Spin Transfer Research Articles

Accelerating Graph-Connected Component Computation With Emerging Processing-In-Memory Architecture

Computing the connected component (CC) of a graph is a basic graph computing problem, which has numerous applications like graph partitioning and pattern recognition. Existing methods for computing CC suffer from memory wall problems because of the frequent data transmission between CPU and memory. To overcome this challenge, in this article, we propose to accelerate CC computation with the emerging processing-in-memory (PIM) architecture through an algorithm–architecture co-design manner. The innovation lies in computing CC with bitwise logical operations (such as AND and OR), and the customized data flow management methods to accelerate computation and reduce energy consumption. As a proof of concept, experimental results with computational spin-transfer torque magnetic RAM (STT-MRAM) arrays demonstrate on average <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$19.8\times $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$12.4\times $ </tex-math></inline-formula> speedups compared with the CPU and GPU implementations, and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$35.4 \times $ </tex-math></inline-formula> energy efficiency improvement over the CPU implementation. Moreover, we investigate the potential associations between graph computing and bitwise Boolean logic, which could help design more general in-memory graph computing accelerators in the future.

Nonlinear chiral photocurrent in parity-violating magnetic Weyl semimetals

The strong correlation between the non-trivial band topology and the magnetic texture makes magnetic Weyl semimetals excellent candidates for the manipulation and detection of magnetization dynamics. The parity violation together with the Pauli blocking cause only one Weyl node to contribute to the photocurrent response, which in turn affects the magnetic texture due to the spin transfer torque. Utilizing the Landau-Lifshitz-Gilbert equation and the spin-transfer torque in non-centrosymmetric Weyl magnets, we show that the chiral photocurrent rotates the magnetization from the easy c axis to the a or b axis, which leads to an exotic current next to the photocurrent response. The chiral photocurrent is calculated in the context of quantum kinetic theory and it has a strong resonance on the order of mA/W near the Weyl nodes, the magnitude of which is controlled by the momentum relaxation time. Remarkably, we study the influence of magnetic texture dynamics on the topological nonlinear photocurrent response, including shift and injection currents along with the new chiral photocurrent, and show that both the magnitude and the in-plane orientation of the chiral photocurrent are strongly correlated with the direction of the magnetic moments.

Absorption of transverse spin current in ferromagnetic NiCu: Dominance of bulk dephasing over spin-flip scattering

In ferromagnetic metals, transverse spin currents are thought to be absorbed via dephasing—i.e., destructive interference of spins precessing about the strong exchange field. Yet, due to the ultrashort coherence length of ≈1 nm in typical ferromagnetic thin films, it is difficult to distinguish dephasing in the bulk from spin-flip scattering at the interface. Here, to assess which mechanism dominates, we examine transverse spin-current absorption in ferromagnetic NiCu alloy films with reduced exchange fields. We observe that the coherence length increases with decreasing Curie temperature, as weaker dephasing in the film bulk slows down spin absorption. Moreover, nonmagnetic Cu impurities do not diminish the efficiency of spin-transfer torque from the absorbed spin current. Our findings affirm that the transverse spin current is predominantly absorbed by dephasing inside the nanometer-thick ferromagnetic metals, even with high impurity contents.

Spatially nonuniform oscillations in ferrimagnets based on an atomistic model

The ferrimagnets, such as GdxFeCo(1-x), can produce ultrafast magnetic switching and oscillation due to the strong exchange field. The two-sublattices macrospin model has been widely used to explain the experimental results. However, it fails in describing the spatial nonuniform magnetic dynamics which gives rises to many important phenomenons such as the domain walls and skyrmions. Here we develop the two-dimensional atomistic model and provide a torque analysis method to study the ferrimagnetic oscillation. Under the spin-transfer torque, the magnetization oscillates in the exchange mode or the flipped exchange mode. When the Gd composition is increased, the exchange mode firstly disappears, and then appears again as the magnetization compensation point is reached. We show that these results can only be explained by analyzing the spatial distribution of magnetization and effective fields. In particular, when the sample is small, a spatial nonuniform oscillation is also observed in the square film. Our work reveals the importance of spatial magnetic distributions in understanding the ferrimagnetic dynamics. The method developed in this paper provides an important tool to gain a deeper understanding of ferrimagnets and antiferromagnets. The observed ultrafast dynamics can also stimulate the development of THz oscillators.

Modeling thermal effects in STT-MRAM

We employ the stochastic Landau–Lifschitz–Gilbert (sLLG) equation to explore thermal effects on switching in the spin-transfer torque magnetoresistive random access memory (STT-MRAM). The distribution of the switching times depends on the meshes used for the discretization within the finite element method (FEM) implementation and we introduce an effective temperature scaling in the thermal field calculation to mitigate the switching time distribution dependencies on the element size. Furthermore, we investigate the switching statistics of the STT-MRAM at different temperatures and show that the switching time distribution has a lower mean value, but possesses a longer tail of long switching times for the higher operating temperatures. As a result, the STT-MRAM switching with a fixed voltage pulse duration becomes more error-prone at elevated temperatures.

Double magnetic tunnel junction two bit memory and nonvolatile logic for in situ computing

In exascale computing, a huge amount of data is processed in real-time. Conventional CMOS-based computing paradigms follow the read, compute, and write back mechanism. This approach consumes significant power and time to compute and store data. in situ computation – where data are processed within the memory system – is considered a platform for exascale computation. Spin transfer torque perpendicular magnetic tunnel junctions (PMTJ) is a nonvolatile memory device with several potential advantages (fast read/write, high endurance, and CMOS compatibility) to become a next generation memory solution. A double magnetic tunnel junction (DMTJ) consists of two PMTJs constructed in a vertical arrangement. In this paper, DMTJ offers the possibility of constructing not only standalone and embedded RAM but also MTJ-based VLSI computing. A DMTJ-based two bit memory cell that supports a nonvolatile logic compute paradigm is presented. The multi-level cell supports both a high speed read/write two bit memory cell and a nonvolatile logic gate that computes and stores input data in real-time.

π-Stacked Ion Pairs: Tightly Associated Charged Porphyrins in Ordered Arrangement Enabling Radical-Pair Formation.

π-Electronic ion pairs are of interest for fabricating electronic materials that use intermolecular interactions based on electrostatic and dispersion forces, defined as iπ-iπ interactions, to provide dimension-controlled assemblies. Porphyrin ions, whose charge is delocalized in the core units, are suitable for ordered arrangement and assemblies by ion pairing. Herein, charged porphyrins were found to form solid-state assemblies and solution-state stacked ion pairs according to the peripheral electron-donating groups (EDGs) and electron-withdrawing groups (EWGs). The concentration-dependent 1H NMR signal shifts of a porphyrin ion pair, comprising a meso-EWG cation and a meso-EWG anion, provided a hetero-dimerization constant of 2.8 × 105 M-1 in CD2Cl2 at 20 °C. In the ion pair of a meso-EWG cation and a meso-EDG anion, the electron transfer in the steady and excited states according to solvent polarity and photoexcitation, respectively, produced the radical pairs. The electron spin resonance analysis in frozen toluene revealed the formation of a heterodiradical in a closely stacked structure by the antiferromagnetic dipolar interaction and temperature-dependent spin transfer behavior.

Spin-transfer and spin-orbit torques in the Landau–Lifshitz–Gilbert equation

Dynamic simulations of spin-transfer and spin-orbit torques are increasingly important for a wide range of spintronic devices including magnetic random access memory, spin-torque nano-oscillators and electrical switching of antiferromagnets. Here we present a computationally efficient method for the implementation of spin-transfer and spin-orbit torques within the Landau–Lifshitz–Gilbert equation used in micromagnetic and atomistic simulations. We consolidate and simplify the varying terminology of different kinds of torques into a physical action and physical origin that clearly shows the common action of spin torques while separating their different physical origins. Our formalism introduces the spin torque as an effective magnetic field, greatly simplifying the numerical implementation and aiding the interpretation of results. The strength of the effective spin torque field unifies the action of the spin torque and subsumes the details of experimental effects such as interface resistance and spin Hall angle into a simple transferable number between numerical simulations. We present a series of numerical tests demonstrating the mechanics of generalised spin torques in a range of spintronic devices. This revised approach to modelling spin-torque effects in numerical simulations enables faster simulations and a more direct way of interpreting the results, and thus it is also suitable to be used in direct comparisons with experimental measurements or in a modelling tool that takes experimental values as input.

Skyrmion nucleation on the surface of a topological insulator

Skyrmion nucleation induced by spin-transfer torques at an interface of a topological insulator and a ferromagnetic insulator is investigated. Due to strong spin-orbit coupling on a surface of topological insulators, which enhances the effect of spin torques, efficient manipulation of skyrmions is expected, and therefore, topological insulators could provide the ideal platform to achieve high-performance skyrmionic devices. Using micromagnetic simulations and energetics, we evaluate properties of the skyrmion nucleation on a surface of topological insulators, such as nucleation time, critical electric field, and skyrmion numbers. We show that the nucleation time is inversely proportional to the applied electric field. We also identify the Gilbert damping and temperature dependencies of the critical field. Furthermore, we analytically evaluate the effect of the Dzyaloshinskii-Moriya interaction and demonstrate that the temperature dependence can be explained by the reduction of a magnon excitation gap due to the self-energy corrections.

Sub-volt switching of nanoscale voltage-controlled perpendicular magnetic tunnel junctions

Magnetic random-access memory (MRAM) based on voltage-controlled magnetic anisotropy in magnetic tunnel junctions (MTJs) is a promising candidate for high-performance computing applications, due to its lower power consumption, higher bit density, and the ability to reduce the access transistor size when compared to conventional current-controlled spin-transfer torque MRAM. The key to realizing these advantages is to have a low MTJ switching voltage. Here, we report a perpendicular MTJ structure with a high voltage-controlled magnetic anisotropy coefficient ~130 fJ/Vm and high tunnel magnetoresistance exceeding 150%. Owing to the high voltage-controlled magnetic anisotropy coefficient, we demonstrate sub-nanosecond precessional switching of nanoscale MTJs with diameters of 50 and 70 nm, using a voltage lower than 1 V. We also show scaling of this switching mechanism down to 30 nm MTJs, with voltages close to 2 V. The results pave the path for the future development and application of voltage-controlled MRAMs and spintronic devices in emerging computing systems.

Emerging tunnel FET and spintronics-based hardware-secure circuit design with ultra-low energy consumption

Present complementary metal–oxide–semiconductor (CMOS) technology with scaled channel lengths exhibits higher energy consumption in designing secure electronic circuits against hardware vulnerabilities and breaches. Specifically, CMOS sense amplifier-based secure differential power analysis (DPA) countermeasures at scaled channel lengths show large energy consumption, with increased vulnerability. Additionally, spin-transfer torque magnetic tunnel junction (STT-MTJ) and CMOS-based logic-in-memory (LiM) cells demonstrate high energy consumption due to the large write current requirement of the STT-MTJ and poor MOS device performance at scaled channel lengths. This paper for the first time leverages emerging tunnel field effect transistor (TFET) steep-slope device characteristics and compatible non-volatile STT-MTJ devices for enhanced hardware security with ultra-low energy consumption at lower supply voltages. TFET-based sense amplifier-based logic (SABL) gates are proposed that achieve 3× lower energy consumption than the Si FinFET SABL designs. Further, utilizing TFET SABL gates, a TFET PRIDE S-box is designed that exhibits higher DPA resilience with 3.2× lower energy consumption than the FinFET designs. With the resulting lower static power consumption, TFET SABL-based cryptosystems are thus less vulnerable to static power side-channel attacks. Additionally, the proposed STT-MTJ and TFET LiM gates achieve 4× lower energy consumption than the STT-MTJ and FinFET designs. Lastly, these gates are explored in a logic encryption/locking technique that shows 3.1× lower energy consumption than the STT-MTJ and FinFET-based design.

Hybrid magnonic-oscillator system

We propose a hybrid magnonic-oscillator system based on the combination of a spin transfer auto-oscillator and a magnonic waveguide to open new perspectives for spin-wave based circuits. The system is composed of a spin transfer oscillator based on a vortex state which is dipolarly coupled to a nanoscale spin-wave waveguide with longitudinal magnetization. In its auto-oscillating regime, the oscillator emits coherent spin waves with tunable and controllable frequencies, directions, and amplitudes into the waveguide. We demonstrate the principle of this method using micromagnetic simulations and show that reconfiguration of the system is possible by changing the chirality and polarity of the magnetic vortex. Spin waves are emitted into the waveguide with high non-reciprocity and the preferred direction depends on the core polarity of the vortex. In contrast, different vortex chiralities lead to different amplitudes of the emitted waves. Our findings open up a novel way to design an agile spintronic device for the coherent and tunable generation of propagating spin waves.

Solvent-Induced Degradation of Electrochemically Exfoliated Vanadium Selenide Visualized by Electron Microscopy.

Recently discovered two-dimensional ferromagnetic materials (2DFMs) have rapidly gained much interest in the fields of spintronics and computing, where they may prove powerful tools for miniaturizing devices such as magnetic tunnel junctions and spin-transfer torque memory bits. In addition, heterojunctions and twisted bilayer stacks of such materials may yield exotic spin textures. However, preparation of such devices is complicated by the air sensitivity of many 2DFMs. Here, we report details on the preparation of few-to-monolayer flakes of vanadium selenide (VSe2) using electrochemical exfoliation in propylene carbonate. We also present a detailed study of the effects of air on the structure and magnetic properties of bare and passivated VSe2 after different concentrations of surface passivation treatment. We characterized the microstructure of holes in the VSe2 flakes and the formation of new compounds arising from air exposure, solvent exposure during the exfoliating process, and deliberate electron beam irradiation (sculpting). We sculpt VSe2 flakes while retaining the 1T-VSe2 lattice structure, opening the door for top-down patterned high-resolution 2DFM nanostructures. Additionally, investigation of the magnetic response of nanosheets using magnetic force microscopy (MFM) showed that the oxidation-induced damage only affects the surface fields locally and does not quench large-scale magnetic signal. The findings of this study pave the way toward practical incorporation of 2D ferromagnetic materials in nanoelectronics.

Current-Induced Magnetic Skyrmions with Controllable Polarities in the Helical Phase

We report the current-induced creation of magnetic skyrmions in a chiral magnet FeGe nanostructure by using in situ Lorentz transmission electron microscopy. We show that magnetic skyrmions with controllable polarity can be transferred from the helical ground state simply by controlling the direction of the current flow at zero magnetic fields. The force analysis and symmetry consideration, backed up by micromagnetic simulations, well explain the experimental results, where magnetic skyrmions are created because of the edge instability of the helical state in the presence of spin-transfer torque. The on-demand generation of skyrmions and control of their polarity by electric current without the need for a magnetic field will enable novel purely electric-controlled skyrmion devices.

Unified theory of spin and charge in a ferromagnet

We derive a unified theory of spin and charge degrees of freedom in a ferromagnet. The spin-transfer torque and spin electromotive force are examined from the coarse-grained perspective of collective coordinates. The resulting equations of motion reflect a balance of conservative, gyroscopic (Berry-phase), and dissipative forces. We then expand the space of collective coordinates by adding the electric charge. The adiabatic spin-transfer torque and spin electromotive force (emf) turn out to be a gyroscopic force; their nonadiabatic counterparts are a dissipative force.

High-dose X-ray radiation induced MgO degradation and breakdown in spin transfer torque magnetic tunnel junctions

Magnetic tunnel junction (MTJ) with magnesium oxide (MgO) tunnel barrier is the core element of spin transfer torque-based magnetic random access memory. For the application in the space environment, the total ionizing dose radiation effects on MTJs need to be evaluated. In this work, the MTJs were exposed to X-ray radiation with different doses of up to 10 Mrad(Si). Measurements of current induced magnetization switching (CIMS) behavior of these MTJs were performed before and after radiation. The results show negligible changes in the tunneling magnetoresistance and current switching properties after 8 Mrad(Si) X-ray radiation. However, with a total dose of 9 Mrad(Si), a significant reduction in junction resistance of a fairly large number of MTJs was observed, which showed characteristics of MTJ breakdown. Moreover, in this study, all experimental MTJs became functionally disabled due to MgO breakdown under 10 Mrad(Si) X-ray radiation. The CoFeB/MgO/CoFeB interface microstructure was observed using X-ray photoelectron spectroscopy and high-resolution transmission electron microscopy (HRTEM). Interfacial structural results indicate that the MgO degradation and breakdown behavior caused by X-ray ionizing radiation can give rise to radiation-induced oxygen vacancies across the tunnel barrier oxide layer.

A Universal Compact Model for Spin-Transfer Torque-Driven Magnetization Switching in Magnetic Tunnel Junction

Current-induced magnetization switching through spin-transfer torque (STT) has shown great potential for low-power information storage. However, predicting its mesoscopic behavior induced by both electrical current and thermal fluctuation is a fundamental challenge in spintronics. Moreover, the physical models in different switching regimes have not been properly unified. Here, we propose a novel analytical model to describe the mean magnetization switching time in general terms. By incorporating a nondimensional parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula> in (0,1) to elucidate the relative impact of thermal activation and current, the unified model shows good agreement with the experimental data in all the regimes, including high current regime, thermal activation regime, and the intermediate regime between them. Finally, we develop an electrical model of magnetic tunnel junction (MTJ) device with Verilog-A language and perform transient simulation to demonstrate its functionality with Spectre. The Monte Carlo simulations have also been implemented to confirm their stochastic switching behavior. This model will be greatly beneficial for accurate and efficient designs for spintronic-based integrated circuits.

Process Variation Based Electrical Model of STT-Assisted VCMA-MTJ and Its Application in NV-FA

Fast switching speed, low power consumption, and good stability are some of the important properties of spin transfer torque assisted voltage controlled magnetic anisotropy magnetic tunnel junction (STT-assisted VCMA-MTJ) which makes the non-volatile full adder (NV-FA) based on it attractive for Internet of Things. However, the effects of process variations on the performances of STT-assisted VCMA-MTJ and NV-FA will be more and more obvious with the downscaling of STT-assisted VCMA-MTJ and the improvement of chip integration. In this paper, a more accurate electrical model of STT-assisted VCMA-MTJ is established on the basis of the magnetization dynamics and the process variations in film growth process and etching process. In particular, the write voltage is reduced to 0.7 V as the film thickness is reduced to 0.9 nm. The effects of free layer thickness variation (γtf) and oxide layer thickness variation (γtox) on the state switching as well as the effect of tunnel magnetoresistance ratio variation (β) on the sensing margin (SM) are studied in detail. Considering that the above process variations follow Gaussian distribution, Monte Carlo simulation is used to study the effects of the process variations on the writing and output operations of NV-FA. The result shows that the state of STT-assisted VCMA-MTJ can be switched under -0.3%≤γtf≤6% or -23%≤γtox≤0.2%. SM is reduced by 16.0% with β increases from 0 to 30%. The error rates of writing ‘0’ in the NV-FA can be reduced by increasing Vb1 or increasing positive Vb2. The error rates of writing ‘1’ can be reduced by increasing Vb1 or decreasing negative Vb2. The reduction of the output error rates can be realized effectively by increasing the driving voltage (Vdd).

MFA-MTJ Model: Magnetic-Field-Aware Compact Model of pMTJ for Robust STT-MRAM Design

The popularity of perpendicular magnetic tunnel junction (pMTJ)-based spin-transfer torque magnetic random access memories (STT-MRAMs) is growing very fast. The performance of such memories is very sensitive to magnetic fields, including both internal and external ones. This article presents a magnetic-field-aware compact model of pMTJ, named the MFA-magnetic tunnel junction (MTJ) model, for magnetic/electrical co-simulation of MTJ/CMOS circuits. Magnetic measurement data of MTJ devices, with diameters ranging from 35 to 175 nm, are used to calibrate an in-house magnetic coupling model. This model is subsequently integrated into our developed compact pMTJ model, which is implemented in Verilog-A. The superiority of the proposed MFA-MTJ model for device/circuit co-design of STT-MRAM is demonstrated by simulating a single pMTJ as well as STT-MRAM full circuits. The design space is explored under PVT variations and various configurations of magnetic fields.

Nonequilibrium dynamics in a spin valve with noncollinear magnetization

We utilize a hybrid quantum-classical equation of motion approach to investigate the spin dynamics and spin-transfer torque in a spin valve under bias voltage. We show that the interplay between localized classical magnetic moments and conduction electrons induces a complex effective exchange coupling between the magnetic layers. This leads to a declination of magnetizations from layers anisotropy axes even in equilibrium. Introducing a finite bias voltage triggers spin currents and related spin-transfer torques which further tilt the magnetizations and govern the relaxation processes of the spin dynamics. Analyzing different scenarios of the applied bias voltage, we show that symmetric and asymmetric voltage drops can lead to relaxation times of the spin dynamics that differ by several orders of magnitude at comparable charge currents. In both cases we observe resonant features, where the relaxation is boosted whenever the chemical potential of the leads matches the maxima in the density of the states of the spin-valve electrons.