Nanomagnetic Logic Circuits Research Articles

Efficient architecture for arithmetic designs using perpendicular NanoMagnetic Logic

As the process of scaling down continues at a rapid pace, there is a growing need for an alternative semiconductor device to replace CMOS. One of the alternatives that attracted a lot of attention is called nanomagnetic logic (NML). This is because NML delivers a high device density in addition to a non-volatility of stored information, beyond-CMOS technologies, and device work at room temperature. It is necessary to lower the circuit density and increase the speed of circuits like adders. Using emerging NML logic, we created a full-adder, and ripple carry adder (RCA) with a minimum area. As a result, the invented multilayer-based decimal design makes use of RCA, and full-adder, for innovative 3D topology. We used an NML framework built with perpendicular nanomagnetic (pNML) layers to simulate the characteristics of these devices. With the adder designs that have been offered the latency values are relatively low while performing exhaustive testing. Using pNML technology, a decimal adder has been constructed for the first time in the literature. In addition, simulations are carried out with the help of the Modelsim simulator. During the process of nanomagnetic designing consideration is given to both of these aspects as latency and area. To create an NML circuit, the tool MagCAD is employed. Results are better using the pNML environment-based full adder, RCA and decimal adder.

A nanomagnets majority logic gate based on heterogeneous multiferroic structure global strain clock

<sec>In the post-Moore era, nanomagnetic logic circuits have shown great potential to replace complementary metal oxide semiconductor (CMOS) circuits. A majority logic gate, as the core of a nanomagnetic logic circuit, is equivalent to the inverter in the CMOS circuit. A nanomagnetic logic majority gate generally has four nanomagnets arranged in a “T” shape. The nanomagnets in the three corners of the “T” (<i>I</i><sub>1</sub>, <i>I</i><sub>2</sub>, <i>I</i><sub>3</sub>) are the three inputs, and the middle nanomagnet is the output (<i>O</i>).</sec><sec>This paper proposes a nanomagnet majority logic gate based on the global strain clock of heterogeneous multiferroic structure, by utilizing the difference in response to the same strain between positive magnetostrictive coefficient material (Terfenol-D) and negative magnetostrictive coefficient material (Ni). From bottom to top, the device is mainly composed of a silicon substrate, a piezoelectric layer, and four elliptical cylindrical nanomagnets. PMN-PT is used as the piezoelectric layer’s material, and three Ni-based nanomagnets (<i>I</i><sub>1</sub>, <i>I</i><sub>2</sub>, and <i>I</i><sub>3</sub>) are utilized as input, while Terfenol-D is used as the material for the output nanomagnet (<i>O)</i>.</sec><sec>Besides, a two-step calculation mode of “high-stress start-low-stress calculation” is designed, that is, the <i>O</i> is first switched to the “Null” with a stress of –30 MPa, and then the stress decreases to –15 MPa, so that the <i>O</i> can realize majority calculation under the coupling of <i>I</i><sub>1</sub>, <i>I</i><sub>2</sub>, and <i>I</i><sub>3</sub>. The micromagnetic simulation software MuMax3 is adopted to simulate the performance of the device. The results reveal that the device can successfully perform continuous majority calculation through any three-terminal input combination. By using the two-step calculation mode, the calculation accuracy of the device can reach 100%, its cycle of continuous calculation is 2.75 ns, and the cycle energy consumption is about 64 aJ. It is found that the change of energy potential well, caused by the change of stress anisotropy energy and dipole coupling energy, is the main reason that determines the magnetization dynamic behavior of the device. Therefore, the results of this paper can provide important guidance for designing nanomagnetic logic circuits.</sec>

Two-qubit logic gates based on the ultrafast spin transfer in π-conjugated graphene nanoflakes

Ultrafast optical spin control allows gate operations to be performed within picosecond time scale, orders of magnitude faster than microwave or electrical control. Here, using high-level quantum chemical computations, we suggest several two-qubit logic gates based on the optically induced ultrafast spin-flip and spin-transfer processes on rhombic graphene nanoflakes (Co4-GNF). It is demonstrated that Co atoms chemisorbed on π-conjugated C atoms can significantly influence the spin properties of the system. The spin density of different energy levels is distributed on different Co atoms, thus opening channels for successful spin-transfer processes between the Co atoms. Reversible local spin-flip processes on each Co atom as well as global spin-transfer processes between the Co atoms are realized. By carefully combining the various spin-dynamics processes achieved in our Co4-GNF structure, both classical (OR, AND, NAND) and quantum (CNOT, SWAP) binary logic gates are constructed. All spin manipulation processes finish at the subpicosecond time scale with fidelities above 96%. This theoretical design, which is exclusively based on laser-induced ultrafast spin dynamics, represents a novel implementation of qubit manipulation and can thus pave the way towards the construction of nano magnetic logic circuits and spintronic devices.

Design and implementation of a nano magnetic logic barrel shifter using beyond-CMOS technology

Abstract Bit manipulation plays a significant role in high-speed digital signal processing (DSP) and data computing systems, and shift and rotation operations are crucial functions in it. In general, barrel shifters are used to perform these operations effectively. Nano magnetic logic circuits are among the promising beyond-CMOS alternative technologies for the design of high-speed circuits. Most of the existing circuits that have been developed using nano magnets are combinational circuits. In this work, a barrel shifter is implemented and realised using in-plane nano magnetic logic. The proposed design is the first of its kind nano magnetic logic circuit. The nano magnetic logic circuit implementation, layout generation, simulation, and validation were performed using the ToPoliNano and ModelSim tools. The logical equivalent design was synthesised and evaluated using the Synopsys Design Compiler tool. The proposed barrel shifter was realised using majority logic has 1769037 nano magnets with a boxing area of 481 × 13104 µm2 and 3276 clock zones after optimisation with the Barycenter algorithm. The proposed barrel shifter realised using Boolean logic has 315276 nano magnets with a boxing area of 265 × 5028 µm2 and 1257 clock zones after optimisation with the Barycenter algorithm. The proposed design results demonstrate that complex systems can be developed using nano magnetic logic by combining combinational and sequential circuits.

Design and simulation of reliable and fast nanomagnetic conservative quantum-dot cellular automata (NCQCA) gate

Nanomagnetic logic (NML) is a promising candidate for the real implementation of quantum-dot cellular automata circuits and can be a proper alternative or complement to CMOS circuits. Like any other nanoscale technologies, NML circuits are also subject to fabrication variations. These variations along with fluctuations caused by thermal noise can affect the performance of these circuits. Therefore, design of NML circuits with high testability is an absolute necessity. Circuits based on conservative logic are inherently testable because of their specific properties. In this paper, considering the physical and geometrical properties of nanomagnets, a nanomagnetic conservative quantum-dot cellular automata gate is designed and evaluated. This circuit can be used as the basic block for the realization of more complex conservative NML circuits. To implement this circuit, the design of the clocked nanomagnetic majority gate is also provided. The OOMMF physical simulation tool is used for simulation and evaluation. The results show the correct functionality of the proposed conservative gate at room temperature. It operates about 34% faster than the NML Fredkin gate. Moreover, the NML version of the conventional Fredkin gate takes 90% more area than the proposed design.

Chiral switching and dynamic barrier reductions in artificial square ice

Collective dynamics in lithographically-defined artificial spin ices offer profound insights into emergent correlations and phase transitions of geometrically-frustrated Ising spin systems. Their temporal and spatial evolution are often simulated using kinetic Monte Carlo (kMC) simulations, which rely on the precise knowledge of the switching barriers to obtain predictive results in agreement with experimental observations. In many cases, however, the barriers are derived from simplified assumptions only, and do not take into account the full physical picture of nanomagnetic switching. Here we describe how the immediate magnetic square- or kagome-ice environment of a nanomagnet reversing via quasi-coherent rotation can induce clockwise and counter-clockwise switching channels with different barrier energies. This energy splitting for chiral reversal channels can be sizeable and, as string-method micromagnetic simulations show, is relevant for artificial spin ice systems made of both exchange- as well as magnetostatically-dominated units. Due to the barrier splitting and further reductions due to non-uniform reversal, transition rates can be exponentially enhanced by several orders of magnitude compared to mean-field predictions, especially in the limit of rare switching events where thermal excitation is less likely. This leads to significantly faster relaxation time scales and modified spatial correlations. Our findings are thus of integral importance to achieve realistic kMC simulations of emergent correlations in artificial spin systems, magnonic crystals, or the evolution of nanomagnetic logic circuits.

Two-Qubit Logic Gates Based on the Ultrafast Spin Transfer in π-Conjugated Graphene Nanoflakes

Ultrafast optical spin control allows gate operations to be performed within a picosecond timescale, orders of magnitude faster than microwave or electrical control. Here, using high-level quantum chemical computations, we suggest a two-qubit logic gate based on the optically induced ultrafast spin-flip and spin-transfer processes over rhombic graphene nanoflakes (Co4-GNF). It is demonstrated that the π-conjugated Co atoms can significantly influence the spin properties of the system. The spin density is distributed on different Co atoms in different energy levels, in this way opening a channel for successful spin-transfer processes between the Co atoms. Thus, the reversible local spin-flip processes on each Co atom and global spin-transfer processes between the Co atoms are realized. Importantly, based on various spin-dynamics processes achieved in Co4-GNF structures, both classical (OR, AND, NAND) and quantum (CNOT, SWAP) two-qubit logic gates are constructed, and the spin manipulation process can be completed in subpicosecond timescale with fidelity above 96%. This theoretical design based on the laser-induced ultrafast spin dynamics provides a new implementation of qubit manipulation, which could pave the way towards the construction of nano magnetic logic circuits and spintronic devices.

Design and evaluation of clocked nanomagnetic logic conservative Fredkin gate

Nanomagnetic logic (NML) has recently been proposed as an attractive and promising implementation of QCA and also as a possible alternative to the CMOS technology. With this emerging technology, it is possible to process and store binary information according to the magnetization state of nanomagnets. Similar to other nanotechnologies, NML circuits are also sensitive to fabrication variations and thermal fluctuations. Therefore, it is highly consequential to improve the testability of these circuits. Circuits based on conservative logic inherently enhance test performance. In this paper, the Fredkin gate, which is one of the most famous conservative reversible gates has been designed and simulated in NML by considering the physical properties of nanomagnets. It can be used to design other testable and ultra-low-power NML circuits as well. OOMMF physical simulation tool is used to simulate and validate the proposed gate at room temperature. The results indicate the correct functionality of the design.

Pushing down the lateral dimension of single and coupled magnetic dots to the nanometric scale: Characteristics and evolution of the spin-wave eigenmodes

Planar magnetic nanoelements, either single- or multi-layered, are exploited in a variety of current or forthcoming spintronic and/or ICT devices, such as read heads, magnetic memory cells, spin-torque nano-oscillators, nanomagnetic logic circuits, magnonic crystals and artificial spin-ices. The lateral dimensions of the elemental magnetic components have been squeezed down during the last decade to a few tens of nanometers, but they are still an order of magnitude larger that the exchange correlation length of the constituent materials. This means that the spectrum of spin-wave eigenmodes, occurring in the GHz range, is relatively complex and cannot be described within a simple macrospin approximation. On the other hand, a detailed knowledge of the dynamical spectrum is needed to understand or to predict crucial characteristics of the devices. With this focused review we aim at the analysis and the rationalization of the characteristics of the eigenmodes spectrum of magnetic nanodots, paying special attention to the following key points: (i) Consider and compare the case of in-plane and out of-plane orientation of the magnetization, as well as of single- and multi-layered dots, putting in evidence similarities and diversities, and proposing a unifying nomenclature and labelling scheme; (ii) Underline the evolution of the spectrum when the lateral size of magnetic dots is squeezed down from hundreds to tens of nanometers, as in current devices, with emphasis given to the occurrence of soft modes and to the change of spatial localization of the fundamental mode for in-plane magnetized dots; (iii) Extend the analysis from isolated elements to twins of dots, as well as to dense arrays of dipolarly interacting dots, showing how the discretized eigenmodes distinctive of the single element transform in finite-width frequency bands of spin waves propagating through the array.

Physical Simulations of High Speed and Low Power NanoMagnet Logic Circuits

Among all “beyond CMOS” solutions currently under investigation, nanomagnetic logic (NML) technology is considered to be one of the most promising. In this technology, nanoscale magnets are rectangularly shaped and are characterized by the intrinsic capability of enabling logic and memory functions in the same device. The design of logic architectures is accomplished by the use of a clocking mechanism that is needed to properly propagate information. Previous works demonstrated that the magneto-elastic effect can be exploited to implement the clocking mechanism by altering the magnetization of magnets. With this paper, we present a novel clocking mechanism enabling the independent control of each single nanodevice exploiting the magneto-elastic effect and enabling high-speed NML circuits. We prove the effectiveness of this approach by performing several micromagnetic simulations. We characterized a chain of nanomagnets in different conditions (e.g., different distance among cells, different electrical fields, and different magnet geometries). This solution improves NML, the reliability of circuits, the fabrication process, and the operating frequency of circuits while keeping the energy consumption at an extremely low level.

NMLSim: a Nanomagnetic Logic (NML) circuit designer and simulation tool

Nanomagnetic Logic (NML) is a new technology based on nanomagnets. Logic operations are performed at room temperature through dipolar magnetostatic interactions. The low switching energies involved in the operation of NML circuits in addition to the possibility of higher integration density are remarkable advantages of this technology over CMOS-based systems. Although intense work has been done on the physical behavior of the NML systems, simulation tools for the study of large and complex NML architectures are lacking. In this paper, we present a fast and robust computational tool that allows the design and simulation of complex NML circuits. We developed a new fast simulation engine based on single-domain approximation able to capture both the static and dynamic behaviors of the system. The tool simulates the clock, the magnet influence in between neighbors and the thermal effect on the circuit. Initial results show a good agreement with experimental and micromagnetic simulations works. To the best of our knowledge, this is the first open-source NML simulator available and serves as a complete tool to design and evaluate complex NML circuits.

Shape Anisotropy and Resonance Mode Guided Reliable Interconnect Design for In-plane Magnetic Logic**Supported by the National Natural Science Foundation of China under Grant No 61302022.

Dipole coupled nanomagnets controlled by the static Zeeman field can form various magnetic logic interconnects. However, the corner wire interconnect is often unreliable and error-prone at room temperature. In this study, we address this problem by making it into a reliable type with trapezoid-shaped nanomagnets, the shape anisotropy of which helps to offer the robustness. The building method of the proposed corner wire interconnect is discussed, and both its static and dynamic magnetization properties are investigated. Static micromagnetic simulation demonstrates that it can work correctly and reliably. Dynamic response results are reached by imposing an ac microwave field on the proposed corner wire. It is found that strong ferromagnetic resonance absorption appears at a low frequency. With the help of a very small ac field with the peak resonance frequency, the required static Zeeman field to switch the corner wire is significantly decreased by ∼21 mT. This novel interconnect would pave the way for the realization of reliable and low power nanomagnetic logic circuits.

MagCAD: Tool for the Design of 3-D Magnetic Circuits

The post-CMOS scenario poses many challenges to researchers. Innovative solutions must be found to further improve electronic circuits. Exploiting the potential offered by the third dimension is clearly one of the best possibilities available. However, due to the lack of a simple and straightforward methodology, it is difficult to analyze and compare beyond-CMOS technologies. We tackle this challenge by presenting a framework that enables the design of 3-D circuits based on field-coupled technologies. The tool is called MagCAD and is part of the ToPoliNano design suite, created to design and simulate circuits based on emerging technologies by applying a top–down methodology. Right now, MagCAD supports the two main implementations of nanomagnetic logic (NML), the in-plane NML, and the perpendicular NML (pNML). However, it is designed to be easily extended to other beyond-CMOS technologies. Researchers can design pNML circuits by using MagCAD, which embeds design rules, physical models, and technological parameters. The compact model and the physical properties of these cells are based on experimental results. After the design phase, a register-transfer-level model of the circuit is automatically extracted by MagCAD. The model is written in VHSIC Hardware Description Language and has been validated through experiments. The extracted model can be simulated with fast HDL-simulators; this makes it possible to verify the behavior and extract the performance of the designed circuit. With MagCAD, designers have the possibility to easily design, simulate, and compare 3-D NML circuits, exploring the advantages provided by the third dimension freely.

Controlling operation timing and data flow direction between nanomagnet logic elements with spatially uniform clock fields

We demonstrate a reliable method for controlling the operation timing and data flow direction in a nanomagnet logic (NML) circuit with spatially uniform magnetic fields. We introduce a data and buffer nanomagnet, which have the same shape, but their magnetic easy axes are at an angle of 45° to each other. We also introduce a ferromagnetically and an antiferromagnetically coupled arrangement of the nanomagnets. Using this method, we perform bit shift operations on 3-bit NML shift registers. This method provides a means of fabricating highly integrated NML circuits with a simplified structure.

Domain Wall Interconnections for NML

Nanomagnet logic (NML) is one of the most novel solutions studied as complementary technology to CMOS transistors. Information propagation involves only a change in spin orientation, no charge movement is present. Since the basic element is a nanomagnet, NML circuits have no stand-by power consumption and the ability to mix logic and memory in the same device. While CMOS is a multilayer technology, until now NML is confined to one single physical layer. The consequence is that circuit area grows exponentially due to interconnections overhead. In this paper, we present an innovative solution that drastically reduces the area wasted for interconnection wires relying on the properties of domain walls (DWs). We mix DWs and NML technologies in a unique DW logic (DWL) solution that exploits the advantages of both technologies. The proposed solution is technologically compatible with up-to-date fabrication processes. All the results here presented for the NML logic blocks and the DWs interconnections and their combination are obtained through rigorous micromagnetic simulations. Moreover, we implemented as a case study an high performance adder (Pentium 4 adder) and evaluated its features with increasing parallelism and compared with the simple NML implementation in order to explore the potential of DWL technology at circuit and architectural level. The reduction in circuit area corresponds to a notable reduction in both the latency and power consumption. The improvements in NML technology are shown by both the remarkable performance improvement and new possibilities offered by this novel solution.

Design of MRAM-Based Magnetic Logic Circuits

Emerging technologies are gaining an increasing attention due to the slowdown of CMOS development. NanoMagnet Logic (NML), among emerging technologies, increases the potentials for developing fully magnetic circuits. Using a magnet as a building block for logic circuits has the advantage to merge logic and memory in the same device. Moreover, circuits have low dynamic and no stand-by power consumption. Even though demonstrations exist for small circuits, the experimental feasibility of complex NML circuits still represents a critical point for this technology. In this paper, we outline the possibility to design NML circuits based on the technological structure of magnetic RAMs (MRAMs). NML circuits based on MRAMs rely on a well-developed technology that provides a natural interface with CMOS world. To study this new NML implementation a novel tool, NANOcom, was developed to easily design complex circuits. Simulations were then performed using an high-level behavioral model described using VHDL language. Two types of circuit layouts, based on different technological constraints, are investigated. To evaluate the performance of this new NML implementation, a 4-bit Galois multiplier is used as a testbench. The Galois multiplier is the basic block of cryptographic circuits, an ideal target for this technology. Results obtained are encouraging and can unlock interesting options for the future development of NML technology.

Analysis of the Magnetostatic Energy of Chains of Single-Domain Nanomagnets for Logic Gates

Nanomagnet logic (NML) circuits are magnetic field-coupled interacting structures built up from nanoscaled magnets to perform logic operations. The bistable character of nanomagnets’ magnetization is associated with “0” and “1” logic states, which may be used to perform Boolean operations. In this paper, we first investigate the limits of single-domain magnetic structure in modeling the magnetostatic energy of particles of several polyhedron shapes. The model, which is based on the evaluation of multidimensional integrals through the Monte Carlo method, includes the demagnetizing energy of individual magnetic specimens and the dipolar coupling between two or more nanomagnets. The accuracy and the limits of the model are evaluated through comparison with a well-established numerical micromagnetic solver. The magnetostatic behavior for several configurations of horizontal chain of interacting nanomagnets (NML wire) is investigated. Rectangular nanomagnets present weak dipolar antiferromagnetic (AF) coupling that may result in error during information propagation across the chain. We examine a novel wire structure formed by a sequence of different slanted nanomagnets that yield strong dipolar coupling. For this system, error during information propagation is very unlikely, since the magnetic energy of the particles has single global minima corresponding to stable AF alignment. The proposed model can be readily applied as a tool for the study of advanced NML circuits and systems.

ToPoliNano: A CAD Tool for Nano Magnetic Logic

In the post-CMOS scenario, field coupled nanotechnologies represent an innovative and interesting new direction for electronic nanocomputing. Among these technologies, nanomagnet logic (NML) makes it possible to finally embed logic and memory in the same device. To fully analyze the potential of NML circuits, design tools that mimic the CMOS design-flow should be used for circuit design. We present, in this paper, the latest and improved version of Torino Politecnico Nanotechnology (ToPoliNano), our design and simulation framework for field coupled nanotechnologies. ToPoliNano emulates the top-down design process of CMOS technology. Circuits are described with a VHSIC hardware description language netlist and layout is then automatically generated considering in-plane NML (iNML) technology. The resulting circuits can be simulated and performance can be analyzed. In this paper, we describe several enhancements to the tool itself, like a circuit editor for custom design of field coupled nanodevices, improved algorithms for netlist optimization and new algorithms for the place and route of iNML circuits. We have validated and analyzed the tool by using extensive metrics, both by using standard circuits and ISCAS’85 benchmarks. This contribution highlights the improvements of ToPoliNano, which is now a innovative and complete tool for the development of iNML technology.

Reconfigurable Systolic Array: From Architecture to Physical Design for NML

NanoMagnet logic (NML) is among the emerging technologies that might replace CMOS in the next decades. According to its physical characteristics, to better exploit the potential of this technology—and of other similar ones—the use of parallel architectures with regular layout that avoid long interconnection signals is advised. Systolic arrays (SAs) are among these architectures, being composed of a grid of equal processing elements that are locally interconnected. However, they are usually implemented to execute only a small set of algorithms, and for this reason, throughout the years, they have not been an appealing solution for CMOS. To seriously analyze the potentials of NML, complex architectures must be conceived, and their physical implementation explored considering realistic technological constraints. With the increasing complexity of NML circuits, two issues, then, are noticed: 1) the need for a regular structure arises, that at the same time helps to reduce the intrinsic pipelining nature of NML and can be configured to be used for several applications without developing a dedicated design for each algorithm and 2) the capability to synthesize, place and route NML circuits is fundamental to demonstrate the feasibility of the architecture in two important conditions: efficiently managing the complexity of the design and sticking to the characteristics that are technologically feasible at the time of writing. In this paper, we address these issues presenting a new reconfigurable SA that can be programmed to execute different algorithms, and we provide two examples to show its working principle. Moreover, the array is synthesized and simulated with the aid of the first real tool for nanotechnology circuits that we have conceived, Torino Politecnico Nanotechnology tool. The joint contribution at both the architectural and physical design levels gives a relevant step forward to the state of the art in the demonstration of this emerging technology potential.

Modeling, Design, and Analysis of MagnetoElastic NML Circuits

With the predicted end of CMOS scaling process, researchers started to study several alternative technologies. Among them NanoMagnet Logic (NML) offers advantages complementary to MOS transistors especially for its magnetic nature. Its intrinsic memory capability makes it suitable for zero stand-by power and logic-in-memory applications. NML requires a clock system that, if based on a magnetic field, highly increases the circuit dynamic power consumption. We have recently proposed a solution based on the magnetoelastic effect (ME-NML) [1] and on currently available fabrication processes, which drastically reduces dynamic power consumption. However, many questions still remain unanswered. Which kind of applications are best suited for this technology? How can we effectively design, analyze, and compare ME-NML circuits? Does it really offer advantages over state-of-the-art CMOS transistors? In this paper, we provide answers to all these questions and the results prove that this technology offers indeed extremely good performance. We have designed a Galois field multiplier with a systolic array structure to reduce interconnection overhead. We developed a new RTL model that allows us to easily describe and simulate circuits of any complexity, evaluating at the same time the performance and keeping into account technology constraints. We approach for the first time in the NML scenario the design of ME-NML circuits adopting the standard-cell method used in standard technologies and fulfill the design down to the physical level. The same circuit is designed also with NML technology based on magnetic fields and with a 28 nm low power CMOS bulk technology for comparison. The CMOS circuit is obtained through physical place&route with a commercial tool, providing, therefore, the most accurate comparison ever presented in literature. Power analysis shows that ME-NML circuits have a considerable advantage over both NML and state-of-the-art CMOS bulk technology. As a further by-product results clearly highlight which kind of architectures can better exploit the true potential of NML technology.