Brataas, A., Kent, A. D. & Ohno, H. Current-induced torques in magnetic materials. Nat. Mater. 11, 372 (2012).
Manchon, A. et al. Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev. Mod. Phys. 91, 35004 (2019).
Shao, Q. et al. Roadmap of spin-orbit torques. IEEE Trans. Magn. 57, 800439 (2021).
Matsukura, F., Tokura, Y. & Ohno, H. Control of magnetism by electric fields. Nat Nanotechnol 10, 209–220 (2015).
Finley, J. & Liu, L. Spin-orbit-torque efficiency in compensated ferrimagnetic cobalt-terbium alloys. Phys. Rev. Appl. 6, 54001 (2016).
Kim, K. J. et al. Fast domain wall motion in the vicinity of the angular momentum compensation temperature of ferrimagnets. Nat Mater 16, 1187–1192 (2017).
Caretta, L. et al. Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet. Nat. Nanotechnol. 13, 1154–1160 (2018).
Kim, S. K. et al. Ferrimagnetic spintronics. Nat. Mater. 21, 24–34 (2022).
Jungwirth, T., Marti, X., Wadley, P. & Wunderlich, J. Antiferromagnetic spintronics. Nat Nanotechnol. 11, 231–241 (2016).
Baltz, V. et al. Antiferromagnetic spintronics. Rev. Mod. Phys. 90, 15005 (2018).
Han, J., Cheng, R., Liu, L., Ohno, H. & Fukami, S. Coherent antiferromagnetic spintronics. Nat. Mater. 22, 684–695 (2023).
He, Q. L., Hughes, T. L., Armitage, N. P., Tokura, Y. & Wang, K. L. Topological spintronics and magnetoelectronics. Nat. Mater. 21, 15–23 (2022).
Lin, X., Yang, W., Wang, K. L. & Zhao, W. Two-dimensional spintronics for low-power electronics. Nat. Electron. 2, 274–283 (2019).
Liu, Y. & Shao, Q. Two-dimensional materials for energy-efficient spin-orbit torque devices. ACS Nano 14, 9389–9407 (2020).
Yang, H. et al. Two-dimensional materials prospects for non-volatile spintronic memories. Nature 606, 663–673 (2022).
Chappert, C., Fert, A. & Van Dau, F. N. The emergence of spin electronics in data storage. Nat. Mater. 6, 813–823 (2007).
Dieny, B. et al. Opportunities and challenges for spintronics in the microelectronics industry. Nat. Electron. 3, 446–459 (2020).
Torrejon, J. et al. Neuromorphic computing with nanoscale spintronic oscillators. Nature 547, 428–431 (2017).
Romera, M. et al. Vowel recognition with four coupled spin-torque nano-oscillators. Nature 563, 230–234 (2018).
Allwood, D. A. et al. Magnetic domain-wall logic. Science 309, 1688–1692 (2005).
Parkin, S. & Yang, S. H. Memory on the racetrack. Nat. Nanotechnol. 10, 195–198 (2015).
Fert, A., Reyren, N. & Cros, V. Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2, 17031 (2017).
Li, S. et al. Magnetic skyrmions for unconventional computing. Mater. Horizons 8, 854–868 (2021).
Kang, W., Huang, Y., Zhang, X., Zhou, Y. & Zhao, W. Skyrmion-electronics: an overview and outlook. Proc. IEEE 104, 2040–2061 (2016).
Chumak, A. V., Vasyuchka, V. I. I., Serga, A. A. A. & Hillebrands, B. Magnon spintronics. Nat. Phys. 11, 453 (2015).
Borders, W. A. et al. Integer factorization using stochastic magnetic tunnel junctions. Nature 573, 390–393 (2019).
Fukami, S. & Ohno, H. Perspective: spintronic synapse for artificial neural network. J. Appl. Phys. 124, 151904 (2018).
Grollier, J. et al. Neuromorphic spintronics. Nat. Electron. 3, 360–370 (2020).
Marković, D., Mizrahi, A., Querlioz, D. & Grollier, J. Physics for neuromorphic computing. Nat. Rev. Phys. 2, 499–510 (2020).
Jung, S. et al. A crossbar array of magnetoresistive memory devices for in-memory computing. Nature 601, 211–216 (2022).
Manipatruni, S., Nikonov, D. E. & Young, I. A. Beyond CMOS computing with spin and polarization. Nat. Phys. 14, 338–343 (2018).
Zázvorka, J. et al. Thermal skyrmion diffusion used in a reshuffler device. Nat. Nanotechnol. 14, 658–661 (2019).
Borders, W. A. et al. Analogue spin–orbit torque device for artificial-neural-network-based associative memory operation. Appl. Phys. Express 10, 13007 (2017).
Kurenkov, A. et al. Artificial neuron and synapse realized in an antiferromagnet/ferromagnet heterostructure using dynamics of spin–orbit torque switching. Adv. Mater. 31, 1900636 (2019).
Song, K. M. et al. Skyrmion-based artificial synapses for neuromorphic computing. Nat. Electron. 3, 148–155 (2020).
Manipatruni, S. et al. Scalable energy-efficient magnetoelectric spin-orbit logic. Nature 565, 35–42 (2019).
Luo, Z, et al. Chirally coupled nanomagnets. Science 363, 1435–1439 (2019).
Luo, Z. et al. Current-driven magnetic domain-wall logic. Nature 579, 214–218 (2020).
Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. The missing memristor found. Nature 453, 80–83 (2008).
Prezioso, M. et al. Training and operation of an integrated neuromorphic network based on metal-oxide memristors. Nature 521, 61–64 (2015).
Wang, Z. et al. Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing. Nat. Mater. 16, 101–108 (2017).
Zidan, M. A., Strachan, J. P. & Lu, W. D. The future of electronics based on memristive systems. Nat. Electron. 1, 22–29 (2018).
Ielmini, D. & Wong, H.-S. P. In-memory computing with resistive switching devices. Nat. Electron. 1, 333–343 (2018).
Ambrogio, S. et al. Equivalent-accuracy accelerated neural-network training using analogue memory. Nature 558, 60–67 (2018).
Xia, Q. & Yang, J. J. Memristive crossbar arrays for brain-inspired computing. Nat Mater 18, 309–323 (2019).
Sebastian, A., Le Gallo, M., Khaddam-Aljameh, R. & Eleftheriou, E. Memory devices and applications for in-memory computing. Nat. Nanotechnol. 15, 529–544 (2020).
Sangwan, V. K. & Hersam, M. C. Neuromorphic nanoelectronic materials. Nat. Nanotechnol. 15, 517–528 (2020).
Wang, Z. et al. Resistive switching materials for information processing. Nat. Rev. Mater. 5, 173–195 (2020).
Wuttig, M. & Yamada, N. Phase-change materials for rewriteable data storage. Nat. Mater. 6, 824–832 (2007).
Zhang, W., Mazzarello, R., Wuttig, M. & Ma, E. Designing crystallization in phase-change materials for universal memory and neuro-inspired computing. Nat. Rev. Mater. 4, 150–168 (2019).
Kumar, S., Williams, R. S. & Wang, Z. Third-order nanocircuit elements for neuromorphic engineering. Nature 585, 518–523 (2020).
Kumar, S., Strachan, J. P. & Williams, R. S. Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing. Nature 548, 318–321 (2017).
Chanthbouala, A. et al. A ferroelectric memristor. Nat. Mater. 11, 860–864 (2012).
Grollier, J., Querlioz, D. & Stiles, M. D. Spintronic nanodevices for bioinspired computing. Proc. IEEE 104, 2024–2039 (2016).
Chen, A. A review of emerging non-volatile memory (NVM) technologies and applications. Solid. State. Electron. 125, 25–38 (2016).
González, V. H., Litvinenko, A., Kumar, A., Khymyn, R. & Åkerman, J. Spintronic devices as next-generation computation accelerators. Curr. Opin. Solid State Mater. Sci. 31, 101173 (2024).
Marrows, C. H., Barker, J., Moore, T. A. & Moorsom, T. Neuromorphic computing with spintronics. npj Spintron. 2, 12 (2024).
Selcuk, K. et al. Connecting physics to systems with modular spin-circuits. npj Spintron 2, 53 (2024).
Roy, K. et al. Spintronic neural systems. Nat. Rev. Electr. Eng. 1, 714–729 (2024).
Incorvia, J. A. C. et al. Spintronics for achieving system-level energy-efficient logic. Nat. Rev. Electr. Eng. 1, 700–713 (2024).
Editors:, Bandyopadhyay, S. & Barman, A. Nanomagnets as Dynamical Systems: Physics and Applications. (Springer, 2024).
Chua, L. O. Memristor—the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519 (1971).
Chua, L. O. & Kang, S. M. Memristive devices and systems. Proc. IEEE 64, 209–223 (1976).
Di Ventra, M., Pershin, Y. V. & Chua, L. O. Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc. IEEE 97, 1717–1724 (2009).
Chua, L. Resistance switching memories are memristors. Appl. Phys. A 102, 765–783 (2011).
Bao, H., Hu, A., Liu, W. & Bao, B. Hidden bursting firings and bifurcation mechanisms in memristive neuron model with threshold electromagnetic induction. IEEE Trans. Neural Networks Learn. Syst. 31, 502–511 (2020).
Li, K. et al. Memristive rulkov neuron model with magnetic induction effects. IEEE Trans. Ind. Informatics 18, 1726–1736 (2022).
He, S., Zhan, D., Wang, H., Sun, K. & Peng, Y. Discrete memristor and discrete memristive systems. Entropy 24, 786 (2022).
Kumar, S., Wang, X., Strachan, J. P., Yang, Y. & Lu, W. D. Dynamical memristors for higher-complexity neuromorphic computing. Nat. Rev. Mater. 7, 575–591 (2022).
Ikeda, S. et al. A perpendicular-anisotropy CoFeB-MgO magnetic tunnel junction. Nat. Mater. 9, 721–724 (2010).
Kiselev, S. I. et al. Microwave oscillations of a nanomagnet driven by a spin-polarized current. Nature 425, 380–383 (2003).
Shao, Q. & Wang, K. L. Heat-assisted microwave amplifier. Nat. Nanotechnol. 14, 9–11 (2019).
Liu, X. et al. Overview of spintronic sensors with internet of things for smart living. IEEE Trans. Magn. 55, 0800222 (2019).
Zhang, X. et al. Spin-torque memristors based on perpendicular magnetic tunnel junctions for neuromorphic computing. Adv. Sci. 8, 2004645 (2021).
Fukami, S., Zhang, C., DuttaGupta, S., Kurenkov, A. & Ohno, H. Magnetization switching by spin-orbit torque in an antiferromagnet-ferromagnet bilayer system. Nat. Mater. 15, 535–541 (2016).
Skjærvø, S. H., Marrows, C. H., Stamps, R. L. & Heyderman, L. J. Advances in artificial spin ice. Nat. Rev. Phys. 2, 13–28 (2019).
Hu, W. et al. Distinguishing artificial spin ice states using magnetoresistance effect for neuromorphic computing. Nat. Commun. 14, 2562 (2023).
Parkin, S. S. P. S., Hayashi, M. & Thomas, L. Magnetic domain-wall racetrack memory. Science 320, 190–194 (2008).
Jiang, W. et al. Direct imaging of thermally driven domain wall motion in magnetic insulators. Phys. Rev. Lett. 110, 177202 (2013).
Han, J., Zhang, P., Hou, J. T., Siddiqui, S. A. & Liu, L. Mutual control of coherent spin waves and magnetic domain walls in a magnonic device. Science 366, 1121–1125 (2019).
Lequeux, S. et al. A magnetic synapse: multilevel spin-torque memristor with perpendicular anisotropy. Sci. Rep. 6, 31510 (2016).
Wang, D. et al. Spintronic leaky-integrate-fire spiking neurons with self-reset and winner-takes-all for neuromorphic computing. Nat. Commun. 14, 1068 (2023).
Göbel, B., Mertig, I. & Tretiakov, O. A. Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles. Phys. Rep. 895, 1–28 (2021).
Jiang, W. et al. Direct observation of the skyrmion Hall effect. Nat. Phys. 13, 162–169 (2016).
Wang, Z. et al. Thermal generation, manipulation and thermoelectric detection of skyrmions. Nat. Electron. 3, 672–679 (2020).
Upadhyaya, P., Yu, G., Amiri, P. K. & Wang, K. L. Electric-field guiding of magnetic skyrmions. Phys. Rev. B 92, 134411 (2015).
Kang, W. et al. Voltage controlled magnetic skyrmion motion for racetrack memory. Sci. Rep. 6, 23164 (2016).
Jiang, W. et al. Blowing magnetic skyrmion bubbles. Science 349, 283–286 (2015).
Woo, S. et al. Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets. Nat. Mater. 15, 501–506 (2016).
Yu, X. Z. et al. Skyrmion flow near room temperature in an ultralow current density. Nat. Commun. 3, 988 (2012).
Jonietz, F. et al. Spin transfer torques in MnSi at ultralow current densities. Science 330, 1648–1651 (2010).
Li, S. et al. Experimental demonstration of skyrmionic magnetic tunnel junction at room temperature. Sci. Bull. 67, 691–699 (2022).
Guang, Y. et al. Electrical detection of magnetic skyrmions in a magnetic tunnel junction. Adv. Electron. Mater. 9, 2200570 (2023).
Chen, S. et al. All-electrical skyrmionic magnetic tunnel junction. Nature 627, 522–527 (2024).
Kruglyak, V. V., Demokritov, S. O. & Grundler, D. Magnonics. J. Phys. D. Appl. Phys. 43, 264001 (2010).
Pirro, P., Vasyuchka, V. I., Serga, A. A. & Hillebrands, B. Advances in coherent magnonics. Nat. Rev. Mater. 6, 1114–1135 (2021).
Kajiwara, Y. et al. Transmission of electrical signals by spin-wave interconversion in a magnetic insulator. Nature 464, 262 (2010).
Cornelissen, L. J. et al. Long-distance transport of magnon spin information in a magnetic insulator at room temperature. Nat. Phys. 11, 1022 (2015).
Khitun, A., Bao, M. & Wang, K. L. Magnonic logic circuits. J. Phys. D. Appl. Phys. 43, 264005 (2010).
Serga, A. A., Chumak, A. V. & Hillebrands, B. Y. I. G. magnonics. J. Phys. D. Appl. Phys. 43, 264002 (2010).
Sebastian, T., Schultheiss, K., Obry, B., Hillebrands, B. & Schultheiss, H. Micro-focused Brillouin light scattering: imaging spin waves at the nanoscale. Front. Phys. 3, 35 (2015).
Guckenheimer, J. & Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. vol. 42 (Springer New York, 1983).
Shilnikov, L. P., Shilnikov, A. L., Turaev, D. V. & Chua, L. O. Methods of Qualitative Theory in Nonlinear Dynamics. vol. 5 (WORLD SCIENTIFIC, 2001).
Wiggins, S. Introduction to Applied Nonlinear Dynamical Systems and Chaos. Introduction to Applied Nonlinear Dynamical Systems and Chaos vol. 2 (Springer-Verlag, 2003).
Wang, K. L. et al. Electric-field control of spin-orbit interaction for low-power spintronics. Proc. IEEE 104, 1974–2008 (2016).
Grimaldi, E. et al. Single-shot dynamics of spin–orbit torque and spin transfer torque switching in three-terminal magnetic tunnel junctions. Nat. Nanotechnol. 15, 111–117 (2020).
Yu, G. et al. Room-temperature skyrmion shift device for memory application. Nano Lett. 17, 261–268 (2017).
Doevenspeck, J. et al. Multi-pillar SOT-MRAM for accurate analog in-memory DNN inference. Symp. VLSI Technol. T11-2 (2021).
Chanthbouala, A. et al. Vertical-current-induced domain-wall motion in MgO-based magnetic tunnel junctions with low current densities. Nat. Phys. 7, 626–630 (2011).
Rippard, W. H., Pufall, M. R., Kaka, S., Russek, S. E. & Silva, T. J. Direct-current induced dynamics in Co90Fe10/Ni80Fe20 point contacts. Phys. Rev. Lett. 92, 4 (2004).
Slavin, A. & Tiberkevich, V. Spin wave mode excited by spin-polarized current in a magnetic nanocontact is a standing self-localized wave bullet. Phys. Rev. Lett. 95, 237201 (2005).
Grollier, J. et al. Field dependence of magnetization reversal by spin transfer. Phys. Rev. B 67, 174402 (2003).
Liu, L., Pai, C.-F., Ralph, D. C. & Buhrman, R. A. Magnetic oscillations driven by the spin Hall effect in 3-terminal magnetic tunnel junction devices. Phys. Rev. Lett. 109, 186602 (2012).
Locatelli, N., Cros, V. & Grollier, J. Spin-torque building blocks. Nat Mater 13, 11–20 (2014).
Zhang, S. et al. Current-induced magnetic skyrmions oscillator. New J. Phys. 17, 023061 (2015).
Mochizuki, M. et al. Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect. Nat Mater 13, 241–246 (2014).
Pribiag, V. S. et al. Magnetic vortex oscillator driven by d.c. spin-polarized current. Nat. Phys. 3, 498–503 (2007).
Mistral, Q. et al. Current-driven vortex oscillations in metallic nanocontacts. Phys. Rev. Lett. 100, 257201 (2008).
Onose, Y., Okamura, Y., Seki, S., Ishiwata, S. & Tokura, Y. Observation of magnetic excitations of Skyrmion crystal in a helimagnetic insulator Cu2OSeO3. Phys Rev Lett 109, 37603 (2012).
Satywali, B. et al. Microwave resonances of magnetic skyrmions in thin film multilayers. Nat. Commun. 12, 1909 (2021).
Gartside, J. C. et al. Reconfigurable training and reservoir computing in an artificial spin-vortex ice via spin-wave fingerprinting. Nat. Nanotechnol. 17, 460–469 (2022).
Saitoh, E., Miyajima, H., Yamaoka, T. & Tatara, G. Current-induced resonance and mass determination of a single magnetic domain wall. Nature 432, 203–206 (2004).
Rable, J., Dwivedi, J. & Samarth, N. Off-resonant detection of domain wall oscillations using deterministically placed nanodiamonds. npj Spintron 1, 2 (2023).
Ono, T. & Nakatani, Y. Magnetic domain wall oscillator. Appl. Phys. Express 1, 061301 (2008).
Bisig, A., Heyne, L., Boulle, O. & Kläui, M. Tunable steady-state domain wall oscillator with perpendicular magnetic anisotropy. Appl. Phys. Lett 95, 162504 (2009).
Xiong, Y. et al. Experimental parameters, combined dynamics, and nonlinearity of a magnonic-opto-electronic oscillator (MOEO). Rev. Sci. Instrum. 91, 125105 (2020).
Watt, S. & Kostylev, M. Reservoir computing using a spin-wave delay-line active-ring resonator based on Yttrium-Iron-Garnet Film. Phys. Rev. Appl. 13, 034057 (2020).
Litvinenko, A. et al. A spinwave Ising machine. Commun. Phys. 6, 227 (2023).
Won Ho Choi et al. A magnetic tunnel junction based true random number generator with conditional perturb and real-time output probability tracking. In 2014 IEEE International Electron Devices Meeting 12.5.1–12.5.4. https://doi.org/10.1109/IEDM.2014.7047039 (IEEE, 2014).
Fukushima, A. et al. Spin dice: a scalable truly random number generator based on spintronics. Appl. Phys. Express 7, 083001 (2014).
Vincent, A. F. et al. Spin-transfer torque magnetic memory as a stochastic memristive synapse for neuromorphic systems. IEEE Trans. Biomed. Circuits Syst. 9, 166–174 (2015).
Hayakawa, K. et al. Nanosecond random telegraph noise in in-plane magnetic tunnel junctions. Phys. Rev. Lett. 126, 117202 (2021).
Zhao, L. et al. Topology-dependent brownian gyromotion of a single skyrmion. Phys. Rev. Lett. 125, 027206 (2020).
Kerber, N. et al. Anisotropic skyrmion diffusion controlled by magnetic-field-induced symmetry breaking. Phys. Rev. Appl. 15, 044029 (2021).
Lachman, E. O. et al. Visualization of superparamagnetic dynamics in magnetic topological insulators. Sci Adv 1, e1500740 (2015).
Farhan, A. et al. Direct observation of thermal relaxation in artificial spin ice. Phys. Rev. Lett. 111, 057204 (2013).
Farhan, A. et al. Exploring hyper-cubic energy landscapes in thermally active finite artificial spin-ice systems. Nat. Phys. 9, 375–382 (2013).
Ghosh, S. Spintronics and security: prospects, vulnerabilities, attack models, and preventions. Proc. IEEE 104, 1864–1893 (2016).
Li, Z., Li, Y. C. & Zhang, S. Dynamic magnetization states of a spin valve in the presence of dc and ac currents: synchronization, modification, and chaos. Phys. Rev. B 74, 054417 (2006).
Yang, Z., Zhang, S. & Li, Y. C. Chaotic dynamics of spin-valve oscillators. Phys. Rev. Lett. 99, 134101 (2007).
Montoya, E. A. et al. Magnetization reversal driven by low dimensional chaos in a nanoscale ferromagnet. Nat. Commun. 10, 543 (2019).
Shen, L. et al. Current-induced dynamics and chaos of antiferromagnetic bimerons. Phys. Rev. Lett. 124, 037202 (2020).
Petit-Watelot, S. et al. Commensurability and chaos in magnetic vortex oscillations. Nat. Phys. 8, 682–687 (2012).
Devolder, T. et al. Chaos in magnetic nanocontact vortex oscillators. Phys. Rev. Lett. 123, 147701 (2019).
Gusakova, D. et al. Spin-polarized current-induced excitations in a coupled magnetic layer system. Phys. Rev. B 79, 104406 (2009).
Matsumoto, R., Lequeux, S., Imamura, H. & Grollier, J. Chaos and relaxation oscillations in spin-torque windmill spiking oscillators. Phys. Rev. Appl. 11, 044093 (2019).
Chen, L. et al. Dynamical mode coexistence and chaos in a nanogap spin Hall nano-oscillator. Phys. Rev. B 100, 104436 (2019).
Okuno, H. & Homma, T. Chaotic oscillation of domain wall in non-equilibrium state. IEEE Trans. Magn. 29, 2506–2511 (1993).
Shen, L. et al. Signal detection based on the chaotic motion of an antiferromagnetic domain wall. Appl. Phys. Lett. 118, 012402 (2021).
Wang, Z. et al. Chaotic spin-wave solitons in magnetic film feedback rings. Phys. Rev. Lett. 107, 114102 (2011).
Matsunaga, S. et al. Fabrication of a nonvolatile full adder based on logic-in-memory architecture using magnetic tunnel junctions. Appl. Phys. Express 1, 0913011–0913013 (2008).
Jain, S., Ranjan, A., Roy, K. & Raghunathan, A. Computing in memory with spin-transfer torque magnetic RAM. IEEE Trans. Very Large Scale Integr. Syst. 26, 470–483 (2018).
Sakimura, N., Sugibayashi, T., Nebashi, R. & Kasai, N. Nonvolatile magnetic flip-flop for standby-power-free SoCs. IEEE J. Solid-State Circuits 44, 2244–2250 (2009).
Hanyu, T. et al. Standby-power-free integrated circuits using MTJ-based VLSI computing. Proc. IEEE 104, 1844–1863 (2016).
Natsui, M. et al. A 47.14-μW 200-MHz MOS/MTJ-hybrid nonvolatile microcontroller unit embedding STT-MRAM and FPGA for IoT applications. IEEE J. Solid-State Circuits 54, 2991–3004 (2019).
Rossi, D. et al. 4.4 A 1.3TOPS/W @ 32GOPS fully integrated 10-core SoC for IoT end-nodes with 1.7 μW cognitive wake-up from MRAM-based state-retentive sleep mode. In 2021 IEEE International Solid- State Circuits Conference (ISSCC) 60–62. https://doi.org/10.1109/ISSCC42613.2021.9365939 (IEEE, 2021).
Sun, B. et al. MRAM Co-designed Processing-in-Memory CNN Accelerator for Mobile and IoT Applications. https://arxiv.org/abs/1811.12179 (2018).
Chang, T.-C. et al. 13.4 A 22 nm 1 Mb 1024b-read and near-memory-computing dual-mode STT-MRAM macro with 42.6GB/s read bandwidth for security-aware mobile devices. In 2020 IEEE International Solid- State Circuits Conference – (ISSCC) 224–226. https://doi.org/10.1109/ISSCC19947.2020.9063072 (IEEE, 2020).
Cai, H. et al. A survey of in-spin transfer torque MRAM computing. Sci. China Inf. Sci. 64, 160402 (2021).
Khitun, A. & Wang, K. L. Non-volatile magnonic logic circuits engineering. J. Appl. Phys. 110, 34306 (2011).
Kostylev, M. P., Serga, A. A., Schneider, T., Leven, B. & Hillebrands, B. Spin-wave logical gates. Appl. Phys. Lett. 87, 1–3 (2005).
Schneider, T. et al. Realization of spin-wave logic gates. Appl. Phys. Lett. 92, 022505 (2008).
Wang, K. L. & Amiri, P. K. Nonvolatile spintronics: perspectives on instant-on nonvolatile nanoelectronic systems. Spin 02, 1250009 (2012).
Fischer, T. et al. Experimental prototype of a spin-wave majority gate. Appl. Phys. Lett. 110, 152401 (2017).
Chumak, A. V., Serga, A. A. & Hillebrands, B. Magnon transistor for all-magnon data processing. Nat. Commun. 5, 4700 (2014).
Behin-Aein, B., Datta, D., Salahuddin, S. & Datta, S. Proposal for an all-spin logic device with built-in memory. Nat. Nanotechnol. 5, 266–270 (2010).
Pham, V. T. et al. Spin–orbit magnetic state readout in scaled ferromagnetic/heavy metal nanostructures. Nat. Electron. 3, 309–315 (2020).
Imre, A. et al. Majority logic gate for magnetic quantum-dot cellular automata. Science 311, 205–208 (2006).
Datta, S. & Das, B. Electronic analog of the electro-optic modulator. Appl. Phys. Lett. 56, 665–667 (1990).
Dery, H., Dalal, P., Cywiński, Ł. & Sham, L. J. Spin-based logic in semiconductors for reconfigurable large-scale circuits. Nature 447, 573–576 (2007).
Zhang, X., Ezawa, M. & Zhou, Y. Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions. Sci. Rep. 5, 9400 (2015).
Zhang, X. et al. Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications. J. Phys. Condens. Matter 32, 143001 (2020).
Hayashi, M., Thomas, L., Moriya, R., Rettner, C. & Parkin, S. S. P. Current-controlled magnetic domain-wall nanowire shift register. Science 320, 209–211 (2008).
Franken, J. H., Swagten, H. J. M. & Koopmans, B. Shift registers based on magnetic domain wall ratchets with perpendicular anisotropy. Nat. Nanotechnol. 7, 499–503 (2012).
Golonzka, O. et al. MRAM as embedded non-volatile memory solution for 22FFL FinFET technology. 2018 Int. Electron Devices Meet. 18.1.1–18.1.4. https://doi.org/10.1109/iedm.2018.8614620 (2018).
Wen, W. et al. CD-ECC: Content-dependent error correction codes for combating asymmetric nonvolatile memory operation errors. IEEE/ACM Int. Conf. Comput. Des. Dig. Tech. Pap. ICCAD 1–8. https://doi.org/10.1109/ICCAD.2013.6691090 (2013).
Han, J. & Orshansky, M. Approximate computing: an emerging paradigm for energy-efficient design. In 2013 18TH IEEE EUROPEAN TEST SYMPOSIUM (ETS) 1–6. https://doi.org/10.1109/ETS.2013.6569370 (IEEE, 2013).
Li, Y. et al. A survey of MRAM-centric computing: from near memory to in memory. IEEE Trans. Emerg. Top. Comput. 11, 318–330 (2023).
Wang, X., Chen, Y., Xi, H., Li, H. & Dimitrov, D. Spintronic memristor through spin-torque-induced magnetization motion. IEEE Electron Device Lett. 30, 294–297 (2009).
Shibata, T. et al. Linear and symmetric conductance response of magnetic domain wall type spin-memristor for analog neuromorphic computing. Appl. Phys. Express 13, 043004 (2020).
Huang, Y., Kang, W., Zhang, X., Zhou, Y. & Zhao, W. Magnetic skyrmion-based synaptic devices. Nanotechnology 28, 08LT02 (2017).
Zabihi, M. et al. In-memory processing on the spintronic CRAM: from hardware design to application mapping. IEEE Trans. Comput. 68, 1159–1173 (2019).
Doevenspeck, J. et al. SOT-MRAM based analog in-memory computing for DNN inference. Symp. VLSI Technol. (2020).
Shao, Q., Wang, Z. & Yang, J. J. Efficient AI with MRAM. Nat. Electron. 5, 67–68 (2022).
Xiao, Z. et al. Device variation-aware adaptive quantization for mram-based accurate in-memory computing without on-chip training. IEEE Internatinal Electron Devices Meeting (IEDM) 10.5.1–10.5.4. https://doi.org/10.1109/IEDM45625.2022.10019482 (2022).
Gerstner, W., Kistler, W. M., Naud, R. & Paninski, L. Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. https://doi.org/10.1017/CBO9781107447615 (2014).
Caporale, N. & Dan, Y. Spike timing–dependent plasticity: a Hebbian learning rule. Annu. Rev. Neurosci. 31, 25–46 (2008).
Krzysteczko, P., Münchenberger, J., Schäfers, M., Reiss, G. & Thomas, A. The memristive magnetic tunnel junction as a nanoscopic synapse-neuron system. Adv. Mater. 24, 762–766 (2012).
Chua, L., Sbitnev, V. & Kim, H. Hodgkin-Huxley axon is made of memristors. Int. J. Bifurc. Chaos 22, 1230011 (2012).
Yi, W. et al. Biological plausibility and stochasticity in scalable VO 2 active memristor neurons. Nat. Commun. 9, 4661 (2018).
Hassan, N. et al. Magnetic domain wall neuron with lateral inhibition. J. Appl. Phys. 124, 152127 (2018).
Li, S. et al. Magnetic skyrmion-based artificial neuron device. Nanotechnology 28, 31LT01 (2017).
Chen, X. et al. A compact skyrmionic leaky–integrate–fire spiking neuron device. Nanoscale 10, 6139–6146 (2018).
Yang, Q. et al. Spintronic integrate-fire-reset neuron with stochasticity for neuromorphic computing. Nano Lett. 22, 8437–8444 (2022).
Tanaka, G. et al. Recent advances in physical reservoir computing: a review. Neural Networks 115, 100–123 (2019).
Wu, X., Tong, Z. & Shao, Q. Optimizing reservoir computing based on an alternating input-driven spin-torque oscillator. Phys. Rev. Appl. 20, 024069 (2023).
Papp, Á., Porod, W. & Csaba, G. Nanoscale neural network using non-linear spin-wave interference. Nat. Commun. 12, 6422 (2021).
Prychynenko, D. et al. Magnetic skyrmion as a nonlinear resistive element: a potential building block for reservoir computing. Phys. Rev. Appl. 9, 014034 (2018).
Pinna, D., Bourianoff, G. & Everschor-Sitte, K. Reservoir computing with random skyrmion textures. Phys. Rev. Appl. 14, 054020 (2020).
Yokouchi, T. et al. Pattern recognition with neuromorphic computing using magnetic field–induced dynamics of skyrmions. Sci. Adv. 8, eabq5652 (2022).
Sun, Y. et al. Experimental demonstration of a skyrmion-enhanced strain-mediated physical reservoir computing system. Nat. Commun. 14, 3434 (2023).
Appeltant, L. et al. Information processing using a single dynamical node as complex system. Nat. Commun. 2, 468 (2011).
Furuta, T. et al. Macromagnetic simulation for reservoir computing utilizing spin dynamics in magnetic tunnel junctions. Phys. Rev. Appl. 10, 034063 (2018).
Tsunegi, S. et al. Physical reservoir computing based on spin torque oscillator with forced synchronization. Appl. Phys. Lett. 114, 164101 (2019).
Marković, D. et al. Reservoir computing with the frequency, phase, and amplitude of spin-torque nano-oscillators. Appl. Phys. Lett. 114, 012409 (2019).
Riou, M. et al. Temporal pattern recognition with delayed-feedback spin-torque nano-oscillators. Phys. Rev. Appl. 12, 024049 (2019).
Dvornik, M., Awad, A. A. & Åkerman, J. Origin of magnetization auto-oscillations in constriction-based spin hall nano-oscillators. Phys. Rev. Appl. 9, 014017 (2018).
Leroux, N. et al. Radio-frequency multiply-and-accumulate operations with spintronic synapses. Phys. Rev. Appl. 15, 034067 (2021).
Leroux, N. et al. Hardware realization of the multiply and accumulate operation on radio-frequency signals with magnetic tunnel junctions. Neuromorphic Comput. Eng. 1, 011001 (2021).
Zahedinejad, M. et al. Memristive control of mutual spin Hall nano-oscillator synchronization for neuromorphic computing. Nat. Mater. 21, 81–87 (2022).
Ross, A. et al. Multilayer spintronic neural networks with radiofrequency connections. Nat. Nanotechnol. 18, 1273–1280 (2023).
Jiang, W. et al. Physical reservoir computing using magnetic skyrmion memristor and spin torque nano-oscillator. Appl. Phys. Lett. 115, 192403 (2019).
Ababei, R. V. et al. Neuromorphic computation with a single magnetic domain wall. Sci. Rep. 11, 15587 (2021).
Lee, O. et al. Task-adaptive physical reservoir computing. Nat. Mater. 23, 79–87 (2023).
Stenning, K. D. et al. Neuromorphic overparameterisation and few-shot learning in multilayer physical neural networks. Nat. Commun. 15, 7377 (2024).
Rippard, W. H. et al. Injection locking and phase control of spin transfer nano-oscillators. Phys. Rev. Lett. 95, 067203 (2005).
Mancoff, F. B., Rizzo, N. D., Engel, B. N. & Tehrani, S. Phase-locking in double-point-contact spin-transfer devices. Nature 437, 393–395 (2005).
Kaka, S. et al. Mutual phase-locking of microwave spin torque nano-oscillators. Nature 437, 389–392 (2005).
Grollier, J., Cros, V. & Fert, A. Synchronization of spin-transfer oscillators driven by stimulated microwave currents. Phys. Rev. B 73, 060409 (2006).
Yogendra, K., Fan, D. & Roy, K. Coupled spin torque nano oscillators for low power neural computation. IEEE Trans. Magn. 51, 1–9 (2015).
Awad, A. A. et al. Long-range mutual synchronization of spin Hall nano-oscillators. Nat. Phys. 13, 292–299 (2017).
Lebrun, R. et al. Mutual synchronization of spin torque nano-oscillators through a long-range and tunable electrical coupling scheme. Nat. Commun. 8, 15825 (2017).
Zahedinejad, M. et al. Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for neuromorphic computing. Nat. Nanotechnol. 15, 47–52 (2020).
Jin, C. et al. Array of synchronized nano-oscillators based on repulsion between domain wall and skyrmion. Phys. Rev. Appl. 9, 044007 (2018).
Csaba, G. & Porod, W. Coupled oscillators for computing: a review and perspective. Appl. Phys. Rev. 7, 011302 (2020).
Nikonov, D. E. et al. Coupled-oscillator associative memory array operation for pattern recognition. IEEE J. Explor. Solid-State Comput. Devices Circuits 1, 85–93 (2015).
Pufall, M. R. et al. Physical implementation of coherently coupled oscillator networks. IEEE J. Explor. Solid-State Comput. Devices Circuits 1, 76–84 (2015).
Litvinenko, A., Khymyn, R., Ovcharov, R. & Åkerman, J. A 50-spin surface acoustic wave Ising machine. Commun. Phys. 8, 58 (2025).
Mohseni, N., McMahon, P. L. & Byrnes, T. Ising machines as hardware solvers of combinatorial optimization problems. Nat. Rev. Phys. 4, 363–379 (2022).
Brächer, T., Pirro, P. & Hillebrands, B. Parallel pumping for magnon spintronics: Amplification and manipulation of magnon spin currents on the micron-scale. Phys. Rep. 699, 1–34 (2017).
Kumar, A. et al. Fabrication of voltage-gated spin Hall nano-oscillators. Nanoscale 14, 1432–1439 (2022).
Kumar, A. et al. Robust mutual synchronization in long spin hall nano-oscillator chains. Nano Lett 23, 6720–6726 (2023).
Choi, J.-G. et al. Voltage-driven gigahertz frequency tuning of spin Hall nano-oscillators. Nat. Commun. 13, 3783 (2022).
Khademi, M., Kumar, A., Rajabali, M., Dash, S. P. & Åkerman, J. Large non-volatile frequency tuning of spin hall nano-oscillators using circular memristive nano-gates. IEEE Electron Device Lett 45, 268–271 (2024).
Kumar, A. et al. Spin-wave-mediated mutual synchronization and phase tuning in spin Hall nano-oscillators. Nat. Phys. https://doi.org/10.1038/s41567-024-02728-1 (2025).
Wittrock, S. et al. Non-hermiticity in spintronics: oscillation death in coupled spintronic nano-oscillators through emerging exceptional points. Nat. Commun. 15, 971 (2024).
Chen, T. et al. Spin-torque and spin-hall nano-oscillators. Proc. IEEE 104, 1919–1945 (2016).
Wiesenfeld, K. & Moss, F. Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature 373, 33–36 (1995).
Phan, N.-T. et al. Unbiased random bitstream generation using injection-locked spin-torque nano-oscillators. Phys. Rev. Appl. 21, 034063 (2024).
Srinivasan, G., Sengupta, A. & Roy, K. Magnetic tunnel junction based long-term short-term stochastic synapse for a spiking neural network with on-chip STDP learning. Sci. Rep. 6, 29545 (2016).
Cai, J. et al. Voltage-controlled spintronic stochastic neuron based on a magnetic tunnel junction. Phys. Rev. Appl. 11, 034015 (2019).
Farcis, L. et al. Spiking dynamics in dual free layer perpendicular magnetic tunnel junctions. Nano Lett. 23, 7869–7875 (2023).
Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).
Camsari, K. Y., Faria, R., Sutton, B. M. & Datta, S. Stochastic p-bits for invertible logic. Phys. Rev. X 7, 031014 (2017).
Yin, J. et al. Scalable ising computer based on ultra-fast field-free spin orbit torque stochastic device with extreme 1-bit quantization. IEEE International Electron Devices Meeting (IEDM) 36.1.1–36.1.4. https://doi.org/10.1109/IEDM45625.2022.10019520 (2022).
Shao, Y. et al. Probabilistic computing with voltage-controlled dynamics in magnetic tunnel junctions. Nanotechnology 34, 495203 (2023).
Chowdhury, S. et al. A full-stack view of probabilistic computing with p-bits: devices, architectures, and algorithms. IEEE J. Explor. Solid-State Comput. Devices Circuits 9, 1–11 (2023).
Grimaldi, A. et al. Experimental evaluation of simulated quantum annealing with MTJ-augmented p-bits. IEEE Electron Devices Meeting (IEDM) 22.4.1–22.4.4. https://doi.org/10.1109/IEDM45625.2022.10019530 (2022).
Chai, X., Fu, X., Gan, Z., Lu, Y. & Chen, Y. A color image cryptosystem based on dynamic DNA encryption and chaos. Sig. Process. 155, 44–62 (2019).
Chua, L. O. Memristors on ‘edge of chaos’. Nat. Rev. Electr. Eng. 1, 614–627 (2024).
Yang, K. et al. Transiently chaotic simulated annealing based on intrinsic nonlinearity of memristors for efficient solution of optimization problems. Sci. Adv. 6, eaba9901 (2020).
Yoo, M.-W. et al. Pattern generation and symbolic dynamics in a nanocontact vortex oscillator. Nat. Commun. 11, 601 (2020).
Wang, L. et al. Cascadable in-memory computing based on symmetric writing and readout. Sci. Adv. 8, eabq6833 (2022).
Mellnik, A. R. et al. Spin-transfer torque generated by a topological insulator. Nature 511, 449–451 (2014).
Fan, Y. et al. Magnetization switching through giant spin-orbit torque in a magnetically doped topological insulator heterostructure. Nat Mater 13, 699–704 (2014).
Shao, Q. et al. Room temperature highly efficient topological insulator/Mo/CoFeB spin-orbit torque memory with perpendicular magnetic anisotropy. In IEEE International Electron Devices Meeting (IEDM) 36.3.1-36.3.4 https://doi.org/10.1109/IEDM.2018.8614499 (2018).
Song, T. et al. Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures. Science 360, 1214–1218 (2018).
Liu, Y. et al. Cryogenic in-memory computing using magnetic topological insulators. Nat. Mater. https://doi.org/10.1038/s41563-024-02088-4 (2025).
Jinnai, B. et al. High-performance shape-anisotropy magnetic tunnel junctions down to 2.3 nm. In 2020 IEEE International Electron Devices Meeting (IEDM) 24.6.1–24.6.4. https://doi.org/10.1109/IEDM13553.2020.9371972 (IEEE, 2020).
Igarashi, J. et al. Single-nanometer CoFeB/MgO magnetic tunnel junctions with high-retention and high-speed capabilities. npj Spintron 2, 1 (2024).
Behera, N. et al. Ultra-low current 10 nm spin hall nano-oscillators. Adv. Mater. 36, 2305002 (2024).
Leonard, T. et al. Shape-dependent multi-weight magnetic artificial synapses for neuromorphic computing. Adv. Electron. Mater. 8, 2200563 (2022).
Raymenants, E. et al. Nanoscale domain wall devices with magnetic tunnel junction read and write. Nat. Electron. 4, 392–398 (2021).
Larrañaga, by J. U. et al. Electrical detection and nucleation of a magnetic skyrmion in a magnetic tunnel junction observed via operando magnetic microscopy. Nano Lett. 24, 3557–3565 (2024).
Liu, C. et al. Long-distance propagation of short-wavelength spin waves. Nat. Commun. 9, 738 (2018).
Wang, H. et al. Long-distance coherent propagation of high-velocity antiferromagnetic spin waves. Phys. Rev. Lett. 130, 096701 (2023).
Connelly, D. A. et al. Efficient electromagnetic transducers for spin-wave devices. Sci. Rep. 11, 18378 (2021).
Schuman, C. D. et al. Opportunities for neuromorphic computing algorithms and applications. Nat. Comput. Sci. 2, 10–19 (2022).
Lucas, A. Ising formulations of many NP problems. Front. Phys. 2, 5 (2014).
Corinto, F., Forti, M. & Chua, L. O. Nonlinear Circuits and Systems with Memristors. https://doi.org/10.1007/978-3-030-55651-8 (Springer International Publishing, 2021).
Kim, J. Y. et al. Tuning spin-orbit torques across the phase transition in VO2/NiFe heterostructure. Adv. Funct. Mater. 32, 2111555 (2022).
Jones, N. How to stop data centres from gobbling up the world’s electricity. Nature 561, 163–166 (2018).