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Multistate memory systems have the ability to store and process more data in the same physical space as binary memory systems, making them a potential alternative to existing binary memory systems. In the past, it has been demonstrated that voltage-controlled magnetic anisotropy (VCMA) based writing is highly energy-efficient compared to other writing methods used in non-volatile nano-magnetic binary memory systems. In this study, we introduce a new, VCMA-based and skyrmion-mediated non-volatile ternary memory system using a perpendicular magnetic tunnel junction (p-MTJ) in the presence of room temperature thermal perturbation. We have also shown that ternary states {-1, 0, +1} can be implemented with three magnetoresistance values obtained from a p-MTJ corresponding to ferromagnetic up, down, and skyrmion state, with 99% switching probability in the presence of room temperature thermal noise in an energy-efficient way, requiring ~3 fJ energy on an average for each switching operation. Additionally, we show that our proposed ternary memory demonstrates an improvement in area and energy by at least 2X and ~60X respectively, compared to state-of-the-art spin-transfer torque (STT)-based non-volatile magnetic multistate memories. Furthermore, these three states can be potentially utilized for energy-efficient, high-density in-memory quantized deep neural network implementation.

The development of energy-efficient neuromorphic hardware using spintronic devices based on antiferromagnetic (AFM) skyrmion motion on nanotracks has gained considerable interest. Owing to its properties such as robustness against external magnetic fields, negligible stray fields, and zero net topological charge, AFM skyrmions follow straight trajectories that prevent their annihilation at nanoscale racetrack edges. This makes the AFM skyrmions a more favorable candidate over the ferromagnetic (FM) skyrmion for future spintronic applications. This work proposes an AFM skyrmion-based neuron device exhibiting the leaky-integrate-fire (LIF) functionality by exploiting thermal gradient or alternatively perpendicular magnetic anisotropy (PMA) gradient in the nanotrack for leaky behavior by moving the skyrmion in the direction to minimize the system energy. Furthermore, it is shown that the AFM skyrmion couples efficiently to the soft ferromagnetic layer of a magnetic tunnel junction enabling efficient read-out of the skyrmion. The maximum change of 9.2% in tunnel magnetoresistance (TMR) is estimated for detecting the AFM skyrmion. Moreover, the proposed neuron device has the energy dissipation of 4.32 fJ per LIF operation thus, paving the path for developing energy-efficient devices in antiferromagnetic spintronics for neuromorphic computing.

Reservoir computing (RC) has received recent interest because reservoir weights do not need to be trained, enabling extremely low-resource consumption implementations, which could have a transformative impact on edge computing and in-situ learning where resources are severely constrained. Ideally, a natural hardware reservoir should be passive, minimal, expressive, and feasible; to date, proposed hardware reservoirs have had difficulty meeting all of these criteria. We therefore propose a reservoir that meets all of these criteria by leveraging the passive interactions of dipole-coupled, frustrated nanomagnets. The frustration significantly increases the number of stable reservoir states, enriching reservoir dynamics, and as such these frustrated nanomagnets fulfill all of the criteria for a natural hardware reservoir. We likewise propose a complete frustrated nanomagnet reservoir computing (NMRC) system with low-power complementary metal-oxide semiconductor (CMOS) circuitry to interface with the reservoir, and initial experimental results demonstrate the reservoir's feasibility. The reservoir is verified with micromagnetic simulations on three separate tasks demonstrating expressivity. The proposed system is compared with a CMOS echo-state-network (ESN), demonstrating an overall resource decrease by a factor of over 10,000,000, demonstrating that because NMRC is naturally passive and minimal it has the potential to be extremely resource efficient.

We present a systematic numerical modeling investigation of magnetization dynamics and thermal magnetic moment fluctuations of single magnetic domain nanoparticles in a configuration applicable to enhancing inductive magnetic resonance detection signal to noise ratio (SNR). Previous proposals for oriented anisotropic single magnetic domain nanoparticle amplification of magnetic flux in MRI coil focused only on the coil pick-up voltage signal enhancement. Here we extend the analysis to the numerical evaluation of the SNR by modeling the inherent thermal magnetic noise introduced into the detection coil by the insertion of such anisotropic nanoparticle-filled coil core. We utilize the Landau-Lifshitz-Gilbert equation under the Stoner-Wohlfarth single magnetic domain (macrospin) assumption to simulate the magnetization dynamics in such nanoparticles due to AC drive field as well as thermal noise. These simulations are used to evaluate the nanoparticle configurations and shape effects on enhancing SNR. Finally, we explore the effect of narrow band filtering of the broadband magnetic moment thermal fluctuation noise on the SNR. Our results provide the impetus for relatively simple modifications to existing MRI systems for achieving enhanced detection SNR in scanners with modest polarizing magnetic fields.

One method of creating and annihilating skyrmions in confined geometries is to use Voltage-Controlled Magnetic Anisotropy (VCMA) [1, 2, 3]. Previous study shows that robust voltage controlled ferromagnetic reversal from up to down state in the soft layer of a perpendicular Magnetic Tunnel Junction (p-MTJ) can be achieved by creating and subsequently annihilating an intermediate skyrmion state [4] in the presence of room temperature thermal noise and anisotropy variation across grains [4]. However, when scaling to 20 nm, thermal noise can annihilate the skyrmions, for example, by randomly moving the core towards the boundary of the nanostructure. In this work, we study three p-MTJs of different dimensions, particularly lateral dimensions of 100nm, 50nm and 20 nm and investigate the change in switching behavior as the dimension is decreased. Particularly, our focus is to investigate to what extent skyrmion mediated switching scheme can be employed below ~50nm lateral dimensions in the presence of thermal perturbation.

We have investigated Surface Acoustic Wave (SAW) induced ferromagnetic resonance (FMR) assisted Spin Transfer Torque (STT) switching of perpendicular MTJ (p-MTJ) with inhomogeneities using micromagnetic simulations that include the effect of thermal noise. With suitable frequency excitation, the SAW can induce ferromagnetic resonance in magnetostrictive materials, and the magnetization can precesses in a cone with high deflection from the perpendicular direction. With incorporation of inhomogeneity via lateral anisotropy variation as well as room temperature thermal noise, the magnetization precession in different gains can be significantly incoherent. Interestingly, the precession in different grains are found to be in phase, even though the precession amplitude (angle of deflection from the perpendicular direction) vary across grains of different anisotropy. Nevertheless, the high mean deflection angle can complement the STT switching by reducing the STT current significantly; even though the applied stress induced change in anisotropy is much lower than the total anisotropy barrier. This work indicates that SAW assisted switching can improve energy efficiency while being scalable to very small dimensions, which is technologically important for STT-RAM and elucidates the physical mechanism for the potential robustness of this paradigm in realistic scenarios with thermal noise and material inhomogeneity

In this work, we utilize voltage controlled magnetic anisotropy (VCMA) to manipulate magnetic skyrmions that are fixed in space. Memory devices based on this strategy can potentially be of smaller footprint and better energy efficiency than current-controlled motion-based skyrmionic devices. To demonstrate VCMA induced manipulation of skyrmions, we fabricate antiferromagnet/ferromagnet/oxide heterostructure films where skyrmions can be stabilized without any external magnetic field due to the presence of exchange bias. These isolated skyrmions were annihilated by applying a voltage pulse that increased PMA. On the other hand, decreasing PMA promoted formation of more skyrmions. Furthermore, skyrmions can be created from chiral domains by increasing PMA of the system. To corroborate our experimental observations, we performed micromagnetic simulation. The proposed method could potentially lead to novel skyrmion-based memory devices.

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.

We studied the depth dependent magnetization profile of the magnetostrictive Co thin film layer in a PMN-PT (011)/Ta/Co/Ta structure under both zero and nonzero applied electric field using polarized neutron reflectometry. Application of electric field across the PMN-PT substrate generates a strain, which rotates the magnetization of the Co layer consistent with the Villari effect. At low magnetic fields (near remanence and coercive field conditions), we find that the depth dependent magnetization profile is non-uniform, under both zero and nonzero applied electric fields. These variations are attributable to the depth dependent strain profile in the Co film, as determined by finite element analysis simulations.

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 (DMI) can create 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 (STT) based switching.

Recent work [1,2] suggests that ferromagnetic reversal with spin transfer torque (STT) requires more current in a system in the presence of DMI than switching a typical ferromagnet of the same dimensions and perpendicular magnetic anisotropy (PMA). However, DMI promotes stabilization of skyrmions and we report that when the perpendicular anisotropy is modulated (reduced) for both the skyrmion and ferromagnet, it takes much smaller current to reverse the fixed skyrmion than to reverse the ferromagnet in the same time, or the skyrmion reverses much faster than the ferromagnet at similar levels of current. We show with rigorous micromagnetic simulations and energy portraits that the skyrmion switching proceeds along a different path at very low PMA which results in a significant reduction in the spin current required or time required for reversal. This can have potential for memory application 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 energy efficient and fast magnetic memory device based on the reversal of fixed skyrmions.

We report manipulation of the magnetic states of elliptical cobalt magnetostrictive nanomagnets (of nominal dimensions ~ 340 nm x 270 nm x 12 nm) delineated on bulk 128{\deg} Y-cut lithium niobate with Surface Acoustic Waves (SAWs) launched from interdigitated electrodes. Isolated nanomagnets that are initially magnetized to a single domain state with magnetization pointing along the major axis of the ellipse are driven into a vortex state by surface 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 non-volatile. This phenomenon is modeled and explained using a micromagnetic framework and could lead to the development of extremely energy efficient magnetization switching methodologies.

An energy based stochastic model for temperature dependent anhysteretic magnetization curves of ferromagnetic materials is proposed and bench marked against experimental data. This is based on the calculation of macroscopic magnetic properties by performing an energy weighted average over all possible orientations of the magnetization vector. Most prior approaches that employ this method are unable to independently account for the effect of both inhomogeneity and temperature in performing the averaging necessary to model experimental data. Here we propose a way to account for both effects simultaneously and benchmark the model against experimental data from ~5K to ~300K for two different materials in both annealed (fewer inhomogeneities) and deformed (more inhomogeneities) samples. This demonstrates that the independent accounting for the effect of both inhomogeneity and temperature is necessary to correctly model temperature dependent magnetization behavior., 5 pages

We propose a reconfigurable bit comparator implemented with a nanowire spin valve whose two contacts are magnetostrictive with bistable magnetization. Reference and input bits are "written" into the magnetization states of the two contacts with electrically generated strain and the spin-valve's resistance is lowered if they match. Multiple comparators can be interfaced in parallel with a magneto-tunneling junction to determine if an N-bit input stream matches an N-bit reference stream bit by bit. The system is robust against thermal noise at room temperature and a 16-bit comparator can operate at roughly 416 MHz while dissipating at most 420 aJ per cycle., Submitted to Applied Physics Letters. Version 1 ignored the energy dissipation in the passive resistors since they were very high. However, high resistances increase the RC time constant associated with charging. In version 2, the RC time constant has been reduced at the expense of increased energy dissipation, but the latter is still very small in absolute terms

This is a reply to a comment on our work recently posted in arXiv. To our knowledge, this comment has not been published anywhere else. We show that the points raised in the comment are invalid

Reversible straintronic switching of a nanomagnet's magnetization between two stable or metastable states promises ultra-energy-efficient non-volatile memory. Here, we report strain-induced magnetization switching 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, resulting in "non-toggle" switching. The two states can encode the two binary bits, and, using the right voltage polarity, one can write either bit deterministically.

This is a comment on two recent arXiv postings., Comment: This posting was a response to two earlier postings (by the same author) containing personal attacks on us. Since those two offending postings have been administratively removed by arXiv because of unprofessional personal attacks, our response has become superfluous and is hence being withdrawn

A long-standing goal of computer technology is to process and store digital information with the same device in order to implement new architectures. One way to accomplish this is to use nanomagnetic `non-volatile' logic gates that can perform Boolean operations and then store the output data in the magnetization states of nanomagnets, thereby doubling as both logic and memory. Unfortunately, many proposed nanomagnetic gates do not possess the seven essential characteristics of a Boolean logic gate: concatenability, non-linearity, isolation between input and output, gain, universal logic implementation, scalability and error resilience. More importantly, their energy-delay products and error-rates vastly exceed that of conventional transistor-based logic gates, which is a drawback. Here, we propose a non-volatile voltage-controlled nanomagnetic logic gate that possesses all the necessary characteristics of a logic gate and whose energy-delay product is ~2 orders of magnitude less than that of other nano-magnetic (non-volatile) logic gates and ~1 order of magnitude less than that of (volatile) CMOS-based logic gates. The error-resilience is also superior to that of other known nanomagnetic gates., There were some typographical errors in version 2 which have been corrected

Dipole-coupled nanomagnetic logic (NML), where nanomagnets with bistable magnetization states act as binary switches and information is transferred between them via dipole coupling and Bennett clocking, is a potential replacement for conventional transistor logic since magnets dissipate less energy than transistors when they switch in response to the clock. However, dipole-coupled NML is much more error-prone than transistor logic because thermal noise can easily disrupt magnetization dynamics. Here, we study a particularly energy-efficient version of dipole-coupled NML known as straintronic multiferroic logic (SML) where magnets are clocked/switched with electrically generated mechanical strain. By appropriately shaping the voltage pulse that generates strain, the error rate in SML can be reduced to tolerable limits. In this paper, we describe the error probabilities associated with various stress pulse shapes and discuss the trade-off between error rate and switching speed in SML.

Rotating the magnetization of a magnetostrictive nanomagnet with electrically generated mechanical strain dissipates miniscule amount of energy compared to any other rotation method and would have been the ideal method to write bits in nonvolatile magnetic memory, except strain cannot ordinarily rotate the magnetization of magnet by more than 90 degrees and "flip" it. Here, we describe a scheme to achieve complete 180 degree rotation of the magnetization of a nanomagnet with strain that will enable writing of binary bits in non-volatile magnetic memory implemented with magneto-tunneling junctions whose soft layers are two-phase magnetostrictive/piezoelectric multiferroics. At room temperature, this writing method results in: (1) energy dissipation < 6200 kT per bit, (2) write error probability < 10^-6, (3) write time of ~ 1 ns, and (4) low read error. This could potentially lead to a new genre of non-volatile memory that is extremely reliable, fast and, at the same time, ultra-energy-efficient.

Strain-clocked dipole-coupled nanomagnetic logic is an energy-efficient Boolean logic paradigm whose progress has been stymied by its propensity for high error rates. In an effort to mitigate this problem, we have studied the effect of nanomagnet geometry on error rates, focusing on elliptical and cylindrical geometries. We had previously reported that the out-of-plane excursion of the magnetization vector during switching creates a precessional torque that is responsible for high switching error probability in elliptical nanomagnet geometries. The absence of this torque in cylindrical magnets portends lower error rates, but our simulations show that the error rate actually does not improve significantly compared to elliptical magnets while the switching becomes unacceptably slow. Here, we show that dipole coupled nanomagnetic logic can offer relatively high reliability (switching error probability < 10^-8), moderate clock speed (~ 100 MHz) and 2-3 orders of magnitude energy saving compared to CMOS devices, provided the shape anisotropy energy barrier of the magnet is increased to at least ~5.5 eV to allow engineering a stronger dipole coupling between neighboring nanomagnets., 8 pages

A common ploy to reduce the switching current and energy dissipation in spin-transfer-torque driven magnetization switching of shape-anisotropic single-domain nanomagnets is to employ magnets with low saturation magnetization $M_s$ and high shape-anisotropy. The high shape-anisotropy compensates for low $M_s$ to keep the static switching error rate constant. However, this ploy increases the switching delay, its variance in the presence of thermal noise, and the dynamic switching error rate. Using the stochastic Landau-Lifshitz-Gilbert equation with a random torque emulating thermal noise, we show that pumping some excess spin-polarized current into the nanomagnet during switching will keep the mean switching delay and its variance constant as we reduce $M_s$, while still reducing the energy dissipation significantly.

Nanomagnets with biaxial magnetocrystalline anisotropy have four stable magnetization orientations that can encode 4-state logic bits (00), (01), (11) and (10). Recently, a 4-state NOR gate derived from three such nanomagnets, interacting via dipole interaction, was proposed. Here, we devise a Bennett clocking scheme to propagate 4-state logic bits unidirectionally between such gates. The nanomagnets are assumed to be made of 2-phase strain-coupled magnetostrictive/piezoelectric multiferroic elements, such as nickel and lead zirconate titanate (PZT). A small voltage of 200 mV applied across the piezoelectric layer can generate enough mechanical stress in the magnetostrictive layer to rotate its magnetization away from one of the four stable orientations and implement Bennett clocking. We show that a particular sequence of positive and negative voltages will propagate 4-state logic bits unidirectionally down a chain of such multiferroic nanomagnets for logic flow., Comment: Manuscript submitted for publication in IEEE Transactions on Nanotechnology

In magnetic memory and logic devices, a magnet's magnetization is usually flipped with a spin polarized current delivering a spin transfer torque (STT). This mode of switching consumes too much energy and considerable energy saving can accrue from using a multiferroic nanomagnet switched with a combination of STT and mechanical stress generated with a voltage (VGS). The VGS mode consumes less energy than STT, but cannot rotate magnetization by more than 90?, so that a combination of the two modes is needed for energy-efficient switching., There is supplementary material accompanying this paper