1
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Chen TY, Ren H, Ghazikhanian N, Hage RE, Sasaki DY, Salev P, Takamura Y, Schuller IK, Kent AD. Electrical Control of Magnetic Resonance in Phase Change Materials. NANO LETTERS 2024; 24:11476-11481. [PMID: 39231136 PMCID: PMC11421091 DOI: 10.1021/acs.nanolett.4c02697] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2024] [Revised: 08/23/2024] [Accepted: 08/30/2024] [Indexed: 09/06/2024]
Abstract
Metal-insulator transitions (MITs) in resistive switching materials can be triggered by an electric stimulus that produces significant changes in the electrical response. When these phases have distinct magnetic characteristics, dramatic changes in the spin excitations are also expected. The transition metal oxide La0.7Sr0.3MnO3 (LSMO) is a ferromagnetic metal at low temperatures and a paramagnetic insulator above room temperature. When LSMO is in its metallic phase, a critical electrical bias has been shown to lead to an MIT that results in the formation of a paramagnetic resistive barrier transverse to the applied electric field. Using spin-transfer ferromagnetic resonance spectroscopy, we show that even for electrical biases less than the critical value that triggers the MIT, there is magnetic phase separation, with the spin-excitation resonances varying systematically with applied bias. Therefore, voltage-triggered MITs in LSMO can alter magnetic resonance characteristics, offering an effective method for tuning synaptic weights in neuromorphic circuits.
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Affiliation(s)
- Tian-Yue Chen
- Center
for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, United States
| | - Haowen Ren
- Center
for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, United States
| | - Nareg Ghazikhanian
- Department
of Physics, University of California San
Diego, La Jolla, California 92093, United States
| | - Ralph El Hage
- Department
of Physics, University of California San
Diego, La Jolla, California 92093, United States
| | - Dayne Y. Sasaki
- Department
of Materials Science and Engineering, University
of California−Davis, Davis, California 95616, United States
| | - Pavel Salev
- Department
of Physics and Astronomy, University of
Denver, Denver, Colorado 80210, United States
| | - Yayoi Takamura
- Department
of Materials Science and Engineering, University
of California−Davis, Davis, California 95616, United States
| | - Ivan K. Schuller
- Department
of Physics, University of California San
Diego, La Jolla, California 92093, United States
| | - Andrew D. Kent
- Center
for Quantum Phenomena, Department of Physics, New York University, New York, New York 10003, United States
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2
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Stenning KD, Gartside JC, Manneschi L, Cheung CTS, Chen T, Vanstone A, Love J, Holder H, Caravelli F, Kurebayashi H, Everschor-Sitte K, Vasilaki E, Branford WR. Neuromorphic overparameterisation and few-shot learning in multilayer physical neural networks. Nat Commun 2024; 15:7377. [PMID: 39191747 PMCID: PMC11350220 DOI: 10.1038/s41467-024-50633-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Accepted: 07/17/2024] [Indexed: 08/29/2024] Open
Abstract
Physical neuromorphic computing, exploiting the complex dynamics of physical systems, has seen rapid advancements in sophistication and performance. Physical reservoir computing, a subset of neuromorphic computing, faces limitations due to its reliance on single systems. This constrains output dimensionality and dynamic range, limiting performance to a narrow range of tasks. Here, we engineer a suite of nanomagnetic array physical reservoirs and interconnect them in parallel and series to create a multilayer neural network architecture. The output of one reservoir is recorded, scaled and virtually fed as input to the next reservoir. This networked approach increases output dimensionality, internal dynamics and computational performance. We demonstrate that a physical neuromorphic system can achieve an overparameterised state, facilitating meta-learning on small training sets and yielding strong performance across a wide range of tasks. Our approach's efficacy is further demonstrated through few-shot learning, where the system rapidly adapts to new tasks.
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Affiliation(s)
- Kilian D Stenning
- Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom.
- London Centre for Nanotechnology, Imperial College London, London, SW7 2AZ, United Kingdom.
| | - Jack C Gartside
- Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom
- London Centre for Nanotechnology, Imperial College London, London, SW7 2AZ, United Kingdom
| | - Luca Manneschi
- University of Sheffield, Sheffield, S10 2TN, United Kingdom
| | | | - Tony Chen
- Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom
| | - Alex Vanstone
- Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom
| | - Jake Love
- Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, 47057, Duisburg, Germany
| | - Holly Holder
- Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom
| | - Francesco Caravelli
- Theoretical Division (T4), Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Hidekazu Kurebayashi
- London Centre for Nanotechnology, University College London, London, WC1H 0AH, United Kingdom
- Department of Electronic and Electrical Engineering, University College London, London, WC1H 0AH, United Kingdom
- WPI Advanced Institute for Materials Research, Tohoku University, Sendai, Japan
| | - Karin Everschor-Sitte
- Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, 47057, Duisburg, Germany
| | - Eleni Vasilaki
- University of Sheffield, Sheffield, S10 2TN, United Kingdom
| | - Will R Branford
- Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom
- London Centre for Nanotechnology, Imperial College London, London, SW7 2AZ, United Kingdom
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3
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Bradley H, Quach L, Louis S, Tyberkevych V. Antiferromagnetic artificial neuron modeling of the withdrawal reflex. J Comput Neurosci 2024; 52:197-206. [PMID: 38987452 DOI: 10.1007/s10827-024-00873-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Revised: 05/29/2024] [Accepted: 05/30/2024] [Indexed: 07/12/2024]
Abstract
Replicating neural responses observed in biological systems using artificial neural networks holds significant promise in the fields of medicine and engineering. In this study, we employ ultra-fast artificial neurons based on antiferromagnetic (AFM) spin Hall oscillators to emulate the biological withdrawal reflex responsible for self-preservation against noxious stimuli, such as pain or temperature. As a result of utilizing the dynamics of AFM neurons, we are able to construct an artificial neural network that can mimic the functionality and organization of the biological neural network responsible for this reflex. The unique features of AFM neurons, such as inhibition that stems from an effective AFM inertia, allow for the creation of biologically realistic neural network components, like the interneurons in the spinal cord and antagonist motor neurons. To showcase the effectiveness of AFM neuron modeling, we conduct simulations of various scenarios that define the withdrawal reflex, including responses to both weak and strong sensory stimuli, as well as voluntary suppression of the reflex.
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Affiliation(s)
- Hannah Bradley
- Department of Physics, Oakland University, Rochester, 48309, Michigan, USA.
| | - Lily Quach
- Oakland University William Beaumont School of Medicine, Rochester, 48309, Michigan, USA
| | - Steven Louis
- Department of Electrical and Computer Engineering, Oakland University, Rochester, 48309, Michigan, USA
| | - Vasyl Tyberkevych
- Department of Physics, Oakland University, Rochester, 48309, Michigan, USA
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4
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Querlioz D. Physics solves a training problem for artificial neural networks. Nature 2024; 632:264-265. [PMID: 39112617 DOI: 10.1038/d41586-024-02392-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/10/2024]
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5
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Shen H, Xu L, Jin M, Li H, Yu C, Liu B, Zhou T. Sparse reservoir computing with vertically coupled vortex spin-torque oscillators for time series prediction. NANOTECHNOLOGY 2024; 35:415201. [PMID: 39008966 DOI: 10.1088/1361-6528/ad6328] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2024] [Accepted: 07/15/2024] [Indexed: 07/17/2024]
Abstract
Spin torque nano-oscillators possessing fast nonlinear dynamics and short-term memory functions are potentially able to achieve energy-efficient neuromorphic computing. In this study, we introduce an activation-state controllable spin neuron unit composed of vertically coupled vortex spin torque oscillators and aV-Isource circuit is proposed and used to build an energy-efficient sparse reservoir computing (RC) system to solve nonlinear dynamic system prediction task. Based on micromagnetic and electronic circuit simulation, the Mackey-Glass chaotic time series and the real motor vibration signal series can be predicted by the RC system with merely 20 and 100 spin neuron units, respectively. Further study shows that the proposed sparse reservoir system could reduce energy consumption without significantly compromising performance, and a minimal response from inactivated neurons is crucial for maintaining the system's performance. The accuracy and signal processing speed show the potential of the proposed sparse RC system for high-performance and low-energy neuromorphic computing.
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Affiliation(s)
- Haobo Shen
- School of Electronics and Information Engineering, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, People's Republic of China
| | - Lie Xu
- School of Electronics and Information Engineering, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, People's Republic of China
| | - Menghao Jin
- School of Electronics and Information Engineering, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, People's Republic of China
| | - Hai Li
- School of Electronics and Information Engineering, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, People's Republic of China
| | - Changqiu Yu
- School of Electronics and Information Engineering, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, People's Republic of China
| | - Bo Liu
- Key Laboratory of Spintronics Materials, Devices and Systems of Zhejiang Province, Hangzhou, Zhejiang 311305, People's Republic of China
| | - Tiejun Zhou
- School of Electronics and Information Engineering, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, People's Republic of China
- Key Laboratory of Spintronics Materials, Devices and Systems of Zhejiang Province, Hangzhou, Zhejiang 311305, People's Republic of China
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Liu L, Wang D, Wang D, Sun Y, Lin H, Gong X, Zhang Y, Tang R, Mai Z, Hou Z, Yang Y, Li P, Wang L, Luo Q, Li L, Xing G, Liu M. Domain wall magnetic tunnel junction-based artificial synapses and neurons for all-spin neuromorphic hardware. Nat Commun 2024; 15:4534. [PMID: 38806482 PMCID: PMC11133408 DOI: 10.1038/s41467-024-48631-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2023] [Accepted: 05/06/2024] [Indexed: 05/30/2024] Open
Abstract
We report a breakthrough in the hardware implementation of energy-efficient all-spin synapse and neuron devices for highly scalable integrated neuromorphic circuits. Our work demonstrates the successful execution of all-spin synapse and activation function generator using domain wall-magnetic tunnel junctions. By harnessing the synergistic effects of spin-orbit torque and interfacial Dzyaloshinskii-Moriya interaction in selectively etched spin-orbit coupling layers, we achieve a programmable multi-state synaptic device with high reliability. Our first-principles calculations confirm that the reduced atomic distance between 5d and 3d atoms enhances Dzyaloshinskii-Moriya interaction, leading to stable domain wall pinning. Our experimental results, supported by visualizing energy landscapes and theoretical simulations, validate the proposed mechanism. Furthermore, we demonstrate a spin-neuron with a sigmoidal activation function, enabling high operation frequency up to 20 MHz and low energy consumption of 508 fJ/operation. A neuron circuit design with a compact sigmoidal cell area and low power consumption is also presented, along with corroborated experimental implementation. Our findings highlight the great potential of domain wall-magnetic tunnel junctions in the development of all-spin neuromorphic computing hardware, offering exciting possibilities for energy-efficient and scalable neural network architectures.
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Affiliation(s)
- Long Liu
- Key Lab of Fabrication Technologies for Integrated Circuits, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Di Wang
- Key Lab of Fabrication Technologies for Integrated Circuits, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Dandan Wang
- Hubei Jiufengshan Laboratory, Wuhan, Hubei, 430206, China.
| | - Yan Sun
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China
| | - Huai Lin
- Key Lab of Fabrication Technologies for Integrated Circuits, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Xiliang Gong
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China
| | - Yifan Zhang
- Key Lab of Fabrication Technologies for Integrated Circuits, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Ruifeng Tang
- Key Lab of Fabrication Technologies for Integrated Circuits, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Zhihong Mai
- Hubei Jiufengshan Laboratory, Wuhan, Hubei, 430206, China
| | - Zhipeng Hou
- Institute for Advanced Materials, South China Normal University, Guangzhou, 510006, China
| | - Yumeng Yang
- School of Information Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Peng Li
- School of Microelectronics, University of Science and Technology of China, Hefei, 230026, China
| | - Lan Wang
- Lab of Low Dimensional Magnetism and Spintronic Devices, School of Physics, Hefei University of Technology, Hefei, 230009, Anhui, China
| | - Qing Luo
- Key Lab of Fabrication Technologies for Integrated Circuits, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Ling Li
- Key Lab of Fabrication Technologies for Integrated Circuits, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Guozhong Xing
- Key Lab of Fabrication Technologies for Integrated Circuits, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China.
- University of Chinese Academy of Sciences, Beijing, 100049, China.
| | - Ming Liu
- Key Lab of Fabrication Technologies for Integrated Circuits, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China.
- Frontier Institute of Chip and System, State Key Laboratory of Integrated Chips and Systems, Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, 200433, China.
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7
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Li R, Rezaeiyan Y, Böhnert T, Schulman A, Ferreira R, Farkhani H, Moradi F. Temperature effect on a weighted vortex spin-torque nano-oscillator for neuromorphic computing. Sci Rep 2024; 14:10043. [PMID: 38698145 PMCID: PMC11065860 DOI: 10.1038/s41598-024-60929-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Accepted: 04/26/2024] [Indexed: 05/05/2024] Open
Abstract
In this work, we present fabricated magnetic tunnel junctions (MTJs) that can serve as magnetic memories (MMs) or vortex spin-torque nano-oscillators (STNOs) depending on the device geometry. We explore the heating effect on the devices to study how the performance of a neuromorphic computing system (NCS) consisting of MMs and STNOs can be enhanced by temperature. We further applied a neural network for waveform classification applications. The resistance of MMs represents the synaptic weights of the NCS, while temperature acts as an extra degree of freedom in changing the weights and TMR, as their anti-parallel resistance is temperature sensitive, and parallel resistance is temperature independent. Given the advantage of using heat for such a network, we envision using a vertical-cavity surface-emitting laser (VCSEL) to selectively heat MMs and/or STNO when needed. We found that when heating MMs only, STNO only, or both MMs and STNO, from 25 to 75 °C, the output power of the STNO increases by 24.7%, 72%, and 92.3%, respectively. Our study shows that temperature can be used to improve the output power of neural networks, and we intend to pave the way for future implementation of a low-area and high-speed VCSEL-assisted spintronic NCS.
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Affiliation(s)
- Ren Li
- Department of Electrical and Computer Engineering, Aarhus University, 8200, Aarhus, Denmark.
| | - Yasser Rezaeiyan
- Department of Electrical and Computer Engineering, Aarhus University, 8200, Aarhus, Denmark
| | - Tim Böhnert
- INL-International Iberian Nanotechnology Laboratory, 4715-330, Braga, Portugal
| | - Alejandro Schulman
- INL-International Iberian Nanotechnology Laboratory, 4715-330, Braga, Portugal
| | - Ricardo Ferreira
- INL-International Iberian Nanotechnology Laboratory, 4715-330, Braga, Portugal
| | - Hooman Farkhani
- Department of Electrical and Computer Engineering, Aarhus University, 8200, Aarhus, Denmark
| | - Farshad Moradi
- Department of Electrical and Computer Engineering, Aarhus University, 8200, Aarhus, Denmark.
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8
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Kumar A, Lin DJX, Das D, Huang L, Yap SLK, Tan HR, Tan HK, Lim RJJ, Toh YT, Chen S, Lim ST, Fong X, Ho P. Multistate Compound Magnetic Tunnel Junction Synapses for Digital Recognition. ACS APPLIED MATERIALS & INTERFACES 2024; 16:10335-10343. [PMID: 38376994 DOI: 10.1021/acsami.3c17195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/22/2024]
Abstract
The quest to mimic the multistate synapses for bioinspired computing has triggered nascent research that leverages the well-established magnetic tunnel junction (MTJ) technology. Early works on the spin transfer torque MTJ-based artificial neural network (ANN) are susceptible to poor thermal reliability, high latency, and high critical current densities. Meanwhile, work on spin-orbit torque (SOT) MTJ-based ANN mainly utilized domain wall motion, which yields negligibly small readout signals differentiating consecutive states and has designs that are incompatible with technological scale-up. Here, we propose a multistate device concept built upon a compound MTJ consisting of multiple SOT-MTJs (number of MTJs, n = 1-4) on a shared write channel, mimicking the spin-based ANN. The n + 1 resistance states representing varying synaptic weights can be tuned by varying the voltage pulses (±1.5-1.8 V), pulse duration (100-300 ns), and applied in-plane fields (5.5-10.5 mT). A large TMR difference of more than 13.6% is observed between two consecutive states for the 4-cell compound MTJ, a 4-fold improvement from reported state-of-the-art spin-based synaptic devices. The ANN built upon the compound MTJ shows high learning accuracy for digital recognition tasks with incremental states and retraining, achieving test accuracy as high as 95.75% in the 4-cell compound MTJ. These results provide an industry-compatible platform to integrate these multistate SOT-MTJ synapses directly into neuromorphic architecture for in-memory and unconventional computing applications.
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Affiliation(s)
- Anuj Kumar
- Physics Department, National University of Singapore, 117551 Singapore
| | - Dennis J X Lin
- Institute of Materials Research and Engineering, A*STAR, 138634 Singapore
| | - Debasis Das
- Electrical and Computer Engineering Department, National University of Singapore, 117583 Singapore
| | - Lisen Huang
- Institute of Materials Research and Engineering, A*STAR, 138634 Singapore
| | - Sherry L K Yap
- Institute of Materials Research and Engineering, A*STAR, 138634 Singapore
| | - Hui Ru Tan
- Institute of Materials Research and Engineering, A*STAR, 138634 Singapore
| | - Hang Khume Tan
- Institute of Materials Research and Engineering, A*STAR, 138634 Singapore
| | - Royston J J Lim
- Institute of Materials Research and Engineering, A*STAR, 138634 Singapore
| | - Yeow Teck Toh
- Institute of Materials Research and Engineering, A*STAR, 138634 Singapore
| | - Shaohai Chen
- Institute of Materials Research and Engineering, A*STAR, 138634 Singapore
| | - Sze Ter Lim
- Institute of Materials Research and Engineering, A*STAR, 138634 Singapore
| | - Xuanyao Fong
- Electrical and Computer Engineering Department, National University of Singapore, 117583 Singapore
| | - Pin Ho
- Institute of Materials Research and Engineering, A*STAR, 138634 Singapore
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9
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Wittrock S, Perna S, Lebrun R, Ho K, Dutra R, Ferreira R, Bortolotti P, Serpico C, Cros V. Non-hermiticity in spintronics: oscillation death in coupled spintronic nano-oscillators through emerging exceptional points. Nat Commun 2024; 15:971. [PMID: 38302454 PMCID: PMC10834588 DOI: 10.1038/s41467-023-44436-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 12/13/2023] [Indexed: 02/03/2024] Open
Abstract
The emergence of exceptional points (EPs) in the parameter space of a non-hermitian (2D) eigenvalue problem has long been interest in mathematical physics, however, only in the last decade entered the scope of experiments. In coupled systems, EPs give rise to unique physical phenomena, and enable the development of highly sensitive sensors. Here, we demonstrate at room temperature the emergence of EPs in coupled spintronic nanoscale oscillators and exploit the system's non-hermiticity. We observe amplitude death of self-oscillations and other complex dynamics, and develop a linearized non-hermitian model of the coupled spintronic system, which describes the main experimental features. The room temperature operation, and CMOS compatibility of our spintronic nanoscale oscillators means that they are ready to be employed in a variety of applications, such as field, current or rotation sensors, radiofrequeny and wireless devices, and in dedicated neuromorphic computing hardware. Furthermore, their unique and versatile properties, notably their large nonlinear behavior, open up unprecedented perspectives in experiments as well as in theory on the physics of exceptional points expanding to strongly nonlinear systems.
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Affiliation(s)
- Steffen Wittrock
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 1 Avenue Augustin Fresnel, 91767, Palaiseau, France.
- Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner-Platz 1, 14109, Berlin, Germany.
| | - Salvatore Perna
- Department of Electrical Engineering and ICT, University of Naples Federico II, 80125, Naples, Italy
| | - Romain Lebrun
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 1 Avenue Augustin Fresnel, 91767, Palaiseau, France
| | - Katia Ho
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 1 Avenue Augustin Fresnel, 91767, Palaiseau, France
| | - Roberta Dutra
- Centro Brasileiro de Pesquisas Fésicas (CBPF), Rua Dr. Xavier Sigaud 150, Rio de Janeiro, 22290-180, Brazil
| | - Ricardo Ferreira
- International Iberian Nanotechnology Laboratory (INL), 471531, Braga, Portugal
| | - Paolo Bortolotti
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 1 Avenue Augustin Fresnel, 91767, Palaiseau, France
| | - Claudio Serpico
- Department of Electrical Engineering and ICT, University of Naples Federico II, 80125, Naples, Italy
| | - Vincent Cros
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 1 Avenue Augustin Fresnel, 91767, Palaiseau, France.
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