Spin Transfer Torque Effect Research Articles

Manipulation of Magnonic Activity by Electric Currents in Ferromagnetic Nanocylinders

Electric currents passing through ferromagnets can impact the magnetization dynamics via the so-called spin-transfer torque (STT) effect. In this paper, we present a theoretical study on the current influence on magnonic activity, a recently reported spin wave (SW) chiral effect in ferromagnetic nanotubes. By micromagnetic simulations, we show that an electric current can cause a significant change in the rotatory power of the SW modes propagating in a longitudinally magnetized nanotube. This result is well explained by using the Fresnel model in optics assuming a SW circular birefringence. An analytical method is developed to solve the first-order mode, yielding perfect agreements with the numerical results. Our results provide a new approach to manipulate the SW propagating properties in ferromagnetic nanocylinders.

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.

Design and Assessment of Hybrid MTJ/CMOS Circuits for In-Memory-Computation

Hybrid magnetic tunnel junction/complementary metal oxide semiconductor (MTJ/CMOS) circuits based on in-memory-computation (IMC) architecture is considered as the next-generation candidate for the digital integrated circuits. However, the energy consumption during the MTJ write process is a matter of concern in these hybrid circuits. In this regard, we have developed a novel write circuit for the contemporary three-terminal perpendicular-MTJs that works on the voltage-gated spin orbit torque (VG+SOT) switching mechanism to store the information in hybrid circuits for IMC architecture. Investigation of the novel write circuit reveals a remarkable reduction in the total energy consumption (and energy delay product) of 92.59% (95.81) and 92.28% (42.03%) than the conventional spin transfer torque (STT) and spin-Hall effect assisted STT (SHE+STT) write circuits, respectively. Further, we have developed all the hybrid logic gates followed by nonvolatile full adders (NV-FAs) using VG+SOT, STT, and SHE+STT MTJs. Simulation results show that with the VG+SOT NOR-OR, NAND-AND, XNOR-XOR, and NV-FA circuits, the reduction in the total power dissipation is 5.35% (4.27%), 5.62% (3.2%), 3.51% (2.02%), and 4.46% (2.93%) compared to STT (SHE+STT) MTJs respectively.

Effect of spin transfer torque on antiferromagnetic film: computer simulations

Effect of spin transfer torque on antiferromagnetic film: computer simulations

Peredacha spinovogo momenta i nelineynyy kvantovyy elektronnyy transport v kiral'nykh gelimagnetikakh

We construct a nonlinear theory of electric resistance of chiral helimagnets, in which the shape changes and the magnetization spiral starts rotating during the passage of electric current due to the spin transfer torque effect. It is shown that the rotation of the spin spiral under the action of the passing current, the electric resistance of the helimagnet is always lower than the resistance of a helimagnet in which the spin spiral is stationary. It is found that the current–voltage characteristic of the helimagnet in the presence of the spin transfer torque from the conduction electron system to the system of localized electrons can be essentially nonlinear. The possibility of the spin electric bistability effect in helimagnets is predicted for the situation when the spin contribution to electric resistance of a helimagnet can take two different values for the same value of the current passing through it. The possibility of realization of states with a negative differential resistance in helimagnets is demonstrated.

Energetic perspective on emergent inductance exhibited by magnetic textures in the pinned regime

Spatially varying magnetic textures can exhibit electric-current-induced dynamics as a result of the spin-transfer torque effect. When such a magnetic system is electrically driven, an electric field is generated, which is called the emergent electric field. In particular, when magnetic-texture dynamics are induced under the application of an AC electric current, the emergent electric field also appears in an AC manner, notably, with an out-of-phase time profile, thus exhibiting inductor behavior, often called an emergent inductor. Here we show that the emergent inductance exhibited by magnetic textures in the pinned regime can be explained in terms of the current-induced energy stored in the magnetic system. We numerically find that the inductance values defined from the emergent electric field and the current-induced magnetization-distortion energy, respectively, are in quantitative agreement in the so-called adiabatic limit. Our findings indicate that emergent inductors retain the basic concept of conventional inductors; that is, the energy is stored under the application of electric current.

Field-free domain wall spin torque nano-oscillators with multimodal real-time modulation and high-quality factor

We report on a magnetic domain wall (DW)-based spin torque nano-oscillator (STNO) with real-time multimodal frequency modulation characteristics by engineering the synergistic effect of shape anisotropy, Dzyaloshinskii-Moriya interaction (DMI), and spin-transfer torque. The achieved manageable oscillation and precession of magnetic DW motivate us to implement such attributes into the developed STNO under a low current density of ∼107 A/cm2, which demonstrates outstanding functionality of multimodal real-time modulation ranging from few GHz and sub-THz with corresponding few tens and >104 quality factor (fSTNO/Δf) in absence of external magnetic field. Furthermore, the dynamic process of DW motion and magnetic moment precession under different modes has been revealed systematically, and the frequency dependence of various physical parameters including damping constant, uniaxial anisotropy constant, saturation magnetization, exchange stiffness, and DMI constant has also been summarized in detail. Such a DW-based device enriches the STNO family and promises great potential with a broad spectrum of applications in microwave generators and neuromorphic computing.

Micromagnetic insights on in-plane magnetization rotation and propagation of magnetization waves in nanowires

Utilizing micromagnetic modeling, we have explained the unprobed characteristics of 360° full cycle in-plane magnetization rotation and the resulting propagation of a magnetization wave along a ferromagnet nanowire. The magnetization wave, which is generated by setting off spin oscillation at one end of a ferromagnetic strip, propagates till the end of the wire. A perpendicular spin torque oscillator (STO) could generate magnetization rotation at one end of the ferromagnetic strip that is also part of the STO. Our results demonstrate that the oscillation frequency of the spins along the wire maintains excellent fidelity while the spatial wavelength of the magnetic wave increases. The driving mechanism behind the propagation of the wave is found to be exchange-springs, which enables the propagation of the wave without the need for a 'carrier' force, such as spin-transfer torque (STT) or spin Hall effect (SHE). Furthermore, we demonstrate that the gradient of the exchange energy drives the magnetic wave forward, while the in and out of plane anisotropy fields govern the shape of spin oscillation trajectories along the wire. Additionally, we show that stopping the oscillation at the STO end causes the wave to cease propagation after relaxation, and altering the STO rotational chirality leads to merging and annihilating domain walls of opposite winding numbers.

Interplay between spin wave and magnetic vortex

The interplay between spin wave (SW) and magnetic vortex is studied. We find three types of magnon scatterings: skew scattering, symmetric side deflection, and back reflection, which associate with, respectively, magnetic topology, energy density distribution, and linear momentum transfer torque within the vortex. The vortex core exhibits two translational modes: the intrinsic circular mode and a coercive elliptical mode, which can be excited by the net and oscillating magnon spin-transfer torque effects of SWs. Lastly, we propose a vortex-based SW valve in which we obtain excellent valving performance and access arbitrary control of the phase shift via inhomogeneity modulation. The phase shift arises from the enlarged wavelength of the SW in inhomogeneous magnetization.

Asymmetric scattering behaviors of spin wave dependent on magnetic vortex chirality

We investigate asymmetric spin wave scattering behaviors caused by vortex chirality in a cross-shaped ferromagnetic system by using the micromagnetic simulations. In the system, four scattering behaviors are found: (i) asymmetric skew scattering, depending on the polarity of vortex core, (ii) back scattering (reflection), depending on the vortex core stiffness, (iii) side deflection scattering, depending on structural symmetry of the vortex circulation, and (iv) geometrical scattering, depending on waveguide structure. The first and second scattering behaviors are attributed to nonlinear topological magnon spin Hall effect related to magnon spin-transfer torque effect, which has value for magnonic exploration and application.

Steady-state skyrmion oscillations in a spin valve (SV) nanopillar based on hybrid polarizer: A skyrmion-based spin torque nano-oscillator (STNO)

The skyrmion-based spin torque nano-oscillators (STNOs) have received a lot of interest due to their prospects as microwave signal generators. These oscillators are accessible by achieving consistent circular spinning of the skyrmion in a circular disk, caused by the spin transfer torque (STT) effect. However, the Magnus force effect, that relates to the non-trivial topological part of the skyrmion and driven on by the higher current densities, leads the skyrmion to accumulate in the center or annihilate toward the edge of the device. To counterbalance the Magnus force, we propose a skyrmion-based STNO model built on a circular nanopillar-shaped spin valve having a hybrid polarizer, which is divided into two regions, each with a different polarization angle. Using Thiele equation-based analytical framework in parallel with micromagnetic simulations, we illustrate that the proposed hybrid polarizer system is intended to ensure steady circular motion of the skyrmion without skyrmion annihilation or accumulation, by strengthening the boundary-induced force. Moreover, we also investigate the current density and polarizer parameters effect on skyrmion oscillation frequency. The results show that the frequency that can be limited for a skyrmion-based STNO with a hybrid polarizer is up to 3.35 GHz, which is higher in terms of magnitude than that of the homogeneous polarizer-based STNO. Our findings provide an insight into the phenomenon of skyrmion dynamics in a circular nanopillar-shaped spin valve with hybrid polarizer, which may open up new avenues for overcoming the frequency limit of the skyrmion-based STNOs.

Perpendicular magnetic anisotropy, tunneling magnetoresistance and spin-transfer torque effect in magnetic tunnel junctions with Nb layers

Nb and its compounds are widely used in quantum computing due to their high superconducting transition temperatures and high critical fields. Devices that combine superconducting performance and spintronic non-volatility could deliver unique functionality. Here we report the study of magnetic tunnel junctions with Nb as the heavy metal layers. An interfacial perpendicular magnetic anisotropy energy density of 1.85 mJ/m2 was obtained in Nb/CoFeB/MgO heterostructures. The tunneling magnetoresistance was evaluated in junctions with different thickness combinations and different annealing conditions. An optimized magnetoresistance of 120% was obtained at room temperature, with a damping parameter of 0.011 determined by ferromagnetic resonance. In addition, spin-transfer torque switching has also been successfully observed in these junctions with a quasistatic switching current density of 7.3 times ;10^{5} A/cm2.

Hybrid Multilevel STT/DSHE Memory for Efficient CNN Training

Convolutional neural network (CNN) is one of the most popular deep learning algorithms for artificial intelligence applications. However, due to its data-intensive workloads, the training of deep CNN is constrained by large memory requirements. Previously, spin transfer torque (STT)-based multilevel cells (MLCs) have been used to implement CNN accelerators to address this issue. However, due to multistep write and read operations, energy, latency, and reliability are critical constraints for larger and deeper training models. This article presents a hybrid STT and differential spin Hall effect (DSHE)-MLC-based data-aware memory design to achieve single-step write and read operations. Depending on the data type, the two-bit data are stored in either STT-MLC or DSHE-MLC memory blocks. The proposed scheme improves the training energy and latency in VGG-16, VGG-19, AlexNet, and LeNet CNN architectures by nearly 50% when compared with conventional STT-MLC-based architectures. Moreover, it also allows for the resolution of device-level write and read reliability issues.

Field-free switching model of spin–orbit torque (SOT)-MTJ device with thermal effect based on voltage-controlled magnetic anisotropy (VCMA)

Electrically driven magnetization switch has attracted much attention in the new spintronic memory, especially for spin–orbit torque (SOT)-based magnetic random access memory (MRAM). However, the published models are facing limitations with the continuous shrinkage of the feature size down to nanoscale. Also, the thermal effect caused by switching operation is non-negligible. Therefore, an effective model is needed to represent the switching dynamic of the device concerning the influences of the nanoscale and the thermal effect. In the paper, a compact model of three-terminal SOT-driven switching is established. The influence of the voltage-controlled magnetic anisotropy (VCMA) and spin transfer torque (STT) effect induced by bias voltage on the field-free SOT-driven switching is considered by numerically solving the LLG equations. Furthermore, a 3D model of the SOT-MTJ device is established by finite element method to trace the thermoelectric behavior inside the device. The thermoelectric behavior is integrated into the compact model to show the influence of the temperature on the switching behavior, highlighting the importance of the thermal effect for the realistic modelling of SOT-driven switching. Finally, a novel voltage pulse scheme is proposed, which can effectively shorten the switching time and improve the reliability of the device. The established model could provide strategies and guidelines for next-generation memory design and application.

Perspectives on field-free spin–orbit torque devices for memory and computing applications

The emergence of embedded magnetic random-access memory (MRAM) and its integration in mainstream semiconductor manufacturing technology have created an unprecedented opportunity for engineering computing systems with improved performance, energy efficiency, lower cost, and unconventional computing capabilities. While the initial interest in the existing generation of MRAM—which is based on the spin-transfer torque (STT) effect in ferromagnetic tunnel junctions—was driven by its nonvolatile data retention and lower cost of integration compared to embedded Flash (eFlash), the focus of MRAM research and development efforts is increasingly shifting toward alternative write mechanisms (beyond STT) and new materials (beyond ferromagnets) in recent years. This has been driven by the need for better speed vs density and speed vs endurance trade-offs to make MRAM applicable to a wider range of memory markets, as well as to utilize the potential of MRAM in various unconventional computing architectures that utilize the physics of nanoscale magnets. In this Perspective, we offer an overview of spin–orbit torque (SOT) as one of these beyond-STT write mechanisms for the MRAM devices. We discuss, specifically, the progress in developing SOT-MRAM devices with perpendicular magnetization. Starting from basic symmetry considerations, we discuss the requirement for an in-plane bias magnetic field which has hindered progress in developing practical SOT-MRAM devices. We then discuss several approaches based on structural, magnetic, and chiral symmetry-breaking that have been explored to overcome this limitation and realize bias-field-free SOT-MRAM devices with perpendicular magnetization. We also review the corresponding material- and device-level challenges in each case. We then present a perspective of the potential of these devices for computing and security applications beyond their use in the conventional memory hierarchy.

In-Memory Computing Paradigms by Exploiting the Intrinsic Interactions Between STT and SOT

In-memory computing (IMC) based on magnetic random access memory (MRAM) can effectively overcome the bottlenecks of the Von-Neumann architecture, thanks to its advantages of nonvolatility, high speed, and low power consumption. Especially, the toggle-spin torque (TST)-MRAM with the joint effect of spin-transfer torque (STT) and spin-orbit torque (SOT) is extremely suitable for the IMC paradigms due to the operation flexibility of a pair of currents. In this article, we propose several novel IMC paradigms based on the TST-MRAM using the intrinsic interactions between STT and SOT. The logic operation could be implemented in a compact method. Moreover, the proposed reconfigurable logic shows great efficiency in performing XOR operation. Afterward, we develop a theoretical model for the proposed IMC paradigms to facilitate the performance evaluation. Meanwhile, good agreement between analytical solutions and simulation results is demonstrated. Finally, the functionality of the proposed IMC paradigms is validated by transient simulation. Our proposal provides a novel route for designing MRAM-based IMC paradigms.

Review of voltage-controlled magnetic anisotropy and magnetic insulator

This Festschrift is dedicated to Chia-Ling Chien on the occasion of his eightieth birthday. Prof. Chien is one of the pioneering physicists in the field of spintronics with groundbreaking achievements in giant magnetoresistance, proximity effects in superconductor/ferromagnet multilayers, exchange bias, spin-transfer torque effect, voltage-controlled spin mechanisms, spin-caloritronics and so on. We will focus and give a brief review on the two aspects, the voltage-controlled magnetic anisotropy (VCMA), the magnetic insulator (MI), and related works.

Chirality-dependent spin-transfer torque and current-induced spin rotation in helimagnets

We have built a theory of the spin-transfer torque (STT) effect in a conductive chiral helical magnet (CHM). It is shown that the STT effect induced by a spin current flowing through CHM leads to the rotation of the CHM magnetization spiral around its axis. The frequency of such rotation of the CHM magnetization is found. The former is expressed in terms of the parameters of the quantum-exchange Hamiltonian that specifies helical magnetic ordering in a conductive crystal. We have showcased that both the direction of rotation of the CHM magnetization and the direction of changes in the shape of the magnetic spiral are determined by the electron flow direction and the chirality of the magnet. The theory developed accounts for the generation of an electromagnetic field when rotating the magnetic spiral in the CHM subjected to an electric current flowing through the helimagnet.

Spin-transfer-assisted parametric pumping of magnons in yttrium iron garnet

The combination of parametric pumping and spin-transfer torque is a powerful approach that enables high-level control over magnetic excitations in thin-film ferromagnets. The excitation parameters, such as pumping power and external field strength, affect the instabilities of individual magnon modes. We theoretically explore how the simultaneous effects of parametric pumping and spin transfer torque influence these magnetic instabilities in a thin-film ferromagnet. Within the Landau-Lifshitz-Gilbert framework, we perform micromagnetic simulations of magnon excitations in yttrium iron garnet by pumping, spin transfer torque, and a combination of the two. We find that consistent with experimental results, the magnitude and direction of the spin-transfer torque tune the parametric instability thresholds.

Collective skyrmion motion under the influence of an additional interfacial spin-transfer torque

Here we study the effect of an additional interfacial spin-transfer torque, as well as the well-established spin–orbit torque and bulk spin-transfer torque, on skyrmion collections—group of skyrmions dense enough that they are not isolated from one another—in ultrathin heavy metal/ferromagnetic multilayers, by comparing modelling with experimental results. Using a skyrmion collection with a range of skyrmion diameters and landscape disorder, we study the dependence of the skyrmion Hall angle on diameter and velocity, as well as the velocity as a function of diameter. We show that inclusion of the interfacial spin-transfer torque results in reduced skyrmion Hall angles, with values close to experimental results. We also show that for skyrmion collections the velocity is approximately independent of diameter, in marked contrast to the motion of isolated skyrmions, as the group of skyrmions move together at an average group velocity. Moreover, the calculated skyrmion velocities are comparable to those obtained in experiments when the interfacial spin-transfer torque is included. Our results thus show the significance of the interfacial spin-transfer torque in ultrathin magnetic multilayers, which helps to explain the low skyrmion Hall angles and velocities observed in experiment. We conclude that the interfacial spin-transfer torque should be considered in numerical modelling for reproduction of experimental results.