced Spin-transfer Torque Research Articles

Magnetization dynamics in nanopillars in the diffusive transport regime: Macrospin versus micromagnetic analysis

Current-induced spin-transfer torque in spin valve structures with magnetic layers made of different materials can exhibit a nonstandard, i.e., wavy like, angular variation. Following the diffusive spin transport model, the wavy torque was theoretically found in the Co(8nm)∕Cu(10nm)∕Py(8nm) spin valve, and later was also experimentally confirmed. However, the single domain (macrospin) approximation fails to describe some features of magnetic dynamics observed in experiments, especially the frequency agility with current and its slope for the out-of-plane precessions. Therefore, we have revisited the abovementioned pillar structure and analyzed the conditions for the appearance of the out-of-plane oscillations. In particular, we have studied the possibility of triggering these modes by means of a moderate external magnetic field. We have identified modes supported within the macrospin model and verified the results by full micromagnetic simulations, revealing numerous qualitative discrepancies. For instance, the out-of-plane oscillations have been found in the macrospin model, whereas no such precessions have been observed in micromagnetic simulations even with an external magnetic field.

Direct imaging of current-driven domain walls in ferromagnetic nanostripes

To better understand the response of domain walls to current-induced spin transfer torques, we have directly imaged the internal magnetic structure of domain walls in current-carrying ferromagnetic nanostripes. Domain wall images were acquired both while a constant current was flowing through the wire, and after applying current pulses. Domain walls ranging from vortex walls in wide (1 μm) wires to transverse walls in narrow (100 nm) wires were quantitatively analyzed using scanning electron microscopy with polarization analysis. The domain wall motion is characterized by strong interactions with random pinning sites along the wire. The walls either jump with the electron flow between pinning sites, or the pinned walls are distorted by the current. The domain wall propagation is also associated with transverse motion of the vortex core.

Switching behavior of a Stoner–Wohlfarth particle subjected to spin-torque effect

Recently, the current-induced spin-transfer torque has been proposed as a convenient writing process in high density magnetic random access memory. A spin-polarized current can switch the magnetization of a ferromagnetic layer more efficiently than a current induced magnetic field. Our paper discusses the switching properties of a Stoner–Wohlfarth magnetic particle for the case when spin torques and external field pulses are simultaneously present. The theoretical investigation of precessional motion is described by using Landau–Lifschitz–Gilbert equation with a spin-transfer torque term included. The main goal is to determine the parameters of field pulse for that the fast and stable switching can be achieved.

Free-electron model of current-induced spin-transfer torque in magnetic tunnel junctions

Spin and charge transport in a biased planar tunnel junction with two ferromagnetic electrodes are analyzed theoretically in the spin-polarized free-electron-like model. Tunneling current and both in-plane and out-of-plane components of the current-induced spin torque exerted on ferromagnetic components of the junction are determined as a function of the angle between magnetic moments of the electrodes, barrier height and thickness, and spin polarization of the electrodes. The out-of-plane component of the torque is found to be comparable in magnitude to the in-plane component. Numerical results for junctions with sufficiently high barriers show that the in-plane torque exerted on the sink electrode increases monotonically with increasing spin polarization (spin splitting) of the electron band in the source electrode, while the out-of-plane torque increases with increasing spin polarization of the electron bands in both electrodes. In junctions with thick and low barriers, the torque components can change their sign. The bias voltage dependence of the in-plane torque is not symmetric with respect to the bias reversal, even in symmetric junctions. When one of the ferromagnetic electrodes is replaced by a ferromagnetic layer of finite thickness (followed by a nonmagnetic electrode), both components of the spin torque depend significantly on the layer thickness due to the size effect and quantum well states formed in the thin magnetic layer.

Spin pumping of current in non-uniform conducting magnets

Using irreversible thermodynamics, we show that current-induced spin transfer torque within a magnetic domain implies spin pumping of current within that domain. This has experimental implications for samples both with conducting leads and that are electrically isolated. These results are obtained by deriving the dynamical equations for two models of non-uniform conducting magnets: (1) a generic conducting magnet, with net conduction electron density $n$ and net magnetization $\stackrel{P\vec}{M}$, and (2) a two-band magnet, with up and down spins each providing conduction and magnetism. For both models, in regions where the equilibrium magnetization is non-uniform, voltage gradients can drive adiabatic and nonadiabatic bulk spin torques. Onsager relations then ensure that magnetic torques likewise drive adiabatic and nonadiabatic currents\char22{}what we call bulk spin pumping. For a given amount of adiabatic and nonadiabatic spin torques, the two models yield similar but distinct results for the bulk spin pumping, thus distinguishing the two models. As for recent spin-Berry phase work, we find that within a domain wall, the ratio of the effective electromotive force to the magnetic field is approximately given by $P(2{\ensuremath{\mu}}_{B}∕e)$, where $P$ is the spin polarization. The adiabatic spin torque and spin-pumping terms are shown to be dissipative.

Modelling spin transfer torque and magnetoresistance in magnetic multilayers

Theoretical models of spin-dependent transport in magnetic spin-valves and tunneljunctions are presented. A general definition of current-induced spin transfer torque (STT)and interlayer exchange coupling (IEC) based on the spin density continuity principle isgiven. We then present an extension of the Valet and Fert model, based on the Boltzmanndescription of spin-dependent transport in metallic structures. This model describes STTand IEC in any kind of magnetic metallic multilayer, for any orientation of themagnetization of the ferromagnetic layers. Simulation results show that spin torque andmagnetoresistance originate from the same physical effect. In a second step, we model STTand IEC in magnetic tunnel junctions with an amorphous insulator, using thenon-equilibrium Keldysh technique. The general features of STT and IEC are described,showing an important asymmetry in STT bias dependence. Moreover, the influenceof a layer of impurities in the barrier is investigated and shows an importantenhancement of STT and IEC at resonance. Finally, we apply this model to doublemagnetic tunnel junctions and show that a dramatic enhancement of spin torquecan be obtained when the conditions of resonance in the free layer are fulfilled.

Magnetomechanical Torques in Small Magnetic Cantilevers

We study the dynamics of small magnetic cantilevers, made from either Si covered by a magnetic film or entirely ferromagnetic materials. The magnetomechanical torques cause line splittings in ferromagnetic resonance spectra and magnetization reversal facilitated by mechanical degrees of freedom. We show that the magnetomechanical torques can extend the limits of detecting and exciting motion at the nanoscale. The “nanomotor” described here effectively transforms rf magnetic fields into mechanical oscillations. We furthermore propose to integrate mechanical oscillators into magnetoelectronic devices that make use of current-induced spin-transfer torques. This opens new possibilities for electric transducers of nanomechanical motion.

Spin current and current-induced spin transfer torque in ferromagnet–quantum dot–ferromagnet coupled systems

Based on Keldysh's nonequilibrium Green function method, the spin-dependent transport properties in a ferromagnet--quantum dot (QD)--ferromagnet coupled system are investigated. It is shown the spin current shows quite different characteristics from its electrical counterpart, and by changing the relative orientation of both magnetizations, it can change its magnitude and even sign. The current-induced spin transfer torque (CISTT) is uncovered to be greatly enhanced when the bias voltage meets with the discrete levels of the QD at resonant positions. The relationship between the CISTT, the electrical current, and the spin current, is also addressed.

Current-induced spin transfer torque in ferromagnet-marginal Fermi liquid double tunnel junctions

Current-induced spin transfer torque through a marginal Fermi liquid (MFL) which is connected to two noncollinearly aligned ferromagnets via tunnel junctions is discussed in terms of the nonequilibrium Green function method. It is found that in the absence of the spin–flip scattering, the magnitude of the torque increases with the polarization and the coupling constant λ of the MFL, whose maximum increases with λ linearly, showing that the interactions between electrons tend to enhance the spin torque. When the spin–flip scattering is included, an additional spin torque is induced. It is found that the spin–flip scattering enhances the spin torque and gives rise to a nonlinear angular shift.

Classical description of current-induced spin-transfer torque in multilayer structures

We develop a classical description of the current-induced torque due to spin transfer in a layered system consisting of two ferromagnetic films separated by a nonmagnetic layer. The description is based on the classical equations for time-space evolution of the macroscopic magnetization. It is assumed that the perpendicular component of the nonequilibrium magnetization relaxes very fast in ferromagnetic films. Such a fast relaxation is due to a strong exchange field. Accordingly, the perpendicular component is totally absorbed at the interfaces giving rise to the torque. The longitudinal component, on the other hand, decays on a much longer distance defined by the spin diffusion length.

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 nonequilibrium 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 the product of Bessel functions with the energy levels shifted by $m\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0}.$ The tunneling current can be viewed to occur 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 a decrease of both 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.

Current-induced spin-wave excitations in a single ferromagnetic layer.

Evidence for a current-induced spin-transfer torque effect has been investigated in a series of point contacts to single ferromagnetic layers. At specific current densities, abrupt resistance changes, similar to those attributed to current-induced spin-wave excitations in multilayers, have been observed for one current polarity. The critical current for these resistance changes depends linearly on the external field applied perpendicular to the layer. The observed effect is interpreted as a current-driven heterogeneous instability in an otherwise uniform ferromagnetic layer.

Spin-flip scattering effect on the current-induced spin torque in ferromagnet–insulator–ferromagnet tunnel junctions

We have investigated the current-induced spin transfer torque of a ferromagnet–insulator–ferromagnet tunnel junction by taking the spin-flip scatterings into account. It is found that the spin-flip scattering can induce an additional spin torque, enhancing the maximum of the spin torque and giving rise to an angular shift compared to the case when the spin-flip scatterings are neglected. The effects of the molecular fields of the left and right ferromagnets on the spin torque are also studied. It is found that τ Rx / I e ( τ Rx is the spin-transfer torque acting on the right ferromagnet and I e is the tunneling electrical current) does vary with the molecular fields. At two certain angles, τ Rx / I e is independent of the molecular field of the right ferromagnet, resulting in two crossing points in the curve of τ Rx / I e versus the relevant orientation for different molecular fields.