Reconfigurable stochastic neurons based on strain engineered low barrier nanomagnets.

Stochastic neurons are efficient hardware accelerators for solving a large variety of combinatorial optimization problems. 'Binary' stochastic neurons (BSN) are those whose states fluctuate randomly between two levels +1 and -1, with the probability of being in either level determined by an external bias. 'Analog' stochastic neurons (ASNs), in contrast, can assume any state between the two levels randomly (hence 'analog') and can perform analog signal processing. They may be leveraged for such tasks as temporal sequence learning, processing and prediction. Both BSNs and ASNs can be used to build efficient and scalable neural networks. Both can be implemented with low (potential energy) barrier nanomagnets (LBMs) whose random magnetization orientations encode the binary or analog state variables. The difference between them is that the potential energy barrier in a BSN LBM, albeit low, is much higher than that in an ASN LBM. As a result, a BSN LBM has a cleardouble well potential profile, which makes its magnetization orientation assume one of two orientations at any time, resulting in the binary behavior. ASN nanomagnets, on the other hand, hardly have any energy barrier at all and hence lack the double well feature. That makes their magnetizations fluctuate in an analog fashion. Hence, one can reconfigure an ASN to a BSN, and vice-versa, by simply raising and lowering the energy barrier. If the LBM ismagnetostrictive, then this can be done with local (electrically generated) strain. Such a reconfiguration capability heralds a powerful field programmable architecture for a p-computer whereby hardware forvery different functionalitiessuch as combinatorial optimization and temporal sequence learning can be integrated in the same substrate in the same processing run. This is somewhat reminiscent of heterogeneous integration, except this is integration of functionalities or computational fabrics rather than components. The energy cost of reconfiguration is miniscule. There are also other applications of strain mediated barrier control that do not involve reconfiguring a BSN to an ASN or vice versa, e.g. adaptive annealing in energy minimization computing (Boltzmann or Ising machines), emulating memory hierarchy in a dynamically reconfigurable fashion, and control over belief uncertainty in analog stochastic neurons. Here, we present a study of strain engineered barrier control in unconventional computing.

A spintronic analog of the Landauer residual resistivity dipole on the surface of a topological insulator containing a line defect.

The Landauer 'residual resistivity dipole' is a well-known concept in electron transport through a disordered medium. It is formed when a defect/scatterer reflects an impinging electron causing negative charges to build up on one side of the scatterer and positive charges on the other. This charge imbalance results in the formation of a microscopic electric dipole that affects the electrical resistivity of the medium. Here, we show that an equivalent entity forms in spin polarized electron transport on the surface of a real topological insulator (TI) such as Bi2Te3containing a line defect. When electrons reflect from such a scatterer, a local spin imbalance forms owing to spin accumulation on one side and depletion on the other side of the scatterer, resulting in a spin current that flows either in the same or in the opposite direction as the injected spin current, and hence, either decreases or increases thespin resistivity. Spatially varying local magnetic fields appear in the vicinity of the scatter, which will cause transiting spins to precess and emit electromagnetic waves. If the current injected into the TI is an alternating current, then the magnetic field's polarity will oscillate in time with the frequency of the current and if the spins can follow quasi-statically, then they will radiate electromagnetic waves of the same frequency, thereby making the scatterer act as a miniature antenna.

Spin Wave Electromagnetic Nano-Antenna Enabled by Tripartite Phonon-Magnon-Photon Coupling.

Tripartite coupling between phonons, magnons, and photons in a periodic array of elliptical magnetostrictive nanomagnets delineated on a piezoelectric substrate to form a 2D two-phase multiferroic crystal is investigated. Surface acoustic waves (SAW) (phonons) of 5-35 GHz frequency launched into the substrate cause the magnetizations of the nanomagnets to precess at the frequency of the wave, giving rise to confined spin-wave modes (magnons) within the nanomagnets. The spin waves, in turn, radiate electromagnetic waves (photons) into the surrounding space at the SAW frequency. Here, the phonons couple into magnons, which then couple into photons. This tripartite phonon-magnon-photon coupling is thus exploited to implement an extreme sub-wavelength electromagnetic antenna whose measured radiation efficiency and antenna gain exceed the approximate theoretical limits for traditional antennas of the same dimensions by more than two orders of magnitude at some frequencies. Micro-magnetic simulations are in excellent agreement with experimental observations and provide insight into the spin-wave modes that couple into radiating electromagnetic modes to implement the antenna.

Applications of nanomagnets as dynamical systems: I.

When magnets are fashioned into nanoscale elements, they exhibit a wide variety of phenomena replete with rich physics and the lure of tantalizing applications. In this topical review, we discuss some of these phenomena, especially those that have come to light recently, and highlight their potential applications. We emphasize what drives a phenomenon, what undergirds the dynamics of the system that exhibits the phenomenon, how the dynamics can be manipulated, and what specific features can be harnessed for technological advances. For the sake of balance, we point out both advantages and shortcomings of nanomagnet based devices and systems predicated on the phenomena we discuss. Where possible, we chart out paths for future investigations that can shed new light on an intriguing phenomenon and/or facilitate both traditional and non-traditional applications.

Applications of nanomagnets as dynamical systems: II.

In Part I of this topical review, we discussed dynamical phenomena in nanomagnets, focusing primarily on magnetization reversal with an eye to digital applications. In this part, we address mostly wave-like phenomena in nanomagnets, with emphasis on spin waves in myriad nanomagnetic systems and methods of controlling magnetization dynamics in nanomagnet arrays which may have analog applications. We conclude with a discussion of some interesting spintronic phenomena that undergird the rich physics exhibited by nanomagnet assemblies.

An observable effect of spin inertia in slow magneto-dynamics: increase of the switching error rates in nanoscale ferromagnets.

The Landau-Lifshitz-Gilbert (LLG) equation, used to model magneto-dynamics in ferromagnets, tacitly assumes that the angular momentum associated with spin precession can relax instantaneously when the real or effective magnetic field causing the precession is turned off. This neglect of 'spin inertia' is unphysical and would violate energy conservation. Recently, the LLG equation was modified to account for inertia effects. The consensus, however, seems to be that such effects would be unimportant inslowmagneto-dynamics that take place over time scales much longer that the relaxation time of the angular momentum, which is typically few fs to perhaps ∼100 ps in ferromagnets. Here, we show that there is at least one very serious and observable effect of spin inertia even in slow magneto-dynamics. It involves the switching error probability associated with flipping the magnetization of a nanoscale ferromagnet with an external agent, such as a magnetic field. The switching may take ∼ns to complete when the field strength is close to the threshold value for switching, which is much longer than the angular momentum relaxation time, and yet the effect of spin inertia is felt in the switching error probability. This is because the ultimate fate of a switching trajectory, i.e. whether it results in success or failure, is influenced by what happens in the first few ps of the switching action when nutational dynamics due to spin inertia hold sway. Spin inertiaincreasesthe error probability, which makes the switching more error-prone. This has vital technological significance because it relates to the reliability of magnetic logic and memory.

Resonant amplification of intrinsic magnon modes and generation of new extrinsic modes in a two-dimensional array of interacting multiferroic nanomagnets by surface acoustic waves.

Using time-resolved magneto-optical Kerr effect (TR-MOKE) microscopy, we demonstrate surface-acoustic-wave (SAW) induced resonant amplification of intrinsic spin-wave (SW) modes, as well as generation of new extrinsic or driven modes at the SAW frequency, in a densely packed two-dimensional array of elliptical Co nanomagnets fabricated on a piezoelectric LiNbO3 substrate. This system can efficiently serve as a magnonic crystal (MC), where the intrinsic shape anisotropy and the strong inter-element magnetostatic interaction trigger the incoherent precession of the nanomagnets' magnetization in the absence of any bias magnetic field, giving rise to the 'intrinsic' SW modes. The magnetoelastic coupling leads to a rich variety of SW phenomena when the SAW is launched along the major axis of the nanomagnets, such as 4-7 times amplification of intrinsic modes (at 3, 4, 7 and 10 GHz) when the applied SAW frequencies are resonant with these frequencies, and the generation of new extrinsic modes at non-resonant SAW frequencies. However, when the SAW is launched along the minor axis, a dominant driven mode appears at the applied SAW frequency. This reveals that the magnetoelastic coupling between SW and SAW is anisotropic in nature. Micromagnetic simulation results are in qualitative agreement with the experimental observations and elucidate the underlying dynamics. Our findings lay the groundwork for bias-field free magnonics, where the SW behavior is efficiently tuned by SAWs. It has important applications in the design of energy efficient on-chip microwave devices, SW logic, and extreme sub-wavelength ultra-miniaturized microwave antennas for embedded applications.

Bayesian reasoning machine on a magneto-tunneling junction network.

The recent trend in adapting ultra-energy-efficient (but error-prone) nanomagnetic devices to non-Boolean computing and information processing (e.g. stochastic/probabilistic computing, neuromorphic, belief networks, etc) has resulted in rapid strides in new computing modalities. Of particular interest are Bayesian networks (BN) which may see revolutionary advances when adapted to a specific type of nanomagnetic devices. Here, we develop a novel nanomagnet-based computing substrate for BN that allows high-speed sampling from an arbitrary Bayesian graph. We show that magneto-tunneling junctions (MTJs) can be used for electrically programmable 'sub-nanosecond' probability sample generation by co-optimizing voltage-controlled magnetic anisotropy and spin transfer torque. We also discuss that just by engineering local magnetostriction in the soft layers of MTJs, one can stochastically couple them for programmable conditional sample generation as well. This obviates the need for extensive energy-inefficient hardware like OP-AMPS, gates, shift-registers, etc to generate the correlations. Based on the above findings, we present an architectural design and computation flow of the MTJ network to map an arbitrary Bayesian graph where we develop circuits to program and induce switching and interactions among MTJs. Our discussed framework can lead to a new generation of stochastic computing hardware for various other computing models, such as stochastic programming and Bayesian deep learning. This can spawn a novel genre of ultra-energy-efficient, extremely powerful computing paradigms, which is a transformational advance.

Electrically programmable probabilistic bit anti-correlator on a nanomagnetic platform.

Execution of probabilistic computing algorithms require electrically programmable stochasticity to encode arbitrary probability functions and controlled stochastic interaction or correlation between probabilistic (p-) bits. The latter is implemented with complex electronic components leaving a large footprint on a chip and dissipating excessive amount of energy. Here, we show an elegant implementation with just two dipole-coupled magneto-tunneling junctions (MTJ), with magnetostrictive soft layers, fabricated on a piezoelectric film. The resistance states of the two MTJs (high or low) encode the p-bit values (1 or 0) in the two streams. The first MTJ is driven to a resistance state with desired probability via a current or voltage that generates spin transfer torque, while the second MTJ's resistance state is determined by dipole coupling with the first, thus correlating the second p-bit stream with the first. The effect of dipole coupling can be varied by generating local strain in the soft layer of the second MTJ with a local voltage (~ 0.2 V) and that varies the degree of anti-correlation between the resistance states of the two MTJs and hence between the two streams (from 0 to 100%). This paradigm generates the anti-correlation with "wireless" dipole coupling that consumes no footprint on a chip and dissipates no energy, and it controls the degree of anti-correlation with electrically generated strain that consumes minimal footprint and is extremely frugal in its use of energy. It can be extended to arbitrary number of bit streams. This realizes an "all-magnetic" platform for generating correlations or anti-correlations for probabilistic computing. It also implements a simple 2-node Bayesian network.

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.].

The effect of material defects on resonant spin wave modes in a nanomagnet.

We have theoretically studied how resonant spin wave modes in an elliptical nanomagnet are affected by fabrication defects, such as small local thickness variations. Our results indicate that defects of this nature, which can easily result from the fabrication process, or are sometimes deliberately introduced during the fabrication process, will significantly alter the frequencies, magnetic field dependence of the frequencies, and the power and phase profiles of the resonant spin wave modes. They can also spawn new resonant modes and quench existing ones. All this has important ramifications for multi-device circuits based on spin waves, such as phase locked oscillators for neuromorphic computing, where the device-to-device variability caused by defects can be inhibitory.

Hybrid Magnetodynamical Modes in a Single Magnetostrictive Nanomagnet on a Piezoelectric Substrate Arising from Magnetoelastic Modulation of Precessional Dynamics.

Magnetoelastic (or "straintronic") switching has emerged as an extremely energy-efficient mechanism for switching the magnetization of magnetostrictive nanomagnets in magnetic memory and logic, and non-Boolean circuits. Here, we investigate the ultrafast magnetodynamics associated with straintronic switching in a single quasielliptical magnetostrictive Co nanomagnet deposited on a piezoelectric Pb(Mg1/3Nb2/3)O3-PbTiO3 substrate using time-resolved magneto-optical Kerr effect (TR-MOKE) measurements. The pulsed laser pump beam in the TR-MOKE plays a dual role: it causes precession of the nanomagnet's magnetization about an applied bias magnetic field and it also generates surface acoustic waves in the piezoelectric substrate that produce periodic strains in the magnetostrictive nanomagnet and modulate the precessional dynamics. This modulation gives rise to intriguing hybrid magnetodynamical modes in the nanomagnet, with a rich spin-wave texture. The characteristic frequencies of these modes are 5-15 GHz, indicating that strain can affect magnetization in a magnetostrictive nanomagnet in time scales much smaller than 1 ns (∼100 ps). This can enable ∼10 GHz range magnetoelastic nano-oscillators that are actuated by strain instead of a spin-polarized current, as well as ultrafast magnetoelectric generation of spin waves for magnonic logic circuits, holograms, etc.

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.

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.

Antimicrobial properties of nanorods: killing bacteria via impalement.

Silver is known to possess anti-microbial properties that are of chemical origin. It is believed that either Ag atoms bind to thiol groups in bacterial enzymes or Ag+ ions enter bacterial cells and denature the DNA molecule to kill bacteria. Silver nanorods, however, may kill bacteria by another mechanism: it is possible that the sharp tips of the nanorods puncture bacterial cells and kill bacteria via impalement-a physical mechanism. To test if this can indeed happen, we have compared the anti-microbial properties of silver and CdS nanorods. No significant difference is found between the two even though CdS does not possess the chemical properties of silver. This indicates that the physical kill mechanism is indeed likely and therefore nanorods of any material may possess anti-microbial properties. In that case, it is possible to overcome serious short- and long-term health hazard issues which have been posed by silver nanoparticles by replacing them with nanorods of innocuous elements or compounds. A surface containing nanorods of varying heights presents an undulating bed of spikes to microbes and is most inhospitable to bacteria.

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.