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As nanoelectronics approaches the nanometer scale, a massive effort is underway to identify the next scalable logic technology beyond Complementary Metal Oxide Semiconductor (CMOS) computing. Such computing technology needs to improve switching energy & delay at reduced dimensions, allow improved interconnects and provide a complete logic/memory family. However, a viable beyond-CMOS logic technology has remained elusive. Here, we propose a scalable spintronic logic device which operates via spin-orbit transduction combined with magneto-electric switching. The proposed Magneto-Electric Spin Orbit (MESO) logic enables a new paradigm to continue scaling of logic performance to near thermodynamic limits for GHz logic (100 kT switching energy at 100 ps delay). The proposed MESO devices scale strongly and favorably with critical dimensions of the device, showing a cubic dependence of switching energy on size, (E_m proportional to W^3), and square dependence on voltage (E_m proportional to V^2). The excellent scaling is obtained thanks to the properties of the spin orbit effects (e.g. Inverse Spin Hall Effect (ISHE) and Inverse Rashba-Edelstein Effect (IREE)) and the dependence of capacitance on size. The operating voltages for these devices are predicted to be < 100 mV allowing a significant jump ahead of historic trends of scaling voltage with size and corresponding reduction of energy. Interconnect resistance is a critical obstacle for scaling beyond 10 nm dimensions. We project a less detrimental impact of interconnect resistance and show that MESO logic is amenable for highly resistive interconnects (100 uOhm.cm-1 mOhm.cm) which opens a possibility to use nano-metallic (width < bulk electron mean free path) or doped semiconducting wires (width<5 nm). A scalable, CMOS compatible, non-volatile logic family proposed here may enable the next multi-generational scaling of computing devices., Comment: (60 pages, including supplementary) Updated Figure 3B. Contains expanded energy calculations, effect of SOC resistivity, supported with device simulations in supplementary Sections F,G

Efficient generation of spin currents from charge currents is of high importance for memory and logic applications of spintronics. In particular, generation of spin currents from charge currents in high spin-orbit coupling metals has the potential to provide a scalable solution for embedded memory. We demonstrate a net reduction in critical charge current for spin torque driven magnetization reversal via using spin-orbit mediated spin current generation. We scaled the dimensions of the spin-orbit electrode to 400 nm and the nanomagnet to 270 nm x 68 nm in a three terminal spin-orbit torque, magnetic tunnel junction (SOT-MTJ) geometry. Our estimated effective spin Hall angle is 0.15-0.20 using the ratio of zero temperature critical current from spin Hall switching and estimated spin current density for switching the magnet. We show bidirectional transient switching using spin-orbit generated spin torque at 100 ns switching pulses reliably followed by transient read operations. We finally compare the static and dynamic response of the SOT-MTJ with transient spin circuit modeling showing the performance of scaled SOT-MTJs to enable nanosecond class non-volatile MTJs.

We have measured the spin torques of beta-Tantalum / Co20Fe60B20 bilayers versus Ta thickness at room temperature using an FMR technique. The spin Hall coefficient was calculated both from the observed change in damping coefficient of the ferromagnet with Ta thickness, and from the ratio of the symmetric and anti-symmetric components of the FMR signal. Results from these two methods yielded values for the spin Hall coefficient of -0.090+/-0.005 and -0.11+/-0.01, respectively. We have also identified a significant out-of-plane spin torque originating from Ta, which is constant with Ta thickness. We ascribe this to an interface spin orbit coupling, or Rashba effect, due to the strength and constancy of the torque with Ta thickness. From fitting measured data to a model including interface spin orbit coupling, we have determined the spin diffusion length for beta-Tantalum to be ~2.5 nm., Comment: 18 pages, 10 figures, 1 table, submitted to Science

A coupled oscillator array is shown to approximate convolutions with Gabor filters for image processing tasks. Pixelated image fragments and filter functions are converted to voltages, differenced, and input into a corresponding array of weakly coupled Voltage Controlled Oscillators (VCOs). This is referred to as Frequency Shift Keying (FSK). Upon synchronization of the array, the common node amplitude provides a metric for the degree of match between the image fragment and the filter function. The optimal oscillator parameters for synchronization are determined and favor a moderate value of the Q-factor., Comment: 23 pages, 12 figures

We simulate automotion, the spontaneous transport of a magnetic domain wall under the influence of demagnetization and magnetic anisotropy, in nanoscale spintronic interconnects. In contrast to spin transfer driven magnetic domain wall motion, the proposed interconnects operate with only a transient current pulse and provide favorable scaling down to the 20nm scale. Cases of both in-plane and perpendicular magnetization are considered. Analytical dependence of the velocity of domain walls on the angle of magnetization are compared with full micromagnetic simulations. Deceleration, disappearance, and reflection of domain walls are demonstrated. Dependences of the magnetization angle on the current pulse parameters are studied. The energy and delay analysis suggests that automotion is an attractive option for spintronic logic interconnects., Comment: 9 figures, 25 pages

Multiple beyond-CMOS information processing devices are presently under active research and require methods of benchmarking them. A new approach for calculating the performance metric, energy-delay product, of such devices is proposed. The approach involves estimating the device properties of resistance and switching charge, rather than dynamic evolution characteristics, such as switching energy and time. Application of this approach to a wide class of charge-based and non-charge based devices is discussed. The approach suggests pathways for improving the performance of beyond-CMOS devices and a new realistic limit for energy-delay product in terms of the Planks constant., Comment: 7 pages 2 figures. Submitted to IEEE Transactions on Nanotechnology

Operation of the array of coupled oscillators underlying the associative memory function is demonstrated for various interconnection schemes (cross-connect, star phase keying and star frequency keying) and various physical implementation of oscillators (van der Pol, phase-locked loop, spin torque). The speed of synchronization of oscillators and the evolution of the degree of matching is studied as a function of device parameters. The dependence of errors in association on the number of the memorized patterns and the distance between the test and the memorized pattern is determined for Palm, Furber and Hopfield association algorithms., Comment: 32 pages, 20 figures

Multiple logic devices are presently under study within the Nanoelectronic Research Initiative (NRI) to carry the development of integrated circuits beyond the CMOS roadmap. Structure and operational principles of these devices are described. Theories used for benchmarking these devices are overviewed, and a general methodology is described for consistent estimates of the circuit area, switching time and energy. The results of the comparison of the NRI logic devices using these benchmarks are presented., Comment: 91 pages, 67 figures, 11 tables. Related to the conference presentation D. Nikonov and I. Young, Uniform Methodology for Benchmarking Beyond-CMOS Logic Devices, Proceedings of IEDM, 25.4 (2012)

In this letter, we show that Giant Spin Hall Effect (GSHE) MRAM can enable better energy- delay and voltage performance than traditional MTJ based spin torque devices at scaled nanomagnet dimensions (10-30 nm). Firstly, we derive the effect of dimensional scaling on spin injection efficiency, voltage-delay and energy-delay of spin torque switching using MTJs and GSHE and identify the optimum electrode geometry for low operating voltage (<0.1 V), high speed (>10 GHz) operation. We show that effective spin injection efficiency >100 % can be obtained using optimum spin hall electrode thickness for 30 nm nanomagnet widths. Finally, we derive the energy-delay trajectory of GSHE and MTJ devices to calculate the energy-delay product of GSHE and MTJ devices with an energy minimum at the characteristic time of the magnets. Optimized GSHE devices when combined with PMA can enable MRAM with scaled nanomagnets (30 nm X 60 nm), ultra-low voltage operation (< 0.1 V), fast switching times (10 ps) and switching energy as low as 100 aJ/bit., Comment: 16 pages, 5 figures

Spin torque majority gates are modeled and several regimes of magnetization switching (some leading to failure) are discovered. The switching speed and noise margins are determined for STMGs and an adder based on it. With switching time of 3ns at current of 80uA, the adder computational throughput is comparable to that of a CMOS adder., Comment: 4 pages, 14 figures, IEEE International Magnetic Conference Technical Digest, BT-08 (2012)

All-spin logic devices are promising candidates to augment and complement beyond-CMOS integrated circuit computing due to non-volatility, ultra-low operating voltages, higher logical efficiency, and high density integration. However, the path to reach lower energy-delay product performance compared to CMOS transistors currently is not clear. We show that scaling and engineering the nanoscale magnetic materials and interfaces is the key to realizing spin logic devices that can surpass energy-delay performance of CMOS transistors. With validated stochastic nano-magnetic and vector spin transport numerical models, we derive the target material and interface properties for the nanomagnets and channels. We identified promising new directions for material engineering/discovery focusing on systematic scaling of magnetic anisotropy (Hk) with saturation magnetization (Ms), use of perpendicular magnetic anisotropy, and interface spin mixing conductance of ferromagnet/spin channel interface (Gmix). We provide systematic targets for scaling spin logic energy-delay product toward a 2 aJ.ns energy-delay product, comprehending the stochastic noise for nanomagnets., Comment: 21 pages, 8 figures

We propose an all spin state element to enable all spin state machines using spin currents and nanomagnets. We demonstrate via numerical simulations the operation of a state element a critical building block for synchronous, sequential logic computation. The numerical models encompass Landau-Lifshitz-Gilbert (LLG) nanomagnet dynamics with stochastic models and vector spin-transport in metallic magnetic and non-magnetic channels. Combined with all spin combinatorial logic, the state elements can enable synchronous and asynchronous computing elements., Comment: 21 pages, 6 figures

We introduce an analytical framework to understand the path for scaling nanophotonic interconnects to meet the energy and footprint requirements of CMOS global interconnects. We derive the device requirements for sub 100 fJ/cm/bit interconnects including tuning power, serialization-deserialization energy, optical insertion losses, extinction ratio and bit error rates. Using CMOS with integrated nanophotonics as an example platform, we derive the energy/bit, linear and areal bandwidth density of optical interconnects. We also derive the targets for device performance which indicate the need for continued improvements in insertion losses (<8dB), laser efficiency, operational speeds (>40 Gb/s), tuning power (<100 {\mu}W/nm), serialization-deserialization (< 10 fJ/bit/Operation) and necessity for spectrally selective devices with wavelength multiplexing (> 6 channels)., Comment: Accepted to IEEE Journal of Special Topics in Quantum Electronics

We present a theoretical and a numerical formalism for analysis and design of spintronic integrated circuits (SPINICs). The formalism encompasses a generalized circuit theory for spintronic integrated circuits based on nanomagnetic dynamics and spin transport. We propose an extension to the Modified Nodal Analysis technique for the analysis of spin circuits based on the recently developed spin conduction matrices. We demonstrate the applicability of the framework using an example spin logic circuit described using spin Netlists., Comment: 14 pages, 11 figures; added fig. 2; added citations; modified title to emphasize SPICE; Results unchanged