Magneto-elastic (or "straintronic") switching has emerged as an extremely energy-efficient mechanism for switching the magnetization of magnetostrictive nanomagnets in magnetic memory, logic and non-Boolean circuits. Here, we investigate the ultrafast magneto-dynamics associated with straintronic switching in a single quasi-elliptical magnetostrictive Co nanomagnet deposited on a piezoelectric Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) 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 (SAWs) in the piezoelectric substrate that produce periodic strains in the magnetostrictive nanomagnet and modulate the precessional dynamics. This modulation gives rise to intriguing hybrid magneto-dynamical modes in the nanomagnet, with 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 magneto-elastic nanooscillators that are actuated by strain instead of a spin-polarized current, as well as ultrafast magneto-electric generation of spin waves for magnonic logic circuits, holograms, etc.

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.

Magneto-elastic (straintronic) switching of bistable magnetostrictive nanomagnets is an extremely energyefficient switching methodology for (magnetic) binary switches that has recently attracted widespread attention because of its potential application in ultra-low-power digital computing hardware. Unfortunately, this modality of switching is also error very prone at room temperature. Theoretical studies of switching error probability of magneto-elastic switches have predicted probabilities ranging from 10 -8 -10 -3 at room temperature for ideal, defect-free nanomagnets, but experiments with real nanomagnets show a much higher probability that exceeds 0.1 in some cases. To understand what causes this large difference, we have theoretically studied the effect of common defects (that occur during fabrication) on magneto-elastic switching probability in the presence of room-temperature thermal noise. Surprisingly, we found that even small defects increase the switching error probabilities by orders of magnitude. This could limit or preclude the application of magneto-elastic (straintronic) binary switches in either Boolean logic or memory, despite their excellent energy-efficiency, and restrict them to non-Boolean (e.g. neuromorphic, stochastic) computing applications. We also studied the difference between magneto-elastic switching with a stress pulse of constant amplitude and sinusoidal time-varying amplitude (e.g. due to a surface acoustic wave) and found that the latter method is more reliable and generates lower switching error probabilities in most cases, provided the time variation is reasonably slow.

Hardware based image processing offers speed and convenience not found in software-centric approaches. Here, we show theoretically that a two-dimensional 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.

There is growing interest in exploring nanomagnetic devices as potential replacements for electronic devices (e.g. transistors) in digital switching circuits and systems. A special class of nanomagnetic devices are switched with electrically generated mechanical strain leading to electrical control of magnetism. Straintronic magneto-tunneling junctions (s-MTJ) belong to this category. Their soft layers are composed of two-phase multiferroics comprising a magnetostrictive layer elastically coupled to a piezoelectric layer.Here, we show that a single straintronic magneto-tunneling junction with a passive resistor can act as a microwave oscillator whose traditional implementation would have required microwave operational amplifiers, capacitors and resistors. This reduces device footprint and cost, while improving device reliability. This is an analog application of magnetic devices where magnetic interactions (interaction between the shape anisotropy, strain anisotropy, dipolar coupling field and spin transfer torque in the soft layer of the s-MTJ) are exploited to implement an oscillator with reduced footprint. I.

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.

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 anticorrelation 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. There is an emerging focus on "probabilistic computing" with probabilistic (p-) bits encoded in the resistance states of magneto-tunneling junctions (MTJs) whose soft layers are nanomagnets possessing low energy barriers 1. This paradigm has been shown to be successful in solving computationally-hard problems such as factorization 2 , combinatorial optimization 3 , population coding 4 , invertible logic 5 , and has been used in restricted Boltzmann machines 6 and belief networks 7. p-bit based computing requires stochastic interaction and controlled correlation between p-bits. Controlled correlations are also needed for some graphical circuit models of stochastic computing, computer vision and image processing applications 8-12. These correlations are typically generated with the aid of complex electronic hardware that may involve shift registers, Boolean logic gates, random number generators, multiplexers, binary counters, comparators, etc. or microcontrollers for generating synaptic weights 2-5. They consume large areas on a chip, dissipate enormous amounts of energy, and are expensive to implement. In this paper, we show how to implement an ultra-compact and ultra-energy-efficient p-bit correlator with dipolecoupled MTJs fabricated on a piezoelectric film, with each MTJ hosting a p-bit. The dipole coupling corr...

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.