Experimental Clocking of Nanomagnets with Strain for Ultralow Power Boolean Logic

Quantized Magnetic Domain Wall Synapse for Efficient Deep Neural Networks

The quantization of synaptic weights using emerging nonvolatile memory (NVM) devices has emerged as a promising solution to implement computationally efficient neural networks on resource constrained hardware. However, the practical implementation of such synaptic weights is hampered by the imperfect memory characteristics, specifically the availability of limited number of quantized states and the presence of large intrinsic device variation and stochasticity involved in writing the synaptic states. This article presents ON-chip training and inference of a neural network using quantized magnetic domain wall (DW)-based synaptic array and CMOS peripheral circuits. A rigorous model of the magnetic DW device considering stochasticity and process variations has been utilized for the synapse. To achieve stable quantized weights, DW pinning has been achieved by means of physical constrictions. Finally, VGG8 architecture for CIFAR-10 image classification has been simulated by using the extracted synaptic device characteristics. The performance in terms of accuracy, energy, latency, and area consumption has been evaluated while considering the process variations and nonidealities in the DW device as well as the peripheral circuits. The proposed quantized neural network (QNN) architecture achieves efficient ON-chip learning with 92.4% and 90.4% training and inference accuracy, respectively. In comparison to pure CMOS-based design, it demonstrates an overall improvement in area, energy, and latency by , , and , respectively.

Skyrmion-mediated nonvolatile ternary memory

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 ~ 2 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 ~ 104X 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.

Energy Efficient All-Electric-Field-Controlled Multiferroic Magnetic Domain-Wall Logic

Magnetic domain wall (DW)-based logic devices offer numerous opportunities for emerging electronics applications allowing superior performance characteristics such as fast motion, high density, and nonvolatility to process information. However, these devices rely on an external magnetic field, which limits their implementation; this is particularly problematic in large-scale applications. Multiferroic systems consisting of a piezoelectric substrate coupled with ferromagnets provide a potential solution that provides the possibility of controlling magnetization through an electric field via magnetoelastic coupling. Strain-induced magnetization anisotropy tilting can influence the DW motion in a controllable way. We demonstrate a method to perform all-electrical logic operations using such a system. Ferromagnetic coupling between neighboring magnetic domains induced by the electric-field-controlled strain has been exploited to promote noncollinear spin alignment, which is used for realizing essential building blocks, including DW generation, propagation, and pinning, in all implementations of Boolean logic, which will pave the way for scalable memory-in-logic applications.

Using Dipole Interaction to Achieve Nonvolatile Voltage Control of Magnetism in Multiferroic Heterostructures

Nonvolatile electrical control of magnetism is crucial for developing energy-efficient magnetic memory. Based on strain-mediated magnetoelectric coupling, a multiferroic heterostructure containing an isolated magnet requires nonvolatile strain to achieve this control. However, the magnetization response of an interacting magnet to strain remains elusive. Herein, Co/MgO/CoFeB magnetic tunnel junctions (MTJs) exhibiting dipole interaction on ferroelectric substrates are fabricated. Remarkably, nonvolatile voltage control of the resistance in the MTJs is demonstrated, which originates from the nonvolatile magnetization rotation of an interacting CoFeB magnet driven by volatile voltage-generated strain. Conversely, for an isolated CoFeB magnet, this volatile strain induces volatile control of magnetism. These results reveal that the magnetization response to volatile strain among interacting magnets is different from that among isolated magnets. The findings highlight the role of dipole interaction in multiferroic heterostructures and can stimulate future research on nonvolatile electrical control of magnetism with additional interactions.

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.

Nano-magnetic tunnel junctions controlled by electric field for straintronics

The magnetic tunneling junction (MTJ) controlled by electric field as an alternate approach for energy efficiency is the highlight for nonvolatile RAM, while there is still a lack of research on resistance manipulation with the electric field in nanoscale MTJs. In this study, we integrated nanoscale MTJs on the (011) orientated Pb(Mg_1/3Nb_2/3)_0.7Ti_0.3O₃ (PMN-PT) ferroelectric substrates and systematically investigated the magnetoresistance as a function of the magnetic field and electric field. A single domain state of the nanoscale MTJ was demonstrated by the experimental result and theoretical simulation. Afterward, the obvious electric field control of R-H curves was obtained and explained by the competition between magnetoelastic energy and shape anisotropy. More importantly, simulation results also predicted that the switching pathway of magnetic moments under the magnetic field is strongly dependent on the applied electric field, displaying the electric field control of chiral switching in the nano-MTJ. Our work is a milestone in the realization of the emerging dubbed straintronics field.

Magnetoelectric Memory Based on Ferromagnetic/Ferroelectric Multiferroic Heterostructure

Electric-field control of magnetism is significant for the next generation of large-capacity and low-power data storage technology. In this regard, the renaissance of a multiferroic compound provides an elegant platform owing to the coexistence and coupling of ferroelectric (FE) and magnetic orders. However, the scarcity of single-phase multiferroics at room temperature spurs zealous research in pursuit of composite systems combining a ferromagnet with FE or piezoelectric materials. So far, electric-field control of magnetism has been achieved in the exchange-mediated, charge-mediated, and strain-mediated ferromagnetic (FM)/FE multiferroic heterostructures. Concerning the giant, nonvolatile, and reversible electric-field control of magnetism at room temperature, we first review the theoretical and representative experiments on the electric-field control of magnetism via strain coupling in the FM/FE multiferroic heterostructures, especially the CoFeB/PMN–PT [where PMN–PT denotes the (PbMn_1/3Nb_2/3O₃)_1−x-(PbTiO₃)_x] heterostructure. Then, the application in the prototype spintronic devices, i.e., spin valves and magnetic tunnel junctions, is introduced. The nonvolatile and reversible electric-field control of tunneling magnetoresistance without assistant magnetic field in the magnetic tunnel junction (MTJ)/FE architecture shows great promise for the future of data storage technology. We close by providing the main challenges of this and the different perspectives for straintronics and spintronics.

Electric-field-assisted non-volatile magnetic switching in a magnetoelectronic hybrid structure

Electric-field (E-field) control of magnetic switching provides an energy-efficient means to toggle the magnetic states in spintronic devices. The angular tunneling magnetoresistance (TMR) of an magnetic tunnel junction (MTJ)/PMN-PT magnetoelectronic hybrid indicates that the angle-dependent switching fields of the free layer can decrease significantly subject to the application of an E-field. In particular, the switching field along the major axis is reduced by 59% from 28.0 to 11.5 Oe as the E-field increases from 0 to 6 kV/cm, while the TMR ratio remains intact. The switching boundary angle decreases (increases) for the parallel (antiparallel) to antiparallel (parallel) state switch, resulting in a shrunk switching window size. The non-volatile and reversible 180° magnetization switching is demonstrated by using E-fields with a smaller magnetic field bias as low as 11.5 Oe. The angular magnetic switching originates from competition among the E-field-induced magnetoelastic anisotropy, magnetic shape anisotropy, and Zeeman energy, which is confirmed by micromagnetic simulations.

Finite difference magnetoelastic simulator

We describe an extension of the micromagnetic finite difference simulation software MuMax3 to solve elasto-magneto-dynamical problems. The new module allows for numerical simulations of magnetization and displacement dynamics in magnetostrictive materials and structures, including both direct and inverse magnetostriction. The theoretical background is introduced, and the implementation of the extension is discussed. The magnetoelastic extension of MuMax3 is freely available under the GNU General Public License v3.

A novel and reliable interlayer exchange coupled nanomagnetic universal logic gate design

In this paper, we propose an interlayer exchange coupling (IEC) based 3D universal NAND/NOR gate design methodology for the reliable and robust implementation of nanomagnetic logic design as compared to the state-of-the art architectures. Owing to stronger coupling scheme as compared to the conventional dipole coupling, the random flip of the states of the nanomagnets (i.e. the soft error) is reduced resulting in greater scalability and better data retention at the deep sub-micron level. Results obtained from Object Oriented Micromagnetic Framework micromagnetic simulation show even at a Curie temperature of the nanomagnets coupled through IEC, the logic function works properly as opposed to dipole coupled nanomagnets which fails at 5 K when scaled down to sub 50 nm. Contemplating the fabrication challenges, the robustness of the IEC design was studied for structural defects, positional misalignment, shape, and size variations. This proposed 3D universal gate design methodology benefits from the miniaturization of nanomagnets as well as reduces the effect of thermally induced errors resulting in opening up a new perspective for nanomagnet based design in magneto-logic devices.

The Interaction between Surface Acoustic Waves and Spin Waves: The Role of Anisotropy and Spatial Profiles of the Modes

The interaction between different types of wave excitation in hybrid systems is usually anisotropic. Magnetoelastic coupling between surface acoustic waves and spin waves strongly depends on the direction of the external magnetic field. However, in the present study we observe that even if the orientation of the field is supportive for the coupling, the magnetoelastic interaction can be significantly reduced for surface acoustic waves with a particular profile in the direction normal to the surface at distances much smaller than the wavelength. We use Brillouin light scattering for the investigation of thermally excited phonons and magnons in a magnetostrictive CoFeB/Au multilayer deposited on a Si substrate. The experimental data are interpreted on the basis of a linearized model of interaction between surface acoustic waves and spin waves.

Voltage-induced strain clocking of nanomagnets with perpendicular magnetic anisotropies

Nanomagnetic logic (NML) has attracted attention during the last two decades due to its promise of high energy efficiency combined with non-volatility. Data transmission in NML relies on Bennett clocking through dipole interaction between neighboring nanomagnetic bits. This paper uses a fully coupled finite element model to simulate Bennett clocking based on strain-mediated multiferroic system for Ni, CoFeB and Terfenol-D with perpendicular magnetic anisotropies. Simulation results demonstrate that Terfenol-D system has the highest energy efficiency, which is 2 orders of magnitude more efficient than Ni and CoFeB. However, the high efficiency is associated with switching incoherency due to its large magnetostriction coefficient. It is also suggested that the CoFeB clocking system has lower bit-density than in Ni or Terfenol-D systems due to its large dipole coupling. Moreover, we demonstrate that the precessional perpendicular switching and the Bennett clocking can be achieved using the same strain-mediated multiferroic architecture with different voltage pulsing. This study opens new possibilities to an all-spin in-memory computing system.

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(Mg_1/3Nb_2/3)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.

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.

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.

Large Interfacial Magnetostriction in (Co/Ni)4/Pb(Mg1/3Nb2/3)O3-PbTiO3 Multiferroic Heterostructures

The magnetoelastic behavior of multiferroic heterostructures-coupling of magnetic anisotropy or domain dynamics to structural deformations-has been intensively studied for developing materials for energy-efficient, spin-based applications. Here, we report on a large, interface-dominated magnetostriction in (Co/Ni)₄/Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ multiferroic heterostructures. Ferromagnetic resonance spectroscopy under voltage-induced strains enabled estimation of the saturation magnetostriction as a function of Ni thickness. The volume and the interface components to the saturation magnetostriction are (6.6 ± 0.9) × 10^-6 and (-2.2 ± 0.2) × 10^-14 m, respectively. Similar to perpendicular magnetic anisotropy in Co/Ni, the large, negative magnetostriction originates from the Co/Ni interfaces. This interfacial functionality delivers an effect over 300% larger than the bulk contribution and can enable low-energy, nanoelectronic devices that combine the tunable magnetic and magnetostrictive properties of Co/Ni multilayers with the ferroelectric properties of Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃.

Computational logic with square rings of nanomagnets

Nanomagnets are a promising low-power alternative to traditional computing. However, the successful implementation of nanomagnets in logic gates has been hindered so far by a lack of reliability. Here, we present a novel design with dipolar-coupled nanomagnets arranged on a square lattice to (i) support transfer of information and (ii) perform logic operations. We introduce a thermal protocol, using thermally active nanomagnets as a means to perform computation. Within this scheme, the nanomagnets are initialized by a global magnetic field and thermally relax on raising the temperature with a resistive heater. We demonstrate error-free transfer of information in chains of up to 19 square rings and we show a high level of reliability with successful gate operations of ∼94% across more than 2000 logic gates. Finally, we present a functionally complete prototype NAND/NOR logic gate that could be implemented for advanced logic operations. Here we support our experiments with simulations of the thermally averaged output and determine the optimal gate parameters. Our approach provides a new pathway to a long standing problem concerning reliability in the use of nanomagnets for computation.

Skyrmion-Mediated Voltage-Controlled Switching of Ferromagnets for Reliable and Energy-Efficient Two-Terminal Memory

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 can create an 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-based switching.

Bi-directional coupling in strain-mediated multiferroic heterostructures with magnetic domains and domain wall motion

Strain-coupled multiferroic heterostructures provide a path to energy-efficient, voltage-controlled magnetic nanoscale devices, a region where current-based methods of magnetic control suffer from Ohmic dissipation. Growing interest in highly magnetoelastic materials, such as Terfenol-D, prompts a more accurate understanding of their magnetization behavior. To address this need, we simulate the strain-induced magnetization change with two modeling methods: the commonly used unidirectional model and the recently developed bidirectional model. Unidirectional models account for magnetoelastic effects only, while bidirectional models account for both magnetoelastic and magnetostrictive effects. We found unidirectional models are on par with bidirectional models when describing the magnetic behavior in weakly magnetoelastic materials (e.g., Nickel), but the two models deviate when highly magnetoelastic materials (e.g., Terfenol-D) are introduced. These results suggest that magnetostrictive feedback is critical for modeling highly magnetoelastic materials, as opposed to weaker magnetoelastic materials, where we observe only minor differences between the two methods' outputs. To our best knowledge, this work represents the first comparison of unidirectional and bidirectional modeling in composite multiferroic systems, demonstrating that back-coupling of magnetization to strain can inhibit formation and rotation of magnetic states, highlighting the need to revisit the assumption that unidirectional modeling always captures the necessary physics in strain-mediated multiferroics.

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 Fe_0.8Ga_0.2 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.

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.

Hydrostatic-pressure-induced changes of magnetic anisotropy in (Ga, Mn)As thin films

The impact of hydrostatic pressure on magnetic anisotropy energies in (Ga, Mn)As thin films with in-plane and out-of-plane magnetic easy axes predefined by epitaxial strain was investigated. In both types of sample we observed a clear increase in both in-plane and out-of-plane anisotropy parameters with pressure. The out-of-plane anisotropy constant is well reproduced by the mean-field p-d Zener model; however, the changes in uniaxial anisotropy are much larger than expected in the Mn-Mn dimer scenario.

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.

Binary information propagation in circular magnetic nanodot arrays using strain induced magnetic anisotropy

Nanomagnetic logic has emerged as a potential replacement for traditional Complementary Metal Oxide Semiconductor (CMOS) based logic because of superior energy-efficiency (Salahuddin and Datta 2007 Appl. Phys. Lett. 90 093503, Cowburn and Welland 2000 Science 287 1466-68). One implementation of nanomagnetic logic employs shape-anisotropic (e.g. elliptical) ferromagnets (with two stable magnetization orientations) as binary switches that rely on dipole-dipole interaction to communicate binary information (Cowburn and Welland 2000 Science 287 1466-8, Csaba et al 2002 IEEE Trans. Nanotechnol. 1 209-13, Carlton et al 2008 Nano Lett. 8 4173-8, Atulasimha and Bandyopadhyay 2010 Appl. Phys. Lett. 97 173105, Roy et al 2011 Appl. Phys. Lett. 99 063108, Fashami et al 2011 Nanotechnology 22 155201, Tiercelin et al 2011 Appl. Phys. Lett. 99 , Alam et al 2010 IEEE Trans. Nanotechnol. 9 348-51 and Bhowmik et al 2013 Nat. Nanotechnol. 9 59-63). Normally, circular nanomagnets are incompatible with this approach since they lack distinct stable in-plane magnetization orientations to encode bits. However, circular magnetoelastic nanomagnets can be made bi-stable with a voltage induced anisotropic strain, which provides two significant advantages for nanomagnetic logic applications. First, the shape-anisotropy energy barrier is eliminated which reduces the amount of energy required to reorient the magnetization. Second, the in-plane size can be reduced (∼20 nm) which was previously not possible due to thermal stability issues. In circular magnetoelastic nanomagnets, a voltage induced strain stabilizes the magnetization even at this size overcoming the thermal stability issue. In this paper, we analytically demonstrate the feasibility of a binary 'logic wire' implemented with an array of circular nanomagnets that are clocked with voltage-induced strain applied by an underlying piezoelectric substrate. This leads to an energy-efficient logic paradigm orders of magnitude superior to existing CMOS-based logic that is scalable to dimensions substantially smaller than those for existing nanomagnetic logic approaches. The analytical approach is validated with experimental measurements conducted on dipole coupled Nickel (Ni) nanodots fabricated on a PMN-PT (Lead Magnesium Niobate-Lead Titanate) sample.

Stretching magnetism with an electric field in a nitride semiconductor

The significant inversion symmetry breaking specific to wurtzite semiconductors, and the associated spontaneous electrical polarization, lead to outstanding features such as high density of carriers at the GaN/(Al,Ga)N interface—exploited in high-power/high-frequency electronics—and piezoelectric capabilities serving for nanodrives, sensors and energy harvesting devices. Here we show that the multifunctionality of nitride semiconductors encompasses also a magnetoelectric effect allowing to control the magnetization by an electric field. We first demonstrate that doping of GaN by Mn results in a semi-insulating material apt to sustain electric fields as high as 5 MV cm⁻¹. Having such a material we find experimentally that the inverse piezoelectric effect controls the magnitude of the single-ion magnetic anisotropy specific to Mn³⁺ ions in GaN. The corresponding changes in the magnetization can be quantitatively described by a theory developed here.

The wurtzite crystal structure of nitride semiconductors results in strong piezoelectricity. Here, the authors also achieve electric-field control of the magnetization of gallium manganese nitride, thus showing that piezoelectric and magnetoelectric effects can be combined in the same material.

Acoustic-Wave-Induced Magnetization Switching of Magnetostrictive Nanomagnets from Single-Domain to Nonvolatile Vortex States

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.

Voltage controlled core reversal of fixed magnetic skyrmions without a magnetic field

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.

Fast 180° magnetization switching in a strain-mediated multiferroic heterostructure driven by a voltage

Voltage-driven 180° magnetization switching provides a low-power alternative to current-driven magnetization switching widely used in spintronic devices. Here we computationally demonstrate a promising route to achieve voltage-driven in-plane 180° magnetization switching in a strain-mediated multiferroic heterostructure (e.g., a heterostructure consisting of an amorphous, slightly elliptical Co40Fe40B20 nanomagnet on top of a Pb(Zr,Ti)O3 film as an example). This 180° switching follows a unique precessional path all in the film plane, and is enabled by manipulating magnetization dynamics with fast, local piezostrains (rise/release time <0.1 ns) on the Pb(Zr,Ti)O3 film surface. Our analyses predict ultralow area energy consumption per switching (~0.03 J/m(2)), approximately three orders of magnitude smaller than that dissipated by current-driven magnetization switching. A fast overall switching time of about 2.3 ns is also demonstrated. Further reduction of energy consumption and switching time can be achieved by optimizing the structure and material selection. The present design provides an additional viable route to realizing low-power and high-speed spintronics.

Reversible strain-induced magnetization switching in FeGa nanomagnets: Pathway to a rewritable, non-volatile, non-toggle, extremely low energy straintronic memory

We report reversible strain-induced magnetization switching between two stable/metastable states 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. The two states can encode the two binary bits, and, using the right voltage polarity, one can write either bit deterministically. This portends an ultra-energy-efficient non-volatile "non-toggle" memory.