



Reversible Skyrmion Logic
Reversible skyrmion logic leverages magnetic skyrmions in the first nanoscale realization of conservative logic, providing a vision for energyefficient computation.
In this system, magnetic skyrmions propagate through a twodimensional ferromagnetic structure while performing reversible logic operations at the gate junctions.
A simple global clock enables direct cascading with the potential for scalable highspeed lowpower reversible Boolean and quantum computing.
Magnetic Skyrmion Track
Magnetic skyrmions are stable regions of a ferromagnet in which the magnetization of the skyrmion core is oriented in the opposite direction of the rest of the ferromagnet.
These skyrmions can be moved with an electrical current that transports the magnetic spin information (no physical particles are actually transported).
As shown in the figure, +ydirected electrical current creates a spinHall force that pushes the skyrmion in the +ydirection, while also creating a skyrmionHall force that pushes the skyrmion in the xdirection.
The skyrmion is placed within a track structure that suppresses the lateral skyrmionHall effect and forces the skyrmion to travel along the track.
Reversible Logic Gates
Conservative logic envisions reversible computing with zero energy dissipation, and was originally proposed with an analogy to billiard balls.
Though not dissipationfree, this reversible skyrmion logic system replaces the billiard balls with magnetic skyrmions in the first nanoscale realization of the conservative logic concept.
The skyrmionHall effect and skyrmionskyrmion repulsion can be used together to perform reversible logic operations at the junction between two ferromagnetic tracks.
The simplest conservative logic gate is the ANDOR gate, which conserves the magnetic skyrmions while computing the AND and OR functions of inputs A and B.
The spinHall effect continuously pushes the skyrmions in the +ydirection, and the skyrmionHall effect pushes the skyrmions from the right track to the left track whenever possible.
However, when a skyrmion is already present in the left track, skyrmionskyrmion repulsion prevents the skyrmion on the right from switching to the left track.
Other logic gates have also been demonstrated via micromagnetic simulation, notably the INVCOPY gate which can generate any logical function when coupled with the ANDOR gate.
This reversible logic paradigm also enables a fundamental element of quantum computing, the Fredkin gate, which performs a reversible logic function.
Skyrmion Synchronization, Cascaded Logic Gates, & Pipelined Computing
To ensure proper functionality within a large system, it is critical that the skyrmions enter the logic gate junctions simultaneously.
The skyrmions are therefore synchronized with global clock pulses that provide short current spikes to the entire skyrmion logic circuit that shrink the skyrmions and enable them to simultaneously pass notches within the tracks.
This procedure is illustrated for the onebit full adder, in which seven notches are used to compute the sum and caryout signals in three clock cycles.
Thanks to the synchronizing notches, this reversible logic circuit structure can be scaled up to large computing systems.
The nonvolatility of this system, in concert with the clocked data propagation, enables pipelined logical operations.
Whereas the latency of logical operations may be multiple clock cycles, pipelining enables each logic circuit to provide a throughput of one logical result per clock cycle.
Related Publications
 B. W. Walker, K. Muthukrishnan, R. Thapa, E. Rivas, X. Hu, M. P. Frank, F. GarciaSanchez, A. J. Edwards, J. S. Friedman, Pipelined VoltagePropagated Skyrmion Logic with High Thermal Stability, Joint IEEE International Magnetics Conference & Conference on Magnetism and Magnetic Materials, Jan. 2025.
 B. W. Walker, K. Muthukrishnan, R. Thapa, E. A. Rivas, X. Hu, M. P. Frank, F. GarciaSanchez, A. J. Edwards, J. S. Friedman, VoltagePropagated Reversible Skyrmion Logic with nearLandauer Efficiency, International Conference on Magnetism, JuneJuly 2024.
 B. W. Walker, K. Muthukrishnan, R. Thapa, X. Hu, M. P. Frank, F. GarciaSanchez, A. J. Edwards, J. S. Friedman, NearLandauer Reversible Skyrmion Logic with VoltageBased Propagation, Conference on Magnetism and Magnetic Materials, Oct.Nov. 2023.
 B. W. Walker, F. GarciaSanchez, A. J. Edwards, X. Hu, M. P. Frank, J. S. Friedman, Near Landauer Reversible Skyrmion Logic with VoltageBased Propagation, Joint European Magnetic Symposia, Aug. 2023.
 X. Hu, C. Cui, S. Liu, F. GarciaSanchez, W. H. Brigner, B. W. Walker, A. J. Edwards, T. P. Xiao, C. Bennett, N. Hassan, M. P. Frank, J. A. C. Incorvia, J. S. Friedman, Magnetic Skyrmions and Domain Walls for Logical and Neuromorphic Computing, Neuromorphic Computing and Engineering (accepted).
 B. W. Walker, A. J. Edwards, X. Hu, M. P. Frank, F. GarciaSanchez, J. S. Friedman, NearLandauer Reversible Skyrmion Logic with VoltageBased Propagation, arXiv:2301.10700 (2023).
 B. W. Walker, A. J. Edwards, X. Hu, M. P. Frank, F. GarciaSanchez, J. S. Friedman, NearLandauer Reversible Skyrmion Logic with VoltageBased Propagation, Government Microcircuit Applications & Critical Technology Conference, Mar. 2023.
 J. S. Friedman, X. Hu, M. A. M. Chauwin, Reversible Computing System and Method based on Conservative Magnetic Skyrmion Logic, U.S. Patent #11,539,365 (2022).
 X. Hu, B. W. Walker, F. GarciaSanchez, A. J. Edwards, P. Zhou, J. A. C. Incorvia, A. Paler, M. P. Frank, J. S. Friedman, Logical and Physical Reversibility of Conservative Skyrmion Logic, IEEE Magnetics Letters 13, 4503805 (2022).
 X. Hu, B. W. Walker, F. GarciaSanchez, P. Zhou, J. A. C. Incorvia, A. Paler, M. P. Frank, J. S. Friedman, Logical and Physical Reversibility of Conservative Skyrmion Logic, Government Microcircuit Applications & Critical Technology Conference, Mar. 2022.
 B. W. Walker, C. Cui, F. GarciaSanchez, J. A. C. Incorvia, X. Hu, J. S. Friedman, Conservative Skyrmion Logic with VoltageControlled Magnetic Anisotropy Synchronization, Joint IEEE International Magnetics Conference & Conference on Magnetism and Magnetic Materials, Jan. 2022.
 X. Hu, M. Chauwin, F. GarciaSanchez, B. W. Walker, N. Betrabet, J. A. C. Incorvia, A. Paler, C. Moutafis, J. S. Friedman, Skyrmion Logic System for LargeScale Reversible Computing, IEEE International Conference on Nanotechnology, July 2021.
 B. W. Walker, C. Cui, F. GarciaSanchez, J. A. C. Incorvia, X. Hu, J. S. Friedman, Skyrmion Logic Clocked via VoltageControlled Magnetic Anisotropy, Applied Physics Letters 118, 192404 (2021).
 X. Hu, M. Chauwin, F. GarciaSanchez, N. Betrabet, A. Paler, C. Moutafis, J. S. Friedman, Reversible Skyrmion Logic System, International Conference on Nanomagnetism and Spintronics (Solitons and Skyrmion Magnetism), June 2021.
 B. W. Walker, C. Cui, F. GarciaSanchez, J. A. C. Incorvia, X. Hu, J. S. Friedman, Voltage ControlledClocked Skyrmion Logic Synchronizers, International Conference on Nanomagnetism and Spintronics (Solitons and Skyrmion Magnetism), June 2021.
 X. Hu, M. Chauwin, F. GarciaSanchez, N. Betrabet, A. Paler, C. Moutafis, J. S. Friedman, Reversible Skyrmion Logic System, APS March Meeting, Mar. 2021.
 X. Hu, M. Chauwin, F. GarciaSanchez, N. Betrabet, A. Paler, C. Moutafis, J. S. Friedman, Skyrmion Logic System for LargeScale Reversible Computing, IEEE International Conference on Rebooting Computing, Dec. 2020.
 J. S. Friedman,Scalable Reversible Computing with Skyrmion Billiard Balls, CCC Workshop on Physics & Engineering Issues in Adiabatic/Reversible Classical Computing, Oct. 2020.
 M. Chauwin*, X. Hu*, F. GarciaSanchez, N. Betrabet, A. Paler, C. Moutafis, J. S. Friedman, Skyrmion Logic System for LargeScale Reversible Computation, Physical Review Applied 12:6, 064053 (2019).
• Featured as Editors' Suggestion
 X. Hu, M. Chauwin, F. GarciaSanchez, N. Betrabet, C. Moutafis, J. S. Friedman, Cascaded Skyrmion Logic System Inspired by Conservative Logic, SPIE Spintronics, Aug. 2019 (invited).
 X. Hu, M. Chauwin, F. GarciaSanchez, N. Betrabet, C. Moutafis, J. S. Friedman, Cascaded Skyrmion Logic System Inspired by Conservative Logic, Joint IEEE International Magnetics Conference & Conference on Magnetism and Magnetic Materials, Jan. 2019.
This research is sponsored in part by the National Science Foundation under ECCS award #2343607.
