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.

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.

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.

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.

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