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Integrated magnonic half-adder

Qi Wang, Roman Verba, Thomas Brächer, Florin Ciubotaru, Christoph Adelmann, Sorin D. Cotofana, Philipp Pirro, Andrii V. Chumak

arXiv:1902.02855v2physics.app-phcond-mat.othercs.ET

TL;DR

Integrated magnonic circuits with at least two logic gates suitable for further integration remain an unresolved challenge. This paper numerically tests a magnonic half-adder, whose full functionality uses only three nanowires in one planar layer.

  • Problem

    Realizing integrated magnonic circuits with at least two logic gates suitable for further integration remains an unresolved challenge.

    Source: p. 2

  • Method

    The authors propose and numerically test a magnonic half-adder comprising two logic gates.

    Source: Discussion · p. 15

  • Results

    The half-adder demonstrates its whole functionality using only three nanowires in one planar layer.

    Source: Discussion · pp. 13, 15

  • Takeaways & Limitations

    The integrated circuit is potentially suited for further integration with other logic gates relying on the same concept.

    Source: Discussion · p. 15

    The reported energy consumption accounts only for energy within the magnonic domain.

    Source: Discussion · p. 14

Abstract

from arXiv · show

Spin waves and their quanta magnons open up a promising branch of high-speed and low-power information processing. Several important milestones were achieved recently in the realization of separate magnonic data processing units including logic gates, a magnon transistor and units for non-Boolean computing. Nevertheless, the realization of an integrated magnonic circuit consisting of at least two logic gates and suitable for further integration is still an unresolved challenge. Here we demonstrate such an integrated circuit numerically on the example of a magnonic half-adder. Its key element is a nonlinear directional coupler serving as combined XOR and AND logic gate that utilizes the dependence of the spin wave dispersion on its amplitude. The circuit constitutes of only three planar nano-waveguides and processes all information within the magnon domain. Benchmarking of the proposed device is performed showing the potential for sub-aJ energy consumption per operation.

Discussion

The discussion assesses the half-adder’s energy use, footprint, and delay, along with scaling, amplification costs, and ways to reduce energy consumption. It also considers the numerically tested circuit’s integration of two logic gates, magnon-domain control, and potential for further integration and low energy consumption.

Energy consumption

  • The energy estimate is independent of coupler characteristics and spin-wave amplitude; reducing waveguide cross-section or finding mechanisms with higher nonlinearity are proposed ways to lower it.Exchange spin waves do not reduce energy consumption: their higher group velocity in the exchange region increases it.Source: Discussion · p. 11

Scalability and delay time

  • The device’s estimated minimum N is 6, and a half-adder simulated with N = 6 has total energy and delay close to estimates but a slightly larger area.The simulations used N = 14; the minimum N condition is that Directional Coupler 1 does not significantly change its characteristics at the power needed to switch Directional Coupler 2.Source: Discussion · pp. 11–12
  • The simulated 100 nm half-adder has an area of 5.58 µm2, while the estimated miniaturized device has an area of 1.016 µm2.The core consists of three nanowires in one planar layer; the 1.016 µm2 estimate is not a fundamental limit and reflects current fabrication technology.Source: Discussion · pp. 12–13
  • 150 ns is the input-to-output propagation time in the presented design; the second device is estimated at 18 ns, versus 60 ps for 7 nm CMOS.The authors note that the 18 ns magnonic delay remains much larger than the CMOS delay.Source: Discussion · pp. 13–14, Table 1 · p. 13

Energy consumption

  • The reported total energy consumption for operations is 24.6 aJ, similar to current CMOS at 35.3 aJ calculated using Cadence Genus; the miniaturized device energy is around 1.96 aJ.Source: Discussion · p. 14

Spin-wave amplifiers

  • The output S requires amplification, and simulated parallel parametric pumping consumes around 105 aJ, with potential for a one- or two-order-of-magnitude reduction through optimization.The amplifier energy must be added to the half-adder’s energy consumption.Source: Discussion · p. 14

Discussion

  • Voltage-control magnetic-anisotropy parametric pumping uses rf electric rather than magnetic/current fields, estimated at ~3 aJ per device for nm-thick CoFeB; an experimental realization was reported [49].The energy estimate is for a nm-thick CoFeB film.Source: Discussion · pp. 14–15
  • The voltage-control approach should also apply to YIG if an additional piezoelectric layer is placed on top.Source: Discussion · p. 15
  • The proposed half-adder comprises two logic gates, is numerically tested, and is potentially suited for integration with other gates based on the same concept.Magnons control magnons without conversion to the electric domain, which the authors say ensures low energy consumption.Source: Discussion · p. 15
  • One directional coupler acts as a power splitter and the other as a nonlinear switch, whose operation uses the spin-wave frequency shift with increasing amplitude.An analytic theory describes the shift and is verified numerically along with the half-adder’s functionality.Source: Discussion · p. 15
  • The three-nanowire magnonic half-adder uses one amplifier on output S, substitutes 14 electronic transistors, and at 100 nm has characteristics comparable to a 7 nm CMOS half-adder.The authors also identify potential for miniaturization and further improvement.Source: Discussion · p. 15

Methods

The methods combine linear spin-wave dispersion and nonlinear frequency-shift calculations with GPU-accelerated MuMax3 simulations of a YIG half-adder; the simulations use defect-free waveguides and omit temperature.

Spin-wave dispersion calculation in the linear region

  • The linear-region dispersion used the Landau–Lifshitz equation in the linear, damping-free approximation, following; the coupled-waveguide relation resolves two modes with dynamic magneto-dipolar interaction.Source: Methods · pp. 15–16

Nonlinear frequency shift

  • The isolated-waveguide nonlinear frequency-shift coefficient was calculated using, assuming a uniform mode profile across the waveguide and negligible static demagnetization along its length.The coefficient is given in.Source: Methods · p. 16

Micromagnetic simulations

  • Micromagnetic simulations of the YIG half-adder used exchange constant A = 3.5 pJ/m and Gilbert damping α = 2×10^-4, with no external bias field applied.A sinusoidal magnetic field was applied to excite propagating spin waves, and fast Fourier transformation was performed from 250 ns to 300 ns.Source: Methods · p. 17
  • The simulations assumed defect-free waveguides and omitted temperature; edge roughness, trapezoidal cross-sections, and temperature effects were treated as negligible.Source: Methods · p. 17

Calculation of energy consumption of 7 CMOS half-adder. We considered a 7nm

A Cadence Genus evaluation of a 7nm CMOS half-adder standard cell reports 587.994nW total power consumption, with dynamic power dominating.

Supplementary Material Integrated magnonic half-adder

The supplementary material outlines an energy-consumption estimate for the magnonic half-adder, a modified half-adder with a fan-out gate, and analyses of spin-wave amplifiers.

Section S1

Section S2

Section S3

S1. Energy consumption for magnonic half-adder

The section estimates magnonic-circuit energy from the spin-wave pulse, neglecting transducers, and derives constraints on pulse and coupler parameters. It sets a minimum nonlinear-coupler size of N_min = 6 under the stated same-gap assumption.

S1. Energy consumption for magnonic half-adder

  • Energy is estimated as the spin-wave pulse energy, neglecting transducers, with pulse volume V = S v_gr t.Here S is the waveguide cross-section, v_gr the spin-wave group velocity, and t the pulse duration.Source: S1. Energy consumption for magnonic… · p. 22
  • The spin-wave amplitude must suffice to switch the nonlinear directional coupler, while pulse duration is constrained for stable operation of both coupler types.The stated pulse-width condition is more severe for the nonlinear case than for the linear case.Source: S1. Energy consumption for magnonic… · pp. 22–23
  • N_min = 6 is required so a linear coupler at half its coupling length does not significantly change transmission at the switching power, assuming equal gaps.The linear-regime transmission rate is 1/2.Source: S1. Energy consumption for magnonic… · p. 23

S2 Modified half-adder with fan-out gate

The modified half-adder adds a fan-out gate at Output I, enabling shared inputs to feed two half-adders. With both inputs on, the doubled intensity still triggers nonlinear switching after adapting the working frequency and coupled length.

S2 Modified half-adder with fan-out gate

  • The modified design adds a closely placed waveguide and coupler at Output I and changes the phase difference between inputs A and B from p/2 to 0.The device combines a half-adder with a fan-out gate, producing two half-adders with shared inputs.Source: S2 Modified half-adder with fan-out gate · pp. 24–25
  • For the input combinations A=1, B=0 and A=0, B=1, the modified design’s operation principle is identical to the original half-adder.Source: S2 Modified half-adder with fan-out gate · p. 24
  • With both inputs on, equal-intensity spin waves reach both couplers, doubling the nonlinear coupler’s intensity versus one input—not quadrupling it as in the original design—and still triggering nonlinear switching after frequency and coupled-length adjustment.The switching was achieved after adapting the device’s working frequency and coupled length.Source: S2 Modified half-adder with fan-out gate · p. 25

S3. Energy consumption of parametric amplification

The section compares three amplification approaches and identifies VCMA parametric pumping as the most suitable, estimating its energy use at 3 aJ. Current-driven parametric pumping can provide the needed amplification but has substantially higher estimated energy consumption, while the spin-orbit-torque approach is unsuitable for amplification.

S3. Energy consumption of parametric amplification

  • Spin-orbit torque is unsuitable because propagating spin-wave amplification had not been demonstrated, output intensity remains below input, and the approach requires high-density electric currents.The cited bilayer YIG/Pt result was judged unlikely to amplify propagating spin waves [2]; spin-orbit torque can compensate only for damping caused by spin pumping from the Pt layer.Source: S3. Energy consumption of parametric… · p. 25
  • A 4× spin-wave-intensity amplification required about 8.8 mA of pumping current in the simulated strip-antenna scheme.The simulations show amplification begins before the parametric-generation threshold, so pumping does not directly excite parasitic spin waves; intensity falls at high current due to four-magnon scattering.Source: S3. Energy consumption of parametric… · p. 26, Figure S2 · p. 26
  • Amplification consumes around 105 aJ, potentially reducible by one or two orders of magnitude through pumping-antenna and half-adder size optimization; at optimal MgO thickness d ~ 2.6 nm, energy consumption is ~3 aJ.The amplification energy consumption is much higher than the energy used to process data within the magnonic domain.Source: S3. Energy consumption of parametric… · p. 27

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