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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
TL;DR
Integrated magnonic circuits with multiple logic gates remain an unresolved challenge. This paper numerically demonstrates a magnonic half-adder using an integrated all-magnon design, and reports a three-nanowire core with potentially sub-aJ magnon-domain energy. The energy accounting excludes signal-transfer and amplification costs, and the miniaturized device is an estimation based on current fabrication technology.
Problem
Integrated magnonic circuits containing at least two logic gates and suitable for further integration remain unresolved despite progress on separate magnonic processing units.
Method
The paper numerically proposes and tests an integrated magnonic half-adder in which magnons control magnons without conversion to the electric domain.
Results
The half-adder core consists of three nano-wires in one planar layer, and its full functionality is numerically verified.
Takeaways & Limitations
The proposed circuit is potentially suited for further integration with other logic gates relying on the same concept.
Takeaways & Limitations
The miniaturized-device estimate is not a fundamental limit but is based on the current state of fabrication technology, and reported magnon-domain energy excludes transfer and amplification costs.
Abstract
from arXiv · showhide
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 estimates the half-adder’s energy, area, and delay, showing low magnon-domain energy and potential miniaturization, while identifying amplification and signal-transfer energy as important boundaries.
- Energy optimization: Reducing waveguide cross-section is identified as a feasible route to lower energy, whereas exchange spin waves increase energy through higher group velocity.Alternative improvements include searching for mechanisms with anomalously high nonlinearity.
- Scalability: The proposed core uses only three planar nano-wires, with area potentially decreasing from 5.58 µm2 to 1.016 µm2.The 5.58 µm2 value includes spaces between neighboring logic gates.
- Delay time: The design’s propagation time is about 150 ns, while the estimated calculation time for the smaller device is 18 ns.The 18 ns estimate remains larger than the 60 ps delay reported for 7 nm CMOS.
- Energy consumption: The half-adder’s energy is estimated at 24.6 aJ for all operations, comparable to 35.3 aJ for a CMOS implementation.The estimate uses a 300 ns pulse and includes both input combinations.
- Energy consumption: Miniaturization reduces the estimated energy consumption to around 1.96 aJ.The reduced value is associated with the miniaturized device.
- Scope and limitations: The reported magnon-domain energy excludes signal-transfer and spin-wave-amplification energy, and amplifier consumption can be much higher than data-processing energy.The paper separately reports amplifier energy around 105 aJ.
Methods
The study uses analytical spin-wave calculations and GPU-accelerated MuMax3 simulations to model the magnonic half-adder and benchmark its energy against a 7 nm CMOS half-adder.
- Analytical calculations: Spin-wave dispersion and nonlinear frequency shifts are calculated analytically for coupled waveguides using magnetization dynamics and mode-profile assumptions.The treatment includes magneto-dipolar interactions, exchange effects, and a uniform mode profile across the waveguide dimensions.
- Analytical calculations: The coupled-waveguide dispersion is obtained from the two-mode interaction of the waveguides and their separation-dependent coupling.The coordinate system, waveguide geometry, and interaction tensor define the dispersion calculation.
- Micromagnetic simulations: Micromagnetic simulations use GPU-accelerated MuMax3 to model nanometer-thick YIG waveguides with specified material, damping, mesh, and absorber parameters.The simulations apply no external bias field and rely on spontaneous magnetization alignment from shape anisotropy.
- Simulation assumptions: The simulations assume defect-free waveguides and omit temperature, while edge roughness and trapezoidal cross-sections are treated as negligible.These scope conditions define the simulated operating environment.
Supplementary Material Integrated magnonic half-adder
The supplementary material documents the integrated magnonic half-adder and extends the discussion to a modified device combining half-adder and fan-out functionality.
- Supplementary structure: The supplement first describes the estimation of energy consumption for the magnonic half-adder.This analysis is presented in Section S1.
- Supplementary structure: It also discusses a modified device that operates as a half-adder with an added fan-out gate.The modified architecture is treated in Section S2.
S1. Energy consumption for magnonic half-adder
The energy analysis estimates the minimum spin-wave pulse energy from waveguide geometry, group velocity, pulse duration, and the amplitude required to switch the nonlinear directional coupler.
- Energy model: The spin-wave pulse energy is estimated while neglecting transducer energy and using the waveguide cross-section, group velocity, and pulse duration.The pulse volume is V = Sv_grt, where S is cross-section, v_gr is group velocity, and t is pulse duration.
- Coupler design: The nonlinear coupler requires a minimum size of N_min = 6 when the linear and nonlinear couplers have the same gap.This restriction follows from comparing nonlinear transmission with the linear-regime transmission rate of 1/2.
- Energy model: The pulse amplitude is selected to reach the switching threshold of the nonlinear directional coupler.The required amplitude is derived from the coupler relation and coupling length.
- Pulse conditions: Stable operation requires a sufficiently narrow pulse frequency width for both linear and nonlinear couplers.The nonlinear coupler operates near a transmission maximum or minimum, imposing a stricter condition on the pulse bandwidth.
- Energy model: The final minimum-energy expression is obtained by combining the preceding relations for pulse energy, coupling, and switching conditions.The expression is identified as Eq. 4 in the paper.
S2 Modified half-adder with fan-out gate
The modified half-adder adds fan-out functionality and uses shared inputs to transfer spin waves to both directional couplers while retaining half-adder operation.
- Truth table: Table S1 reports the truth of Output “I” for the modified half-adder configuration.The table summarizes the output logic associated with the input combinations.
- Half-adder operation: Output “I” can also perform the half-adder operation after adding another coupler and changing the input phase difference from p/2 to 0.The additional coupler is introduced by placing another waveguide close to Output “I”.
- Half-adder operation: For single-active-input combinations, the modified operation follows the original half-adder principle.The stated cases are A = 1, B = 0 and A = 0, B = 1.
- Modified architecture: The modified device combines a half-adder with a fan-out gate and transfers spin waves of equal intensity to both directional couplers.This architecture uses shared inputs rather than separate input paths for each coupler.
- Switching operation: The nonlinear directional coupler can still switch when the shared-input configuration doubles the incident spin-wave intensity.The device parameters, including working frequency and coupled length, are adapted for this operation.
S3. Energy consumption of parametric amplification
The paper evaluates parametric-amplification approaches for magnonic circuits, focusing on their energy consumption and suitability for amplifying propagating spin waves. Voltage-Controlled Magnetic Anisotropy (VCMA) pumping is estimated to reduce amplification energy to about 3 aJ, substantially below parallel pumping.
- Approaches: Spin-Orbit Torque amplification is unsuitable because it cannot increase output spin-wave intensity above the input and requires high-density electric currents.The approach can compensate damping from spin pumping but does not provide net amplification in the described system.
- Approaches: Parallel parametric pumping uses an rf Oersted field generated by current through a metallic strip.The pumping frequency is twice the initial spin-wave frequency, and the output intensity is evaluated after the pumping region.
- Parallel pumping: 105 aJ is the estimated energy consumption for fourfold spin-wave amplification with parallel pumping in the half-adder.The estimate uses an approximately 8.8 mA pumping current and a 300 ns pumping time; antenna and half-adder optimization could reduce it by one or two orders of magnitude.
- VCMA pumping: VCMA pumping is identified as the most suitable approach because it replaces the large-current rf magnetic field with an electric rf field.The paper states that this replacement enables a drastic reduction in amplification energy.