Nanomagnet logic: progress toward system-level integration

Magnetic Interconnects Based on Composite Multiferroics

The development of magnetic logic devices dictates a need for a novel type of interconnect for magnetic signal transmission. Fast signal damping is one of the problems which drastically differs from conventional electric technology. Here, we describe a magnetic interconnect based on a composite multiferroic comprising piezoelectric and magnetostrictive materials. Internal signal amplification is the main reason for using multiferroic material, where a portion of energy can be transferred from electric to magnetic domains via stress-mediated coupling. The utilization of composite multiferroics consisting of piezoelectric and magnetostrictive materials offers flexibility for the separate adjustment of electric and magnetic characteristics. The structure of the proposed interconnect resembles a parallel plate capacitor filled with a piezoelectric, where one of the plates comprises a magnetoelastic material. An electric field applied across the plates of the capacitor produces stress, which, in turn, affects the magnetic properties of the magnetostrictive material. The charging of the capacitor from one edge results in the charge diffusion accompanied by the magnetization change in the magnetostrictive layer. This enables the amplitude of the magnetic signal to remain constant during the propagation. The operation of the proposed interconnects is illustrated by numerical modeling. The model is based on the Landau-Lifshitz-Gilbert equation with the electric field-dependent anisotropy term included. A variety of magnetic logic devices and architectures can benefit from the proposed interconnects, as they provide reliable and low-energy-consuming data transmission. According to the estimates, the group velocity of magnetic signals may be up to 10⁵ m/s with energy dissipation less than 10^-18 J per bit per 100 nm. The physical limits and practical challenges of the proposed approach are also discussed.

Voltage control of ferrimagnetic order and voltage-assisted writing of ferrimagnetic spin textures

Voltage control of magnetic order is desirable for spintronic device applications, but 180° magnetization switching is not straightforward because electric fields do not break time-reversal symmetry. Ferrimagnets are promising candidates for 180° switching owing to a multi-sublattice configuration with opposing magnetic moments of different magnitudes. In this study we used solid-state hydrogen gating to control the ferrimagnetic order in rare earth-transition metal thin films dynamically. Electric field-induced hydrogen loading/unloading in GdCo can shift the magnetic compensation temperature by more than 100 K, which enables control of the dominant magnetic sublattice. X-ray magnetic circular dichroism measurements and ab initio calculations indicate that the magnetization control originates from the weakening of antiferromagnetic exchange coupling that reduces the magnetization of Gd more than that of Co upon hydrogenation. We observed reversible, gate voltage-induced net magnetization switching and full 180° Néel vector reversal in the absence of external magnetic fields. Furthermore, we generated ferrimagnetic spin textures, such as chiral domain walls and skyrmions, in racetrack devices through hydrogen gating. With gating times as short as 50 μs and endurance of more than 10,000 cycles, our method provides a powerful means to tune ferrimagnetic spin textures and dynamics, with broad applicability in the rapidly emerging field of ferrimagnetic spintronics.

On the degeneracy of spin ice graphs, and its estimate via the Bethe permanent

The concept of spin ice can be extended to a general graph. We study the degeneracy of spin ice graph on arbitrary interaction structures via graph theory. We map spin ice graphs to the Ising model on a graph and clarify whether the inverse mapping is possible via a modified Krausz construction. From the gauge freedom of frustrated Ising systems, we derive exact, general results about frustration and degeneracy. We demonstrate for the first time that every spin ice graph, with the exception of the one-dimensional Ising model, is degenerate. We then study how degeneracy scales in size, using the mapping between Eulerian trails and spin ice manifolds, and a permanental identity for the number of Eulerian orientations. We show that the Bethe permanent technique provides both an estimate and a lower bound to the frustration of spin ices on arbitrary graphs of even degree. While such a technique can also be used to obtain an upper bound, we find that in all finite degree examples we studied, another upper bound based on Schrijver inequality is tighter.

Nanomagnetic logic based runtime Reconfigurable area efficient and high speed adder design methodology

In this study, we present a runtime reconfigurable nanomagnetic (RRN) adder design offering significant area efficiency and high speed operations. Subsequently, it is implemented using a micromagnetic simulation tool, by exploiting the reversal magnetization and energy minimization nature of the nanomagnets. We compute the carry and sum of the 1-bit full adder using only two majority gates comprising a total of 7 nanomagnets and single design layout. Consequently, the on-chip clocking schematic for the proposed RRN adder implementation for both horizontal and vertical layouts are introduced. The quantitative analysis of the required resources for higher bit adder architecture using the proposed design is performed and compared with state-of-the art. The proposed design methodology leads to ∼86%, ∼83% and ∼93% reduction in the number of nanomagnets, majority gates and clock cycles respectively resulting in an area efficient and high speed RRN adder architecture.

Dipole coupled magnetic quantum-dot cellular automata-based efficient approximate nanomagnetic subtractor and adder design approach

In this paper, we propose a dipole coupled magnetic quantum-dot cellular automata-based approximate nanomagnetic (APN) architectural design approach for subtractor and adder. In addition, we also introduce an APN architecture which offers runtime reconfigurability using a single design layout comprising only four nanomagnets. Subsequently, we propose the APN add/sub architecture by exploiting shape anisotropy and ferromagnetically coupled fixed input majority gate. The proposed APN architecture designs have been implemented using a micromagnetic simulation tool and performance has been compared with the state-of-the-art approach resulting in a ∼50%-80% reduction in the number of nanomagnets and clock cycles without degradation in the accuracy leading to area and energy efficiency.

Emergent Dynamics of Artificial Spin-Ice Lattice Based on an Ultrathin Ferromagnet

We present high-frequency dynamics of magnetic nanostructure lattices, fabricated in the form of "artificial spin-ice", that possess magnetically frustrated states. Dynamics of such structures feature multiple resonance excitation that reveals rich and intriguing microwave characteristics, which are highly dependent on field-cycle history. Geometrical parameters such as dimensions and ferromagnetic layer thickness, which control the interplay of different demagnetizing factors, are found to play a pivotal role in governing the dynamics. Our findings are highlighted by the evolution of unique excitations pertaining to magnetic frustration, which are well supported by static magnetometry studies and micromagnetic simulations.

Nanomagnetic logic design approach for area and speed efficient adder using ferromagnetically coupled fixed input majority gate

In this letter, we introduce the magnetic quantum-dot cellular automata (MQCA) based area and speed efficient design approach for nanomagnetic full adder implementation. We exploited the physical properties of three input MQCA majority gate (MG), where the fixed input of the MG is coupled ferromagnetically to one of the primary input operands. Subsequently we propose a design methodology, mapping logic and micromagnetic software implementation, validation of the binary full adder architecture built using two-three inputs MQCA MGs. In addition, we also analyzed our proposed design for switching errors to ensure bit stability and reliability. Our proposed design leads to ∼36%-69% reduction in the number of nanomagnets, ∼50%-75% reduction in the number of clock cycles and ∼33%-50% reduction in the number of MG operations required for the binary full adder implementation compared to the state of art designs.

Low-bias negative differential resistance in junction of a benzene between zigzag-edged phosphorene nanoribbons

We study the electron transport properties through the junction of a benzene molecule in conjunction with two monolayer zigzag-edged phosphorene nanoribbon (ZPNR) electrodes by applying the nonequilibrium Green's functions in combination with the density functional theory. We find that the molecular junction with two phosphorus-carbon bonds exhibits an interesting low-bias negative differential resistance effect with a peak-to-valley ratio of 29, which originates from the edge states in ZPNR due to the anisotropic band structure of phosphorene. Importantly, the performance of the junction can be tuned via the molecule-ZPNR interface bonding. The findings may be useful in sensitive-device applications. Furthermore, the physical mechanisms are revealed and discussed in terms of the electronic transmission spectrum, the evolution of the frontier molecular orbitals, the local device density of states around the Fermi level, and the projected density of states.

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.

Three-dimensional nanomagnetism

Magnetic nanostructures are being developed for use in many aspects of our daily life, spanning areas such as data storage, sensing and biomedicine. Whereas patterned nanomagnets are traditionally two-dimensional planar structures, recent work is expanding nanomagnetism into three dimensions; a move triggered by the advance of unconventional synthesis methods and the discovery of new magnetic effects. In three-dimensional nanomagnets more complex magnetic configurations become possible, many with unprecedented properties. Here we review the creation of these structures and their implications for the emergence of new physics, the development of instrumentation and computational methods, and exploitation in numerous applications.

Nanoscale magnetic devices play a key role in modern technologies but current applications involve only 2D structures like magnetic discs. Here the authors review recent progress in the fabrication and understanding of 3D magnetic nanostructures, enabling more diverse functionalities.

Interface-Induced Phenomena in Magnetism

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange spring magnets, spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and non-collinear spin textures, non-linear dynamics including spin torque transfer and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes.

Intra-wire coupling in segmented Ni/Cu nanowires deposited by electrodeposition

Segmented magnetic nanowires are a promising route for the development of three dimensional data storage techniques. Such devices require a control of the coercive field and the coupling mechanisms between individual magnetic elements. In our study, we investigate electrodeposited nanomagnets within host templates using vibrating sample magnetometry and observe a strong dependence between nanowire length and coercive field (25 nm-5 μm) and diameter (25-45 nm). A transition from a magnetization reversal through coherent rotation to domain wall propagation is observed at an aspect ratio of approximately 2. Our results are further reinforced via micromagnetic simulations and angle dependent hysteresis loops. The found behavior is exploited to create nanowires consisting of a fixed and a free segment in a spin-valve like structure. The wires are released from the membrane and electrically contacted, displaying a giant magnetoresistance effect that is attributed to individual switching of the coupled nanomagnets. We develop a simple analytical model to describe the observed switching phenomena and to predict stable and unstable regimes in coupled nanomagnets of certain geometries.

Spintronic Nanodevices for Bioinspired Computing

Bioinspired hardware holds the promise of low-energy, intelligent, and highly adaptable computing systems. Applications span from automatic classification for big data management, through unmanned vehicle control, to control for biomedical prosthesis. However, one of the major challenges of fabricating bioinspired hardware is building ultra-high-density networks out of complex processing units interlinked by tunable connections. Nanometer-scale devices exploiting spin electronics (or spintronics) can be a key technology in this context. In particular, magnetic tunnel junctions (MTJs) are well suited for this purpose because of their multiple tunable functionalities. One such functionality, non-volatile memory, can provide massive embedded memory in unconventional circuits, thus escaping the von-Neumann bottleneck arising when memory and processors are located separately. Other features of spintronic devices that could be beneficial for bioinspired computing include tunable fast nonlinear dynamics, controlled stochasticity, and the ability of single devices to change functions in different operating conditions. Large networks of interacting spintronic nanodevices can have their interactions tuned to induce complex dynamics such as synchronization, chaos, soliton diffusion, phase transitions, criticality, and convergence to multiple metastable states. A number of groups have recently proposed bioinspired architectures that include one or several types of spintronic nanodevices. In this paper, we show how spintronics can be used for bioinspired computing. We review the different approaches that have been proposed, the recent advances in this direction, and the challenges toward fully integrated spintronics complementary metal-oxide-semiconductor (CMOS) bioinspired hardware.

Focused-electron-beam-induced-deposited cobalt nanopillars for nanomagnetic logic

Nanomagnetic logic (NML) intends to alleviate problems of continued miniaturization of CMOS-based electronics, such as energy dissipation through heat, through advantages such as low power operation and non-volatile magnetic elements. In line with recent breakthroughs in NML with perpendicularly magnetized elements formed from thin films, we have fabricated NML inverter chains from Co nanopillars by focused electron beam induced deposition (FEBID) that exhibit shape-induced perpendicular magnetization. The flexibility of FEBID allows optimization of NML structures. Simulations reveal that the choice of nanopillar dimensions is critical to obtain the correct antiferromagnetically coupled configuration. Experiments carrying the array through a clocking cycle using the Oersted field from an integrated Cu wire show that the array responds to the clocking cycle.

Deterministic Control of Magnetization Dynamics in Reconfigurable Nanomagnetic Networks for Logic Applications

Information processing based on nanomagnetic networks is an emerging area of spintronics, as the energy consumption and integration density of the current semiconductor technology are reaching their fundamental limits. Nanomagnet-based devices rely on manipulating the magnetic ground states for device operations. While the static behavior of nanomagnets has been explored, little information is available on their dynamic behavior. Here, we demonstrate an additional functionality based on their collective dynamic response and explore the concept utilizing networks of bistable rhomboid nanomagnets. The control of the magnetic ground states of the networks was achieved by the geometrical design of the nanomagnets instead of the conventional interelement dipolar coupling. Dynamic responses of both the ferromagnetic and antiferromagnetic ground states were monitored using broadband ferromagnetic resonance spectroscopy, the Brillouin light scattering technique, and direct magnetic force microscopy. Micromagnetic simulations and numerical calculations validate our experimental observations. This method would have potential implications for low-power magnonic devices based on reconfigurable microwave properties.

Sub-nanosecond signal propagation in anisotropy-engineered nanomagnetic logic chains

Energy efficient nanomagnetic logic (NML) computing architectures propagate binary information by relying on dipolar field coupling to reorient closely spaced nanoscale magnets. Signal propagation in nanomagnet chains has been previously characterized by static magnetic imaging experiments; however, the mechanisms that determine the final state and their reproducibility over millions of cycles in high-speed operation have yet to be experimentally investigated. Here we present a study of NML operation in a high-speed regime. We perform direct imaging of digital signal propagation in permalloy nanomagnet chains with varying degrees of shape-engineered biaxial anisotropy using full-field magnetic X-ray transmission microscopy and time-resolved photoemission electron microscopy after applying nanosecond magnetic field pulses. An intrinsic switching time of 100 ps per magnet is observed. These experiments, and accompanying macrospin and micromagnetic simulations, reveal the underlying physics of NML architectures repetitively operated on nanosecond timescales and identify relevant engineering parameters to optimize performance and reliability.

Closely-spaced anisotropically-engineered single-domain nanomagnets may be exploited to encode and transmit binary information. Here, Gu et al. use time-resolved X-ray microscopy to image signal propagation at the intrinsic nanomagnetic switching limit in permalloy nanomagnet chains.

Multi-bit operations in vertical spintronic shift registers

Spintronic devices have in general demonstrated the feasibility of non-volatile memory storage and simple Boolean logic operations. Modern microprocessors have one further frequently used digital operation: bit-wise operations on multiple bits simultaneously. Such operations are important for binary multiplication and division and in efficient microprocessor architectures such as reduced instruction set computing (RISC). In this paper we show a four-stage vertical serial shift register made from RKKY coupled ultrathin (0.9 nm) perpendicularly magnetised layers into which a 3-bit data word is injected. The entire four stage shift register occupies a total length (thickness) of only 16 nm. We show how under the action of an externally applied magnetic field bits can be shifted together as a word and then manipulated individually, including being brought together to perform logic operations. This is one of the highest level demonstrations of logic operation ever performed on data in the magnetic state and brings closer the possibility of ultrahigh density all-magnetic microprocessors.

Spin-torque building blocks

The discovery of the spin-torque effect has made magnetic nanodevices realistic candidates for active elements of memory devices and applications. Magnetoresistive effects allow the read-out of increasingly small magnetic bits, and the spin torque provides an efficient tool to manipulate - precisely, rapidly and at low energy cost - the magnetic state, which is in turn the central information medium of spintronic devices. By keeping the same magnetic stack, but by tuning a device's shape and bias conditions, the spin torque can be engineered to build a variety of advanced magnetic nanodevices. Here we show that by assembling these nanodevices as building blocks with different functionalities, novel types of computing architecture can be envisaged. We focus in particular on recent concepts such as magnonics and spintronic neural networks.

Probabilistic aspects of magnetization relaxation in single-domain nanomagnets

A single-domain nanomagnet is a basic example of a system where relaxation from high to low energy is probabilistic in nature even when thermal fluctuations are neglected. The reason is the presence of multiple stable states combined with extreme sensitivity to initial conditions. It is demonstrated that for this system the probability of relaxing from high energies to one of the stable magnetization orientations can be tuned to any desired value between 0 and 1 by applying a small transverse magnetic field of appropriate amplitude. In particular, exact analytical predictions are derived for the conditions under which the probability of reaching one of the stable states becomes exactly 0 or 1. Under these conditions, magnetization relaxation is totally insensitive to initial conditions, and the final state can be predicted with certainty, a feature that could be exploited to devise novel magnetization switching strategies or novel methods for the measurement of the magnetization damping constant.