Quantized Magnetic Domain Wall Synapse for Efficient Deep Neural Networks.

The quantization of synaptic weights using emerging nonvolatile memory (NVM) devices has emerged as a promising solution to implement computationally efficient neural networks on resource constrained hardware. However, the practical implementation of such synaptic weights is hampered by the imperfect memory characteristics, specifically the availability of limited number of quantized states and the presence of large intrinsic device variation and stochasticity involved in writing the synaptic states. This article presents on-chip training and inference of a neural network using quantized magnetic domain wall (DW)-based synaptic array and CMOS peripheral circuits. A rigorous model of the magnetic DW device considering stochasticity and process variations has been utilized for the synapse. To achieve stable quantized weights, DW pinning has been achieved by means of physical constrictions. Finally, VGG8 architecture for CIFAR-10 image classification has been simulated by using the extracted synaptic device characteristics. The performance in terms of accuracy, energy, latency, and area consumption has been evaluated while considering the process variations and nonidealities in the DW device as well as the peripheral circuits. The proposed quantized neural network (QNN) architecture achieves efficient on-chip learning with 92.4% and 90.4% training and inference accuracy, respectively. In comparison to pure CMOS-based design, it demonstrates an overall improvement in area, energy, and latency by 13.8 × , 9.6 × , and 3.5 × , respectively.

Healthy and pathological pallidal regulation of thalamic burst versus tonic mode firing: a computational simulation.

The mechanisms by which the basal ganglia influence the pallidal-receiving thalamus remain to be adequately defined. Our prior in vivo recordings in fully alert normal and dystonic rats revealed that normally fast tonic discharging entopeduncular [EP, rodent equivalent of the globus pallidus internus (GPi)] neurons are pathologically slow, highly irregular, and bursty under dystonic conditions. This, in turn, induces pallidal-receiving thalamic movement-related neurons to change from a healthy burst predominant to a pathological tonic-predominant resting firing mode. This study aims to understand the pallidal influence on thalamic firing modes using computational simulations. We inputted various combinations of healthy and pathological (dystonic) in vivo neuronal recordings to the Rubin and Terman's computational model of low threshold spiking pallidothalamic neurons. The input sets consist of representative tonic, burst, irregular tonic and irregular burst inputs collected from EP/GPi in our animal lab. Initial test combinations of EP/ GPi input to the model were identical to the neuronal population distributions observed in vivo. The thalamic neuron model outputted similar firing rate and mode as observed in corresponding in-vivo thalamus. Further influence of each individual patterns was also delineated. By simulating the firing properties of encountered neurons, the basal ganglia output is suggested to critically act as firing mode selector for thalamic motor relay neurons. By selecting and determining the timing and extent of opening of thalamic T-type calcium channels via GABAergic hyperpolarizing input, GPi neurons are in position to precisely orchestrate thalamocortical burst motor signaling.

Robust skyrmion mediated reversal of ferromagnetic nanodots of 20 nm lateral dimension with high Ms and observable DMI.

Implementation of skyrmion based energy efficient and high-density data storage devices requires aggressive scaling of skyrmion size. Ferrimagnetic materials are considered to be a suitable platform for this purpose due to their low saturation magnetization (i.e. smaller stray field). However, this method of lowering the saturation magnetization and scaling the lateral size of skyrmions is only applicable where the skyrmions have a smaller lateral dimension compared to the hosting film. Here, we show by performing rigorous micromagnetic simulation that the size of skyrmions, which have lateral dimension comparable to their hosting nanodot can be scaled by increasing saturation magnetization. Also, when the lateral dimension of nanodot is reduced and thereby the skyrmion confined in it is downscaled, there remains a challenge in forming a stable skyrmion with experimentally observed Dzyaloshinskii-Moriya interaction (DMI) values since this interaction has to facilitate higher canting  per spin to complete a 360° rotation along the diameter. In our study, we found that skyrmions can be formed in 20 nm lateral dimension nanodots with high saturation magnetization (1.30-1.70 MA/m) and DMI values (~ 3 mJ/m2) that have been reported to date. This result could stimulate experiments on implementation of highly dense skyrmion devices. Additionally, using this, we show that voltage controlled magnetic anisotropy based switching mediated by an intermediate skyrmion state can be achieved in the soft layer of a ferromagnetic p-MTJ of lateral dimensions 20 nm with sub 1 fJ/bit energy in the presence of room temperature thermal noise with reasonable DMI ~ 3 mJ/m2.

A 3-D NanoMagnetoElectrokinetic model for ultra-high precision assembly of ferromagnetic NWs using magnetic-field assisted dielectrophoresis.

This report presents a three-dimensional (3-D) magnetoelectrokinetic model to investigate a new approach to magnetic-field assisted dielectrophoresis for ultra-high precision and parallel assembly of ferromagnetic Ni nanowires (NWs) on silicon chips. The underlying assembly methodology relies on a combination of electric and magnetic fields to manipulate single nanowires from a colloidal suspension and yield their assembly on top of electrodes with better than 25 nm precision. The electric fields and the resultant dielectrophoretic forces are generated through the use of patterned gold nanoelectrodes, and deliver long-range forces that attract NWs from farther regions of the workspace and bring them in proximity to the nanoelectrodes. Next, magnetic-fields generated by cobalt magnets, which are stacked on top of the gold nanoelectrodes at their center and pre-magnetized using external magnetic fields, deliver short range forces to capture the nanowires precisely on top of the nanomagnets. The 3-D NanoMagnetoElectrokinetic model, which is built using a finite element code in COMSOL software and with further computations in MATLAB, computes the trajectory and final deposition location as well as orientation for all possible starting locations of a Ni NW within the assembly workspace. The analysis reveals that magnetic-field assisted dielectrophoresis achieves ultra-high precision assembly of NWs on top of the cobalt nanomagnets from a 42% larger workspace volume as compared to pure dielectrophoresis and thereby, establishes the benefits of adding magnetic fields to the assembly workspace. Furthermore, this approach is combined with a strategy to confine the suspension within the reservoir that contains a high density of favorable NW starting locations to deliver high assembly yields for landing NWs on top of contacts that are only twice as wide as the NWs.

Correction: A 3-D NanoMagnetoElectrokinetic model for ultra-high precision assembly of ferromagnetic NWs using magnetic-field assisted dielectrophoresis.

[This corrects the article DOI: 10.1039/D0RA08381J.].

Voltage control of domain walls in magnetic nanowires for energy-efficient neuromorphic devices.

An energy-efficient voltage-controlled domain wall (DW) device for implementing an artificial neuron and synapse is analyzed using micromagnetic modeling in the presence of room temperature thermal noise. By controlling the DW motion utilizing spin transfer or spin-orbit torques in association with voltage generated strain control of perpendicular magnetic anisotropy in the presence of Dzyaloshinskii-Moriya interaction, different positions of the DW are realized in the free layer of a magnetic tunnel junction to program different synaptic weights. The feasibility of scaling of such devices is assessed in the presence of thermal perturbations that compromise controllability. Additionally, an artificial neuron can be realized by combining this DW device with a CMOS buffer. This provides a possible pathway to realize energy-efficient voltage-controlled nanomagnetic deep neural networks that can learn in real time.

Magneto-elastic switching of magnetostrictive nanomagnets with in-plane anisotropy: the effect of material defects.

We theoretically study the effect of a material defect (material void) on switching errors associated with magneto-elastic switching of magnetization in elliptical magnetostrictive nanomagnets having in-plane magnetic anisotropy. We find that the error probability increases significantly in the presence of the defect, indicating that magneto-elastic switching is particularly vulnerable to material imperfections. Curiously, there is a critical stress value that gives the lowest error probability in both defect-free and defective nanomagnets. The critical stress is much higher in defective nanomagnets than in defect-free ones. Since it is more difficult to generate the critical stress in small nanomagnets than in large nanomagnets (having the same energy barrier for thermal stability), it would be a challenge to downscale magneto-elastically switched nanomagnets in memory and other applications where reliable switching is required. This is likely to be further exacerbated by the presence of defects.

Energy-efficient switching of nanomagnets for computing: straintronics and other methodologies.

The need for increasingly powerful computing hardware has spawned many ideas stipulating, primarily, the replacement of traditional transistors with alternate 'switches' that dissipate miniscule amounts of energy when they switch and provide additional functionality that are beneficial for information processing. An interesting idea that has emerged recently is the notion of using two-phase (piezoelectric/magnetostrictive) multiferroic nanomagnets with bistable (or multi-stable) magnetization states to encode digital information (bits), and switching the magnetization between these states with small voltages (that strain the nanomagnets) to carry out digital information processing. The switching delay is ∼1 ns and the energy dissipated in the switching operation can be few to tens of aJ, which is comparable to, or smaller than, the energy dissipated in switching a modern-day transistor. Unlike a transistor, a nanomagnet is 'non-volatile', so a nanomagnetic processing unit can store the result of a computation locally without refresh cycles, thereby allowing it to double as both logic and memory. These dual-role elements promise new, robust, energy-efficient, high-speed computing and signal processing architectures (usually non-Boolean and often non-von-Neumann) that can be more powerful, architecturally superior (fewer circuit elements needed to implement a given function) and sometimes faster than their traditional transistor-based counterparts. This topical review covers the important advances in computing and information processing with nanomagnets, with emphasis on strain-switched multiferroic nanomagnets acting as non-volatile and energy-efficient switches-a field known as 'straintronics'. It also outlines key challenges in straintronics.

Skyrmion-Mediated Voltage-Controlled Switching of Ferromagnets for Reliable and Energy-Efficient Two-Terminal Memory.

We propose a two-terminal nanomagnetic memory element based on magnetization reversal of a perpendicularly magnetized nanomagnet employing a unipolar voltage pulse that modifies the perpendicular anisotropy of the system. Our work demonstrates that the presence of Dzyaloshinskii-Moriya interaction can create an alternative route for magnetization reversal that obviates the need for utilizing precessional magnetization dynamics as well as a bias magnetic field that are employed in traditional voltage control of magnetic anisotropy (VCMA)-based switching of perpendicular magnetization. We show with extensive micromagnetic simulation, in the presence of thermal noise, that the proposed skyrmion-mediated VCMA switching mechanism is robust at room temperature leading to extremely low error switching while also being potentially 1-2 orders of magnitude more energy efficient than state-of-the-art spin transfer torque-based switching.

Static and dynamic magnetic properties of sputtered Fe-Ga thin films.

We present measurements of the static and dynamic properties of polycrystalline iron-gallium films, ranging from 20 nm to 80 nm and sputtered from an Fe0.8Ga0.2 target. Using a broadband ferromagnetic resonance setup in a wide frequency range, perpendicular standing spin-wave resonances were observed with the external static magnetic field applied in-plane. The field corresponding to the strongest resonance peak at each frequency is used to determine the effective magnetization, the g-factor and the Gilbert damping. Furthermore, the dependence of spin-wave mode on field-position is observed for several frequencies. The analysis of broadband dynamic properties allows determination of the exchange stiffness A = (18 ± 4) pJ/m and Gilbert damping α = 0.042 ± 0.005 for 40 nm and 80 nm thick films. These values are approximately consistent with values seen in epitaxially grown films, indicating the potential for industrial fabrication of magnetostrictive FeGa films for microwave applications.

Energy efficient and fast reversal of a fixed skyrmion two-terminal memory with spin current assisted by voltage controlled magnetic anisotropy.

Recent work (P-H Jang et al 2015 Appl. Phys. Lett. 107 202401, J. Sampaio et al 2016 Appl. Phys. Lett. 108 112403) suggests that ferromagnetic reversal with spin transfer torque (STT) requires more current in a system in the presence of Dzyaloshinskii-Moriya interaction (DMI) than switching a typical ferromagnet of the same dimensions and perpendicular magnetic anisotropy (PMA). However, DMI promotes the stabilization of skyrmions and we report that when perpendicular anisotropy is modulated (reduced) for both the skyrmion and ferromagnet, it takes a much smaller current to reverse the fixed skyrmion than to reverse the ferromagnet in the same amount of time, or the skyrmion reverses much faster than the ferromagnet at similar levels of current. We show with rigorous micromagnetic simulations that skyrmion switching proceeds along a different path at very low PMA, which results in a significant reduction in the spin current or time required for reversal. This can offer potential for memory applications where a relatively simple modification of the standard STT-RAM (to include a heavy metal adjacent to the soft magnetic layer and with appropriate design of the tunnel barrier) can lead to an energy efficient and fast magnetic memory device based on the reversal of fixed skyrmions.

Experimental Demonstration of Complete 180° Reversal of Magnetization in Isolated Co Nanomagnets on a PMN-PT Substrate with Voltage Generated Strain.

Rotating the magnetization of a shape anisotropic magnetostrictive nanomagnet with voltage-generated stress/strain dissipates much less energy than most other magnetization rotation schemes, but its application to writing bits in nonvolatile magnetic memory has been hindered by the fundamental inability of stress/strain to rotate magnetization by full 180°. Normally, stress/strain can rotate the magnetization of a shape anisotropic elliptical nanomagnet by only up to 90°, resulting in incomplete magnetization reversal. Recently, we predicted that applying uniaxial stress sequentially along two different axes that are not collinear with the major or minor axis of the elliptical nanomagnet will rotate the magnetization by full 180°. Here, we demonstrate this complete 180° rotation in elliptical Co nanomagnets (fabricated on a piezoelectric substrate) at room temperature. The two stresses are generated by sequentially applying voltages to two pairs of shorted electrodes placed on the substrate such that the line joining the centers of the electrodes in one pair intersects the major axis of a nanomagnet at ∼ +30° and the line joining the centers of the electrodes in the other pair intersects at ∼ -30°. A finite element analysis has been performed to determine the stress distribution underneath the nanomagnets when one or both pairs of electrodes are activated, and this has been approximately incorporated into a micromagnetic simulation of magnetization dynamics to confirm that the generated stress can produce the observed magnetization rotations. This result portends an extremely energy-efficient nonvolatile "straintronic" memory technology predicated on writing bits in nanomagnets with electrically generated stress.

Incoherent magnetization dynamics in strain mediated switching of magnetostrictive nanomagnets.

Micromagnetic studies of the magnetization change in magnetostrictive nanomagnets subjected to stress are performed for nanomagnets of different sizes. The interplay between demagnetization, exchange and stress anisotropy energies is used to explain the rich physics of size-dependent magnetization dynamics induced by modulating stress anisotropy in planar nanomagnets. These studies have important implications for strain mediated ultralow energy magnetization control in nanomagnets and its application in energy-efficient nanomagnetic computing devices.

Magnetic behavior of superatomic-fullerene assemblies.

It has recently been possible to synthesize ordered assemblies composed of magnetic superatomic clusters Ni9Te6(PEt3)8 separated by C60 and study their magnetic behavior. We have carried out theoretical studies on model systems consisting of magnetic superatoms separated by non-magnetic species to examine the evolution in magnetic response as the nature of the magnetic superatom (directions of spin quantization), the strength of isotropic and anisotropic interactions, the magnetic anisotropy energy, and the size of the assembly are varied. We have examined square planar configurations consisting of 16, 24 and 48 sites with 8, 12 and 24 magnetic superatoms respectively. The magnetic atoms are allowed 2 or 5 orientations. The model Hamiltonian includes isotropic exchange interactions with second nearest neighbor ferromagnetic and nearest neighbor antiferromagnetic couplings and anisotropic Dzyaloshinskii-Moriya interactions. It is shown that the inclusion of Dzyaloshinskii-Moriya interaction that cause spin canting is necessary to get qualitative response as observed in experiments.

Acoustic-Wave-Induced Magnetization Switching of Magnetostrictive Nanomagnets from Single-Domain to Nonvolatile Vortex States.

We report experimental manipulation of the magnetic states of elliptical cobalt magnetostrictive nanomagnets (with nominal dimensions of ∼340 nm × 270 nm × 12 nm) delineated on bulk 128° Y-cut lithium niobate with acoustic waves (AWs) launched from interdigitated electrodes. Isolated nanomagnets (no dipole interaction with any other nanomagnet) that are initially magnetized with a magnetic field to a single-domain state with the magnetization aligned along the major axis of the ellipse are driven into a vortex state by acoustic waves that modulate the stress anisotropy of these nanomagnets. The nanomagnets remain in the vortex state until they are reset by a strong magnetic field to the initial single-domain state, making the vortex state nonvolatile. This phenomenon is modeled and explained using a micromagnetic framework and could lead to the development of extremely energy efficient magnetization switching methodologies for low-power computing applications.

Voltage controlled core reversal of fixed magnetic skyrmions without a magnetic field.

Using micromagnetic simulations we demonstrate core reversal of a fixed magnetic skyrmion by modulating the perpendicular magnetic anisotropy of a nanomagnet with an electric field. We can switch reversibly between two skyrmion states and two ferromagnetic states, i.e. skyrmion states with the magnetization of the core pointing down/up and periphery pointing up/down, and ferromagnetic states with magnetization pointing up/down, by sequential increase and decrease of the perpendicular magnetic anisotropy. The switching between these states is explained by the fact that the spin texture corresponding to each of these stable states minimizes the sum of the magnetic anisotropy, demagnetization, Dzyaloshinskii-Moriya interaction (DMI) and exchange energies. This could lead to the possibility of energy efficient nanomagnetic memory and logic devices implemented with fixed skyrmions without using a magnetic field and without moving skyrmions with a current.

Experimental Clocking of Nanomagnets with Strain for Ultralow Power Boolean Logic.

Nanomagnetic implementations of Boolean logic have attracted attention because of their nonvolatility and the potential for unprecedented overall energy-efficiency. Unfortunately, the large dissipative losses that occur when nanomagnets are switched with a magnetic field or spin-transfer-torque severely compromise the energy-efficiency. Recently, there have been experimental reports of utilizing the Spin Hall effect for switching magnets, and theoretical proposals for strain induced switching of single-domain magnetostrictive nanomagnets, that might reduce the dissipative losses significantly. Here, we experimentally demonstrate, for the first time that strain-induced switching of single-domain magnetostrictive nanomagnets of lateral dimensions ∼200 nm fabricated on a piezoelectric substrate can implement a nanomagnetic Boolean NOT gate and steer bit information unidirectionally in dipole-coupled nanomagnet chains. On the basis of the experimental results with bulk PMN-PT substrates, we estimate that the energy dissipation for logic operations in a reasonably scaled system using thin films will be a mere ∼1 aJ/bit.

Reversible strain-induced magnetization switching in FeGa nanomagnets: Pathway to a rewritable, non-volatile, non-toggle, extremely low energy straintronic memory.

We report reversible strain-induced magnetization switching between two stable/metastable states in ~300 nm sized FeGa nanomagnets delineated on a piezoelectric PMN-PT substrate. Voltage of one polarity applied across the substrate generates compressive strain in a nanomagnet and switches its magnetization to one state, while voltage of the opposite polarity generates tensile strain and switches the magnetization back to the original state. The two states can encode the two binary bits, and, using the right voltage polarity, one can write either bit deterministically. This portends an ultra-energy-efficient non-volatile "non-toggle" memory.

Electric field control of magnetic states in isolated and dipole-coupled FeGa nanomagnets delineated on a PMN-PT substrate.

We report observation of a 'non-volatile' converse magneto-electric effect in elliptical FeGa nanomagnets delineated on a piezoelectric PMN-PT substrate. The nanomagnets are first magnetized with a magnetic field directed along their nominal major axes. Subsequent application of a strong electric field across the piezoelectric substrate generates strain in the substrate, which is partially transferred to the nanomagnets and rotates the magnetizations of some of them away from their initial orientations. The rotated magnetizations remain in their new orientations after the field is removed, resulting in 'non-volatility'. In isolated nanomagnets, the magnetization rotates by <90° upon application of the electric field, but in a dipole-coupled pair consisting of one 'hard' and one 'soft' nanomagnet, which are both initially magnetized in the same direction by the magnetic field, the soft nanomagnet's magnetization rotates by [Formula: see text] upon application of the electric field because of the dipole influence of the hard nanomagnet. This effect can be utilized for a nanomagnetic NOT logic gate.