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We show that a surface acoustic wave (SAW) applied across the terminals of a magnetic tunnel junction (MTJ) decreases both the (time-averaged) parallel and antiparallel resistances of the MTJ, with the latter decreasing much more than the former. This results in a decrease in the tunneling magnetoresistance ratio. The coercivities of the free and fixed layers of the MTJ, however, are not affected significantly, suggesting that the SAW does not cause large-angle magnetization rotation in the magnetic layers through the inverse magnetostriction (Villari) effect at the power levels used. This study sheds light on the dynamical behavior of an MTJ under periodic compressive and tensile strain. [ABSTRACT FROM AUTHOR]

This study presents 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 a magnetic resonance imaging (MRI) coil focused only on the coil pick-up voltage signal enhancement. In this study, the numerical evaluation of the SNR has been extended by modeling the inherent thermal magnetic noise introduced into the detection coil by the insertion of such anisotropic nanoparticle-filled coil core. The Landau–Lifshitz–Gilbert equation under the Stoner–Wohlfarth single magnetic domain (macrospin) assumption was utilized to simulate the magnetization dynamics 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. It was observed that for a particular shape of a single nanoparticle, the SNR could be increased up to ∼8 and the choice of an appropriate number of the nanoparticles increases the SNR by several orders of magnitude and could consequently lead to the detectability of a very small field of ∼10 pT. These results could provide an impetus for relatively simple modifications to existing MRI systems for achieving enhanced detection SNR in scanners with modest polarizing magnetic fields. [ABSTRACT FROM AUTHOR]

In the brain, the membrane potential of many neurons oscillates in a subthreshold damped fashion and fire when excited by an input frequency that nearly equals their eigen frequency. In this work, we investigate theoretically the artificial implementation of such "resonate-and-fire" neurons by utilizing the magnetization dynamics of a fixed magnetic skyrmion in the free layer of a magnetic tunnel junction (MTJ). To realize firing of this nanomagnetic implementation of an artificial neuron, we propose to employ voltage control of magnetic anisotropy or voltage generated strain as an input (spike or sinusoidal) signal, which modulates the perpendicular magnetic anisotropy. This results in continual expansion and shrinking (i.e., breathing) of a skyrmion core that mimics the subthreshold oscillation. Any subsequent input pulse having an interval close to the breathing period or a sinusoidal input close to the eigen frequency drives the magnetization dynamics of the fixed skyrmion in a resonant manner. The time varying electrical resistance of the MTJ layer due to this resonant oscillation of the skyrmion core is used to drive a Complementary Metal Oxide Semiconductor buffer circuit, which produces spike outputs. By rigorous micromagnetic simulation, we investigate the interspike timing dependence and response to different excitatory and inhibitory incoming input pulses. Finally, we show that such resonate and fire neurons have potential application in coupled nanomagnetic oscillator based associative memory arrays. [ABSTRACT FROM AUTHOR]

This paper presents numerical and experimental data for dipole-dipole coupled Ni nanodots on a piezoelectric [Pb(Mg1/3Nb2/3)O3]0.68[PbTiO3]0.32 substrate. Simulation results show that the dipole coupling produces artificial ferromagnetic (parallel magnetization alignment in the nanodot arrays) behavior that can be modified to artificial antiferromagnetic behavior with an applied voltage. Experimental results show the trends in Mr and Hc predicted by the model, but discrepancies arise due to geometric defects present in the fabricated samples. Geometric defects are introduced into the Ni nanodot models, thus dramatically improving the correlation between experiments and analysis. This work shows, through numerical simulations, that artificial multiferroic nanostructures can be designed to produce switching from parallel (artificial ferromagnetic) to antiparallel (artificial antiferromagnetic) magnetization ordering by leveraging dipole coupling with voltage induced changes in magnetic anisotropy. [ABSTRACT FROM AUTHOR]

The desire to perform information processing, computation, communication, signal generation, and related tasks, while dissipating as little energy as possible, has inspired many ideas and paradigms. One of the most powerful among them is the notion of using magnetostrictive nanomagnets as the primitive units of the hardware platforms and manipulating their magnetizations (which are the state variables encoding information) with electrically generated static or time-varying mechanical strain to elicit myriad functionalities. This approach has two advantages. First, information can be retained in the devices after powering off since the nanomagnets are nonvolatile unlike charge-based devices, such as transistors. Second, the energy expended to perform a given task is exceptionally low since it takes very little energy to alter magnetization states with strain. This field is now known as "straintronics," in analogy with electronics, spintronics, valleytronics, etc., although it pertains specifically to "magnetic" straintronics and excludes phenomena involving non-magnetic systems. We review the recent advances and trends in straintronics, including digital information processing (logic), information storage (memory), domain wall devices operated with strain, control of skyrmions with strain, non-Boolean computing and machine learning with straintronics, signal generation (microwave sources) and communication (ultra-miniaturized acoustic and electromagnetic antennas) implemented with strained nanomagnets, hybrid straintronics–magnonics, and interaction between phonons and magnons in straintronic systems. We identify key challenges and opportunities, and lay out pathways to advance this field to the point where it might become a mainstream technology for energy-efficient systems. [ABSTRACT FROM AUTHOR]

One method of creating and annihilating skyrmions in confined geometries is to use voltage-controlled magnetic anisotropy (VCMA). The 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 in the presence of room temperature thermal noise and anisotropy variation across grains. However, when scaling to 20 nm, thermal noise can annihilate the skyrmions, for example, by randomly moving the core toward the boundary of the nanostructure. In this work, we study three p-MTJs of different dimensions, specifically lateral dimensions of 100, 50, and 20 nm and investigate the change in switching behavior as the dimension is decreased. In particular, we show that while skyrmion-mediated switching of ferromagnets in the presence of thermal perturbation is feasible down to lateral dimensions ~20 nm, the large values of VCMA and Dzyaloshinskii–Moriya interaction (DMI) needed at ~20 nm lateral dimensions have only been theoretically predicted and are yet to be experimentally demonstrated to date. [ABSTRACT FROM AUTHOR]

This paper presents a ternary content-addressable memory (TCAM) cell based on a skewed straintronic magnetotunneling junction (MTJ) switch. A straintronic magnetotunneling junction (s-MTJ) is a three-terminal switch, where the resistance between two of the terminals switches when a potential is applied to the third (gate) terminal that induces strain in the magnetostrictive free-layer. An s-MTJ is a highly energy-efficient switch that would dissipate only ~aJ of energy during switching. This paper discusses a novel variant of s-MTJ, namely skewed s-MTJ (ss-MTJ), where the MTJ switching can be controlled by two gate terminals. The current through an ss-MTJ is minimum when the potentials at the first and second gate terminals ( V2 and V3 , respectively) obey the relation V3 = V2+VF . Here, VF is a fixed voltage (“offset voltage”). Current in an ss-MTJ increases steeply when V2 and V3 deviate from the above “match” condition. This unconventional I – V characteristic of an ss-MTJ is exploited to design a non-Boolean TCAM cell based on just one transistor, one trench capacitor, and one ss-MTJ. We also discuss search and write operations in the ss-MTJ-TCAM cell, and show that the cell requires very small voltages to operate because of the unique I – V characteristics of the ss-MTJ. [ABSTRACT FROM PUBLISHER]

Hardware-based image processing offers speed and convenience not found in software-centric approaches. Here, we show theoretically that a 2-D periodic array of dipole-coupled elliptical nanomagnets, delineated on a piezoelectric substrate, can act as a dynamical system for specific image processing functions. Each nanomagnet has two stable magnetization states that encode pixel color (black or white). An image containing black and white pixels is first converted to voltage states and then mapped into the magnetization states of a nanomagnet array with magneto-tunneling junctions (MTJs). The same MTJs are employed to read out the processed pixel colors later. Dipole interaction between the nanomagnets implements specific image processing tasks, such as noise reduction and edge enhancement detection. These functions are triggered by applying a global strain to the nanomagnets with a voltage dropped across the piezoelectric substrate. An image containing an arbitrary number of black and white pixels can be processed in few nanoseconds with very low energy cost. [ABSTRACT FROM AUTHOR]

An energy based model for temperature dependent anhysteretic magnetization curves of ferromagnetic materials is proposed and benchmarked 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 ~5 K to ~300 K for two different materials in both annealed (fewer inhomogeneities) and deformed (more inhomogeneities) samples. This demonstrates that this framework is well suited to simulate temperature dependent experimental magnetic behavior. [ABSTRACT FROM AUTHOR]

Dipole-coupled cobalt nanomagnet pairs of elliptical shape (with their major axes parallel) are delineated on 128° Y-cut lithium niobate. Each pair is initially magnetized along the major axis with a magnetic field forming the (↑↑) state. When an acoustic wave (AW) is launched in the substrate from interdigitated electrodes, the softer nanomagnet in the pair flips to produce the (↑↓) state since the AW modulates the stress anisotropy. This executes the logical NOT operation because the output bit encoded in the magnetization state of the softer nanomagnet becomes the logic complement of the input bit encoded in the magnetization of the harder one. The AW acts as a clock to trigger the NOT operation and the energy dissipated is a few tens of aJ. Such AW clocking can be utilized to flip nanomagnets in a chain sequentially to steer logic bits unidirectionally along a nanomagnetic logic wire with miniscule energy dissipation. [ABSTRACT FROM AUTHOR]

Voltage control of magnetization via strain in piezoelectric/magnetostrictive systems is a promising mechanism to implement energy-efficient straintronic memory devices. Here, we demonstrate giant voltage manipulation of MgO magnetic tunnel junctions (MTJ) on a Pb(Mg1/3Nb2/3)0.7Ti0.3O3 piezoelectric substrate with (001) orientation. It is found that the magnetic easy axis, switching field, and the tunnel magnetoresistance (TMR) of the MTJ can be efficiently controlled by strain from the underlying piezoelectric layer upon the application of a gate voltage. Repeatable voltage controlled MTJ toggling between high/low-resistance states is demonstrated. More importantly, instead of relying on the intrinsic anisotropy of the piezoelectric substrate to generate the required strain, we utilize anisotropic strain produced using a local gating scheme, which is scalable and amenable to practical memory applications. Additionally, the adoption of crystalline MgO-based MTJ on piezoelectric layer lends itself to high TMR in the strain-mediated MRAM devices. [ABSTRACT FROM AUTHOR]

Modulation of stress anisotropy of magnetostrictive nanomagnets with strain offers an extremely energy-efficient method of magnetization reversal. The reversal process, however, is often incoherent and hence, error-prone in the presence of thermal noise at room temperature. Occurrence of incoherent metastable states in the potential landscape of the nanomagnet can further exacerbate the error. Stochastic micromagnetic simulations at room temperature are used to understand and calculate energy dissipations and switching error probabilities in this important magnetization switching methodology. We find that these quantities have an intriguing dependence on nanomagnet size. Small nanomagnets perform better owing to the fact that they are more resilient to the formation of metastable states and magnetization dynamics in them is more coherent. However, for a fixed stress anisotropy energy density, smaller nanomagnets will also have poorer resilience against thermal instability. Thus, the challenge in straintronics is to maximize the stress anisotropy energy density by developing materials and processes that yield the largest magnetostriction. [ABSTRACT FROM PUBLISHER]

Strain-clocked dipole-coupled nanomagnetic logic (DC-NML) 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 in elliptical nanomagnets, the out-of-plane excursion of the magnetization vector during switching creates a precessional torque that plays a dual role—it speeds up the switching, but is also responsible for the high switching error probability. The absence of this torque in cylindrical magnets should lower error rates, but our simulations show that the error rate actually does not improve significantly compared with elliptical magnets while the switching becomes unacceptably slow. Here, we show that DC-NML employing elliptical nanomagnets can offer relatively high reliability for NML (switching error probability < 10^-8 ), moderate clock speed ( $\sim 100$ MHz), and two to three orders of magnitude energy saving compared with CMOS devices, provided the shape anisotropy energy barrier of the nanomagnet is increased to at least $\sim 5.5$ eV to allow engineering a stronger dipole coupling between neighboring nanomagnets. [ABSTRACT FROM AUTHOR]

Rotating the magnetization of a magnetostrictive nanomagnet with electrically generated strain dissipates far less energy than any other rotation method and would have been the perfect choice for writing bits in non-volatile magnetic memory, except strain cannot ordinarily rotate the magnetization of magnet in a memory cell by more than 90° and "flip" it. Here, we describe a scheme to achieve complete 180° rotation with strain alone without having to precisely time the strain cycle. 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 ~1ns, and (4) low read error. [ABSTRACT FROM AUTHOR]

We show that the energy dissipated to write bits in spin-transfer-torque random access memory can be reduced by an order of magnitude if a surface acoustic wave (SAW) is launched underneath the magneto-tunneling junctions (MTJs) storing the bits. The SAW-generated strain rotates the magnetization of every MTJs' soft magnet from the easy towards the hard axis, whereupon passage of a small spin-polarized current through a target MTJ selectively switches it to the desired state with > 99.99% probability at room temperature, thereby writing the bit. The other MTJs return to their original states at the completion of the SAW cycle. [ABSTRACT FROM AUTHOR]

The stress-induced switching behavior of a multiferroic nanomagnet, dipole coupled to a hard nanomagnet, is numerically studied by solving the stochastic Landau–Lifshitz–Gilbert equation for a single-domain macrospin state. Different factors were found to affect the switching probability in the presence of thermal noise at room temperature: 1) dipole coupling strength, 2) stress levels, and 3) stress withdrawal rates (ramp rates). We report that the thermal broadening of the magnetization distribution causes large switching error rates. This could render nanomagnetic logic schemes that rely on dipole coupling to perform Boolean logic operations impractical whether they are clocked by stress or field or other means. [ABSTRACT FROM PUBLISHER]

A binary switch is the basic building block for information processing. The potential energy profile of a bistable binary switch is a 'symmetric' double well. The traditional method of switching it from one state (one well) to the other is to tilt the profile towards the desired state. Here, we present a case, where no such tilting is necessary to switch successfully, even in the presence of thermal noise. This happens because of the built-in dynamics inside the switch itself. It differs from the general perception on binary switching that in a 'symmetric' potential landscape, the switching probability is 50% in the presence of thermal noise. Our results, considering the complete three-dimensional potential landscape, demonstrate intriguing phenomena on binary switching mechanism. With experimentally feasible parameters, we theoretically demonstrate such intriguing possibility in electric field induced magnetization switching of a shape-anisotropic single-domain magnetostrictive nanomagnet with two stable states at room-temperature. [ABSTRACT FROM AUTHOR]

A circular magnetic disk with biaxial magnetocrystalline anisotropy has four stable magnetization states which can be used to encode a pixel’s shade in a black/gray/white image. By solving the Landau–Lifshitz–Gilbert equation, we show that if moderate noise deflects the magnetization slightly from a stable state, it always returns to the original state, thereby automatically denoising the corrupted image. The same system can compare a noisy input image with a stored image and make a matching decision using magnetic tunnel junctions. These tasks are executed at ultrahigh speeds (\sim 2 ns for a 512 \times 512 pixel image). [ABSTRACT FROM PUBLISHER]

Nanomagnets with biaxial magnetocrystalline aniso-tropy have four stable magnetization orientations that can encode four-state logic bits (00), (01), (11), and (10). Recently, a four-state nor gate derived from three such nanomagnets, interacting via dipole interaction, was proposed. Here, we devise a Bennett clocking scheme to propagate four-state logic bits unidirectionally between such gates. The nanomagnets are assumed to be made of two-phase strain-coupled magnetostrictive/piezoelectric multiferroic elements, such as nickel and lead zirconate titanate. 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 four-state logic bits unidirectionally down a chain of such multiferroic nanomagnets for logic flow. [ABSTRACT FROM PUBLISHER]

The authors show that the magnetization of a 2-phase magnetostrictive/piezoelectric multiferroic single-domain shape-anisotropic nanomagnet can be switched with very small voltages that generate strain in the magnetostrictive layer. This can be the basis of ultralow power computing and signal processing. With appropriate material choice, the energy dissipated per switching event can be reduced to ∼45 kT at room temperature for a switching delay of ∼100 ns and ∼70 kT for a switching delay of ∼10 ns, if the energy barrier separating the two stable magnetization directions is ∼32 kT. Such devices can be powered by harvesting energy exclusively from the environment without the need for a battery. [ABSTRACT FROM AUTHOR]

Switching the magnetization of a shape-anisotropic 2-phase multiferroic nanomagnet with voltage-generated stress is known to dissipate very little energy (<1 aJ for a switching time of ∼0.5 ns) at 0 K temperature. Here, we show by solving the stochastic Landau-Lifshitz-Gilbert equation that switching can be carried out with ∼100% probability in less than 1 ns while dissipating less than 1.5 aJ at room temperature. This makes nanomagnetic logic and memory systems, predicated on stress-induced magnetic reversal, one of the most energy-efficient computing hardware extant. We also study the dependence of energy dissipation, switching delay, and the critical stress needed to switch, on the rate at which stress on the nanomagnet is ramped up or down. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The switching dynamics of a multiferroic nanomagnetic NAND gate with fan-in/fan-out is simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation while neglecting thermal fluctuation effects. The gate and logic wires are implemented with dipole-coupled two-phase (magnetostrictive/piezoelectric) multiferroic elements that are clocked with electrostatic potentials of ∼50 mV applied to the piezoelectric layer generating 10.1 MPa stress in the magnetostrictive layers for switching. We show that a pipeline bit throughput rate of ∼0.5 GHz is achievable with proper magnet layout and sinusoidal four-phase clocking. The gate operation is completed in 2 ns with a latency of 4 ns. The total (internal &plus; external) energy dissipated for a single gate operation at this throughput rate is found to be only ∼500 kT in the gate and ∼1250 kT in the 12-magnet array comprising two input and two output wires for fan-in and fan-out. This makes it respectively three and five orders of magnitude more energy-efficient than complementary-metal-oxide-semiconductor-transistor (CMOS)-based and spin-transfer-torque-driven nanomagnet-based NAND gates. Finally, we show that the dissipation in the external clocking circuit can always be reduced asymptotically to zero using increasingly slow adiabatic clocking, such as by designing the RC time constant to be three orders of magnitude smaller than the clocking period. However, the internal dissipation in the device must remain and cannot be eliminated if we want to perform fault-tolerant classical computing. [ABSTRACT FROM AUTHOR]

The temporal evolution of the magnetization vector of a single-domain magnetostrictive nanomagnet, subjected to in-plane stress, is studied by solving the Landau-Lifshitz-Gilbert equation. The stress is ramped up linearly in time, and the switching delay, which is the time it takes for the magnetization to flip, is computed as a function of the ramp rate. For high levels of stress, the delay exhibits a nonmonotonic dependence on the ramp rate, indicating that there is an optimum ramp rate to achieve the shortest delay. For constant ramp rate, the delay initially decreases with increasing stress but then saturates, showing that the trade-off between the delay and the stress (or the energy dissipated in switching) becomes less and less favorable with increasing stress. All of these features are due to a complex interplay between the in-plane and out-of-plane dynamics of the magnetization vector induced by stress. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]