Current-induced Spin-transfer Torque Research Articles

The Combined Effect of Spin-Transfer Torque and Voltage-Controlled Strain Gradient on Magnetic Domain-Wall Dynamics: Toward Tunable Spintronic Neuron

Magnetic domain wall (DW), as one of the promising information carriers in spintronic devices, have been widely investigated owing to its nonlinear dynamics and tunable properties. Here, we theoretically and numerically demonstrate the DW dynamics driven by the synergistic interaction between current-induced spin-transfer torque (STT) and voltage-controlled strain gradient (VCSG) in multiferroic heterostructures. Through electromechanical and micromagnetic simulations, we show that a desirable strain gradient can be created and it further modulates the equilibrium position and velocity of the current-driven DW motion. Meanwhile, an analytical Thiele’s model is developed to describe the steady motion of DW and the analytical results are quite consistent with the simulation data. Finally, we find that this combination effect can be leveraged to design DW-based biological neurons where the synergistic interaction between STT and VCSG-driven DW motion as integrating and leaking motivates mimicking leaky-integrate-and-fire (LIF) and self-reset function. Importantly, the firing response of the LIF neuron can be efficiently modulated, facilitating the exploration of tunable activation function generators, which can further help improve the computational capability of the neuromorphic system.

Fully relativistic first-principles quantum transport simulation of noncollinear spin transfer and spin Hall current

In this work, we report the fully relativistic (FR) first-principles quantum transport simulation of noncollinear spin transfer and spin Hall current in the device structure. In this method, the noncollinear FR exact muffin-tin orbital method is combined with Keldysh's nonequilibrium Green's function approach and mean-field theory to account for the multiple disorder scattering. We adopt the Bargmann-Wigner polarization operator to define the appropriate FR spin current so that the current-induced spin transfer, in the noncollinear magnetic device or due to the spin Hall effect, can be studied from first principles. As applications, we calculate the spin transfer torque in noncollinear spin valves Co/Cu/FM/Cu (FM = Co, ${\mathrm{Ni}}_{0.8}{\mathrm{Fe}}_{0.2}$) and spin Hall angles in various ${\mathrm{Pt}}_{1\ensuremath{-}x}{Y}_{x}$ [$Y$ = vacancy (Va), Au, Ag, Pd] alloys. We find that our FR results agree well with previous theoretical simulations and experimental measurements. Moreover, it is found that the applied finite bias can significantly enhance the spin Hall angle in ${\mathrm{Pt}}_{1\ensuremath{-}x}{\mathrm{Va}}_{x}$, and PtAg alloy presents a much higher spin Hall angle than that of PtAu and PtPd alloys. Our implementation of the FR method provides an important first-principles tool for studying various nonequilibrium spin phenomena and the associated relativistic effects in realistic device structures with atomic disorders, including both current-induced spin transfer and spin-orbit torques.

Skyrmion size-tuning in two-dimensional antiferromagnetic monolayers by applying local spin-polarized current-induced spin-transfer torque

Antiferromagnetic (AFM) skyrmions exhibit a variety of outstanding features, including stability, non-volatility, processability, and resistance to the skyrmion Hall effect (SkHE). However, AFM skyrmions are insensitive to an external magnetic field, posing a major challenge for controlling their size. Tuning the key magnetic properties in AFM thin films is a feasible method for controlling skyrmion size, but it may also adversely affect other magnetic characteristics, such as the velocity and stability of the skyrmion, especially for small skyrmion sizes. In this study, we have investigated the size controllability of AFM skyrmions in the presence of the Dzyaloshinskii–Moriya interaction (DMI), applying a pure spin current in a bilayer structure consisting of a 2D AFM nanodisk placed over a thin coating of heavy metal (HM). The method relies on destabilizing the AFM lattice by targeting the 2D AFM nanodisk in a specific area defined by the diameter (dtr) using spin-polarized current-perpendicular-to-plane (CPP), causing a localized magnetization precession induced by spin-transfer torque (STT). As a result, a series of AFM skyrmions of different radii was stabilized depending on the diameter used without resorting to re-tuning the magnetic characteristics of the material. Moreover, we have found that for strong DMI, robust AFM skyrmions of small sizes can also be generated by adopting small diameters. Besides, the impact of spin current and nucleation time has been examined, and it was found that adjusting these parameters does not help to fine-tune the skyrmion size as much as it affects the nucleation process. Finally, we demonstrate how this method may be used to adjust both the radius and site of the skyrmion in the 2D AFM monolayer by simultaneously targeting different locations using pure spin currents. This method allows us to tune the AFM skyrmion size and to directly address the target skyrmion without disturbing the surrounding magnetic environment. Therefore, our results may pave the way for high-functional spintronics applications based on AFM skyrmions.

Angular Dependent Auto-Oscillations by Spin-Transfer and Spin-Orbit Torques in Three-Terminal Magnetic Tunnel Junctions

Spintronic oscillators are promising candidates for neuromorphic computing due to their true miniaturization, non-linearity and synchronization properties. However, spin torque nano-oscillators are excited by current-induced spin-transfer torque which may cause high power consumption and reliability problems. Spin Hall nano-oscillators can realize higher energy efficiency, while their relatively low power emission limits their further applications. Here, we demonstrate three-terminal magnetic tunnel junction based spin torque nano-oscillators excited by the combination of spin-transfer and spin-orbit torques under different angle configurations. Thanks to the large spin Hall angle (-0.278) of W, the ratio between threshold current density of spin-transfer and spin-orbit torques for auto-oscillations can reach 0.6, indicating their high energy efficiency. Furthermore, we observe that the ratio has a sine function dependence on the angle between the spin-polarization directions of spin-transfer and spin-orbit torques. Our work could benefit the development of high-efficiency spintronic oscillators and their large network designs.

Demonstration of in-plane magnetized stochastic magnetic tunnel junction for binary stochastic neuron

A binary stochastic neuron (BSN) or a probabilistic bit (p-bit) randomly fluctuates between digitized “0” and “1” with a controllable functionality of time-averaged value. Such an unconventional bit is the most essential building block for the recently proposed stochastic neural networks and probabilistic computing. Here, we experimentally implement a magnetic tunnel junction (MTJ) for BSN, with relaxation times on the order of tens of milliseconds that can be modulated by a current-induced spin-transfer torque. The NIST Statistical Test Suite (800-22a) is used to verify true random number generation by the BSN-MTJ device. Our results suggest the possibility of using the artificial BSN MTJ device in neuromorphic applications as well as in a recently proposed probabilistic computing.

Hopfield neural network in magnetic textures with intrinsic Hebbian learning

Macroscopic spin ensembles with brainlike features such as nonlinearity, stochasticity, self-oscillations, memory effects, and plasticity, form attractive platforms for neuromorphic computing. We propose an artificial neural network consisting of electric contacts on conducting films with tunable magnetic textures that is superior to conventional implementations, because it does not require resource-demanding external computations during training. Simulations show that the feedback between anisotropic magnetoresistance and current-induced spin-transfer torque in malleable magnetic textures autonomously trains the network according to the Hebbian learning principle. We illustrate the idea by simulating the pattern recognition by a four-node Hopfield neural network.

Role of impurity clusters for the current-driven motion of magnetic skyrmions

We study how impurities influence the current-induced dynamics of magnetic Skyrmions moving in a racetrack geometry. For this, we solve numerically the generalized Landau-Lifshitz-Gilbert equation extended by the current-induced spin transfer torque. In particular, we investigate two classes of impurities, non-conducting and magnetic impurities. The former are magnetically rigid objects and yield to an inhomogeneous current density over the racetrack which we determine separately by solving the fundamental electrostatic equations. In contrast, magnetic impurities leave the applied current density homogeneous throughout the stripe. Depending on parameters, we observe four different scenarios of Skyrmion motions in the presence of disorder, the Skyrmion decay, the pinning, the creation of additional Skyrmions, and ordinary Skyrmion passage. We calculate and discuss phase diagrams in dependence of the impurity concentration and radii of the impurities.

Adiabatic and nonadiabatic spin-transfer torques in antiferromagnets

Electron transport in magnetic orders and the magnetic orders dynamics have a mutual dependence, which provides the key mechanisms in spin-dependent phenomena. Recently, antiferromagnetic orders are focused on as the magnetic order, where current-induced spin-transfer torques, a typical effect of electron transport on the magnetic order, have been debatable mainly because of the lack of an analytic derivation based on quantum field theory. Here, we construct the microscopic theory of spin-transfer torques on the slowly-varying staggered magnetization in antiferromagnets with weak canting. In our theory, the electron is captured by bonding/antibonding states, each of which is the eigenstate of the system, doubly degenerates, and spatially spreads to sublattices because of electron hopping. The spin of the eigenstates depends on the momentum in general, and a nontrivial spin-momentum locking arises for the case with no site inversion symmetry, without considering any spin-orbit couplings. The spin current of the eigenstates includes an anomalous component proportional to a kind of gauge field defined by derivatives in momentum space and induces the adiabatic spin-transfer torques on the magnetization. Unexpectedly, we find that one of the nonadiabatic torques has the same form as the adiabatic spin-transfer torque, while the obtained forms for the adiabatic and nonadiabatic spin-transfer torques agree with the phenomenological derivation based on the symmetry consideration. This finding suggests that the conventional explanation for the spin-transfer torques in antiferromagnets should be changed. Our microscopic theory provides a fundamental understanding of spin-related physics in antiferromagnets.

Numerical computation of spin-transfer torques for antiferromagnetic domain walls

We numerically compute current-induced spin-transfer torques for antiferromagnetic domain walls, based on a linear response theory in a tight-binding model. We find that, unlike for ferromagnetic domain wall motion, the contribution of adiabatic spin torque to antiferromagnetic domain wall motion is negligible, consistent with previous theories. As a result, the non-adiabatic spin-transfer torque is a main driving torque for antiferromagnetic domain wall motion. Moreover, the non-adiabatic spin-transfer torque for narrower antiferromagnetic domain walls increases more rapidly than that for ferromagnetic domain walls, which is attributed to the enhanced spin mistracking process for antiferromagnetic domain walls.

Thermally Assisted Skyrmion Memory (TA-SKM)

A novel thermally assisted skyrmion memory (TA-SKM) has been proposed and studied for the first time. Unidirectional current-induced spin transfer torque (STT) and Joule heating effect are used to induce the magnetization switching between uniform and skyrmion states in the free layer of a magnetic tunnel junction device. Physics-based simulations suggest that TA-SKM offers advantages including unipolar switching feature for cross-point memory integration, better TMR design as compared to STT-MRAM, and improved operation temperature range as compared to TA-MRAM.

Single-shot dynamics of spin-orbit torque and spin transfer torque switching in three-terminal magnetic tunnel junctions.

Current-induced spin-transfer torques (STT) and spin-orbit torques (SOT) enable the electrical switching of magnetic tunnel junctions (MTJs) in non-volatile magnetic random access memories. To develop faster memory devices, an improvement in the timescales that underlie the current-driven magnetization dynamics is required. Here we report all-electrical time-resolved measurements of magnetization reversal driven by SOT in a three-terminal MTJ device. Single-shot measurements of the MTJ resistance during current injection reveal that SOT switching involves a stochastic two-step process that consists of a domain nucleation time and propagation time, which have different genesis, timescales and statistical distributions compared to STT switching. We further show that the combination of SOT, STT and the voltage control of magnetic anisotropy leads to reproducible subnanosecond switching with the spread of the cumulative switching time smaller than 0.2 ns. Our measurements unravel the combined impact of SOT, STT and the voltage control of magnetic anisotropy in determining the switching speed and efficiency of MTJ devices.

Alternating current-induced interfacial spin-transfer torque

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.

Nonvolatile Current-Modulated Four-State Magnetoplasmonic Memory

We model the operation and readout sensitivity of two current-modulated magnetoplasmonic devices which exploit spin Hall effect-like behavior as a function of their device and material parameters. In both devices, current pulses are applied to an electrically-isolated stack, containing an active layer (either a metal with large spin orbit coupling or a topological insulator) embedded within a plasmonic metal (Au). The first device, composed of a ferromagnet and the active layer, illustrates a plasmonic readout scheme for detecting magnetic reorientation driven by current-induced spin transfer torques. The plasmonic readout of these current-modulated non-volatile states may facilitate the development of plasmon-based memory or logic devices. The second device, containing only the active layer, explores the magnetoplasmonic readout conditions required to directly measure the spin accumulation in these materials. The estimated thickness-dependent sensitivity agrees with recent experimental magneto-optical Kerr effect observations.

Long spin coherence length and bulk-like spin-orbit torque in ferrimagnetic multilayers.

Spintronics relies on magnetization switching through current-induced spin torques. However, because spin transfer torque for ferromagnets is a surface torque, a large switching current is required for a thick, thermally stable ferromagnetic cell, and this remains a fundamental obstacle for high-density non-volatile applications with ferromagnets. Here, we report a long spin coherence length and associated bulk-like torque characteristics in an antiferromagnetically coupled ferrimagnetic multilayer. We find that a transverse spin current can pass through >10-nm-thick ferrimagnetic Co/Tb multilayers, whereas it is entirely absorbed by a 1-nm-thick ferromagnetic Co/Ni multilayer. We also find that the switching efficiency of Co/Tb multilayers partially reflects a bulk-like torque characteristic, as it increases with ferrimagnet thickness up to 8 nm and then decreases, in clear contrast to the 1/thickness dependence of ferromagnetic Co/Ni multilayers. Our results on antiferromagnetically coupled systems will invigorate research towards the development of energy-efficient spintronics.

Field Characteristics of Spin-Torque Diode Sensitivity in the Presence of a Bias Current

The use of the spin-torque diode effect, which is generated upon the current-induced transfer of spin angular momentum in magnetic tunnel junctions, opens the prospect of considerably improving microwave sensitivity in the gigahertz frequency band over that of semiconductor Schottky diodes. In this work, the spin-diode effect of microwave signal rectification in a magnetic tunnel junction upon the resonant excitation of spin waves in the free magnetic layer as a result of the current-induced spin-transfer torque effect is analyzed theoretically. Frequency characteristics of the resonant response of a spin-torque diode to a microwave signal are calculated in the linear macrospin approximation as functions of the direction and value of the applied magnetic field and bias current. It is shown that with zero bias current, the maximum rectified voltage across a junction is obtained in the geometry of mutually perpendicular magnetizations of magnetic layers; as the resonant frequency of oscillations in a magnetic field increases, this voltage drops at the retained equilibrium orientation of spins in the layers. After the bias current is switched on, the resonance amplitude of forced oscillations of the free layer spins upon microwave excitation grows sharply at the critical point of the spin-torque diode’s loss of equilibrium state stability. The linewidth at this point is limited only by nonlinear effects. Improving spin-torque diode sensitivity is important for its use in microwave holographic vision systems.

Spin–Orbit Torques in Metallic Magnetic Multilayers: Challenges and New Opportunities

Two decades after the discovery of the giant magnetoresistance that revolutionizes the hard disk drive, the rapid development of spin torque-based magnetic random access memory has once again demonstrated the great potential of spintronics in practical applications. While the industrial application is mainly focusing on the implementation of current-induced spin transfer torque (STT) in magnetic tunnel junctions, a new type of spin torque emerges due to the spin–orbit interaction in magnetic multilayers. A great effort has been devoted by the scientific community to study the so-called spin–orbit torque (SOT), which is not only of interest to fundamental science, but also exhibits potential for the application of current-induced magnetization switching. In this paper, we will review recent development in the SOTs including the fundamental understanding, materials development and measurement techniques. We will also discuss the challenges of using the SOT in potential applications, particularly on the switching of perpendicularly magnetized films.

Geometrical control of pure spin current induced domain wall depinning

We investigate the pure spin-current assisted depinning of magnetic domain walls in half ring based Py/Al lateral spin valve structures. Our optimized geometry incorporating a patterned notch in the detector electrode, directly below the Al spin conduit, provides a tailored pinning potential for a transverse domain wall and allows for a precise control over the magnetization configuration and as a result the domain wall pinning. Due to the patterned notch, we are able to study the depinning field as a function of the applied external field for certain applied current densities and observe a clear asymmetry for the two opposite field directions. Micromagnetic simulations show that this can be explained by the asymmetry of the pinning potential. By direct comparison of the calculated efficiencies for different external field and spin current directions, we are able to disentangle the different contributions from the spin transfer torque, Joule heating and the Oersted field. The observed high efficiency of the pure spin current induced spin transfer torque allows for a complete depinning of the domain wall at zero external field for a charge current density of A m−2, which is attributed to the optimal control of the position of the domain wall.

Spin-transfer-torque-induced zero-field microwave oscillator using a magnetic easy cone state

Current-induced spin-transfer torque can induce magnetization precession in gigahertz ranges, which enables various microwave devices. In most cases, this current-induced precession requires an additional external magnetic field, which is detrimental for device applications. In this work, we show that the current-induced precession is realized even without an external field when the magnetic layer has conical magnetization, caused by the second order easy-axis magnetic anisotropy. We theoretically derive the oscillation frequency and output power and confirm their validity by macrospin simulations. We find that the ratio of the second to the first anisotropy constants is key to determine the maximum frequency and power. Our results will be helpful for the applications of microwave devices utilizing spin-transfer torques and provide a design rule of such devices.

Spin-dependent transport and current-induced spin transfer torque in a disordered zigzag silicene nanoribbon

We study theoretically the spin-dependent transport and the current-induced spin transfer torque (STT) for a zigzag silicene nanoribbon (ZSiNR) with Anderson-type disorders between two ferromagnetic electrodes. By using the nonequilibrium Green's function method, it is predicted that the transport property and STT through the junction depend sensitively on the disorder, especially around the Dirac point. As a result, the conductance decreases and increases for two electrode in parallel and antiparallel configurations, respectively. Due to the disorder, the magnetoresistance (MR) decreases accordingly even within the energy regime for the perfect plateau without disorders. In addition, the conductance versus the relative angle of the magnetization shows a cosine-like behavior. The STT per unit of the bias voltage versus the angle of the magnetization exhibits a sine-like behavior, and versus the Fermi energy is antisymmetrical to the Dirac point and exhibits sharp peaks. Furthermore, the peaks of the STT are suppressed much as the disorder strength increases, especially around the Dirac point. The results obtained here may provide a valuable suggestion to experimentally design spin valve devices based on ZSiNR.

Solitons in Dual-Barrier Magnetic Tunnel Junction

We have investigated the magnetic spin dynamics in a dual-barrier magnetic tunnel junction (MTJ), which consists of a free layer sandwiched between the top and bottom pinned layers. Current-induced spin transfer torque is produced when spin-polarised electrons flow through this spin valve pillar. We have formulated an extended Landau-Lifshitz-Gilbert-Slonczewski equation for dual-barrier spin valve multilayer structure. We have projected the unit sphere of spin onto a complex plane and transformed the equation of motion to a cubic-quintic nonlinear Schrodinger equation. The soliton solutions are constructed by employing Hirota’s Bilinearisation technique. The investigation shows that the amplitude of solitons depends greatly on the system parameters. Solitons emerge from this inhomogeneous nonlinear system representing a balance between the effect of dispersion and nonlinearity. The presence of these solitons as magnetic excitations in a ferromagnetic multilayer system may lead to noise-free nonvolatile data storage, data transmission and also in quantum computations.