Resonate and Fire Neuron with Fixed Magnetic Skyrmions

In the brain, the membrane potential of many neurons oscillates in a subthreshold damped fashion and fire when excited by an input frequency that nearly equals their eigen frequency. In this work, we investigate theoretically the artificial implementation of such "resonate-and-fire" neurons by utilizing the magnetization dynamics of a fixed magnetic skyrmion in the free layer of a magnetic tunnel junction (MTJ). To realize firing of this nanomagnetic implementation of an artificial neuron, we propose to employ voltage control of magnetic anisotropy or voltage generated strain as an input (spike or sinusoidal) signal, which modulates the perpendicular magnetic anisotropy (PMA). This results in continual expansion and shrinking (i.e. breathing) of a skyrmion core that mimics the subthreshold oscillation. Any subsequent input pulse having an interval close to the breathing period or a sinusoidal input close to the eigen frequency drives the magnetization dynamics of the fixed skyrmion in a resonant manner. The time varying electrical resistance of the MTJ layer due to this resonant oscillation of the skyrmion core is used to drive a Complementary Metal Oxide Semiconductor (CMOS) buffer circuit, which produces spike outputs. By rigorous micromagnetic simulation, we investigate the interspike timing dependence and response to different excitatory and inhibitory incoming input pulses. Finally, we show that such resonate and fire neurons have potential application in coupled nanomagnetic oscillator based associative memory arrays

Energy Efficient Spintronic Device for Neuromorphic Computation

Future computing will require significant development in new computing device paradigms. This is motivated by CMOS devices reaching their technological limits, the need for non-Von Neumann architectures as well as the energy constraints of wearable technologies and embedded processors. The first device proposal, an energy-efficient voltage-controlled domain wall device for implementing an artificial neuron and synapse is analyzed using micromagnetic modeling. By controlling the domain wall motion utilizing spin transfer or spin orbit torques in association with voltage generated strain control of perpendicular magnetic anisotropy in the presence of Dzyaloshinskii-Moriya interaction (DMI), different positions of the domain wall are realized in the free layer of a magnetic tunnel junction to program different synaptic weights. Additionally, an artificial neuron can be realized by combining this DW device with a CMOS buffer. The second neuromorphic device proposal is inspired by the brain. Membrane potential of many neurons oscillate in a subthreshold damped fashion and fire when excited by an input frequency that nearly equals their Eigen frequency. We investigate theoretical implementation of such “resonate-and-fire” neurons by utilizing the magnetization dynamics of a fixed magnetic skyrmion based free layer of a magnetic tunnel junction (MTJ). Voltage control of magnetic anisotropy or voltage generated strain results in expansion and shrinking of a skyrmion core that mimics the subthreshold oscillation. Finally, we show that such resonate and fire neurons have potential application in coupled nanomagnetic oscillator based associative memory arrays

Neuromorphic weighted sum with magnetic skyrmions

Integrating magnetic skyrmion properties into neuromorphic computing promises advancements in hardware efficiency and computational power. However, a scalable implementation of the weighted sum of neuron signals, a core operation in neural networks, has yet to be demonstrated. In this study, we exploit the non-volatile and particle-like characteristics of magnetic skyrmions, akin to synaptic vesicles and neurotransmitters, to perform this weighted sum operation in a compact, biologically-inspired manner. To this aim, skyrmions are electrically generated in numbers proportional to the input with an efficiency given by a non-volatile weight. These chiral particles are then directed using localized current injections to a location where their presence is quantified through non-perturbative electrical measurements. Our experimental demonstration, currently with two inputs, can be scaled to accommodate multiple inputs and outputs using a crossbar array design, potentially nearing the energy efficiency observed in biological systems.Comment: 12 pages, 5 figure

A Survey on Reservoir Computing and its Interdisciplinary Applications Beyond Traditional Machine Learning

Reservoir computing (RC), first applied to temporal signal processing, is a recurrent neural network in which neurons are randomly connected. Once initialized, the connection strengths remain unchanged. Such a simple structure turns RC into a non-linear dynamical system that maps low-dimensional inputs into a high-dimensional space. The model's rich dynamics, linear separability, and memory capacity then enable a simple linear readout to generate adequate responses for various applications. RC spans areas far beyond machine learning, since it has been shown that the complex dynamics can be realized in various physical hardware implementations and biological devices. This yields greater flexibility and shorter computation time. Moreover, the neuronal responses triggered by the model's dynamics shed light on understanding brain mechanisms that also exploit similar dynamical processes. While the literature on RC is vast and fragmented, here we conduct a unified review of RC's recent developments from machine learning to physics, biology, and neuroscience. We first review the early RC models, and then survey the state-of-the-art models and their applications. We further introduce studies on modeling the brain's mechanisms by RC. Finally, we offer new perspectives on RC development, including reservoir design, coding frameworks unification, physical RC implementations, and interaction between RC, cognitive neuroscience and evolution.Comment: 51 pages, 19 figures, IEEE Acces

Spin dynamics under spin Hall effect modulation: Skyrmion oscillator

학위논문(박사)--서울대학교 대학원 :자연과학대학 물리·천문학부(물리학전공),2019. 8. 최석봉.A magnet exhibits semi-permanent magnetic field, unless the ordering of magnetic moments does not break by external factors. This so-called non-volatility of magnetization can be harnessed to realize a power-efficient data storage, provided with proper mechanisms to modify the magnetization. These mechanisms were established by the discovery of giant magnetoresistance and spin-polarized current in the 1980s, which enabled the electric detection and control of magnetization, respectively. The concept of spin finally entered the field of electronics, which consecutively led to successful applications in the logic and memory devices. This associated field of study is called the spintronics, also known as the spin electronics. Since the spintronics is involved deeply with the collective ordering of the spins, the constraints bestowed upon the system not only expand the phenomena toward exotic dynamics but also provide design rules to achieve desirable properties. Among various possible constraints, a simple tri-layered system of a ferromagnetic thin film sandwiched between two nonmagnetic layers, exhibit surprisingly complex spin dynamics depending on the choice of the materials and their respective thicknesses. As a result, the current-induced spin dynamics in this tri-layered magnetic system is mainly studied throughout the thesis. Amid the various interesting dynamics of a tri-layered film, the spin-Hall effect (SHE) in the sandwiching heavy metal layers that transfer spin polarized current into the ferromagnetic layer, stands out with its design capabilities. Since the magnitude and sign of the spin polarized current by SHE depends on the material and its thickness, one can manipulate the transferred spin torque by modulating the thickness of the sandwiching layers. This technique is called the spin-Hall-effect modulation and exhibits some interesting features. The thesis is mainly directed on searching what and how exotic spin dynamics happen at the wires with laterally modulated SHE, via micromagnetic simulations and analytic equation analysis. Chapter 2 shows how the current-driven domain wall (DW) pins and depins from various types of spin-Hall-effect-modulation boundaries. The method of unidirectional depinning from given modulation boundaries are investigated. This unidirectional depinning behavior provides a systematic mechanism to precisely move a DW step-by-step toward next modulation boundaries only by alternating the direction of electric current, which will assist the realization of a racetrack memory. Chapter 3 is the highlight of this study where we propose a whole new concept of spin-torque oscillator, based on magnetic skyrmion dynamics subject to lateral modulation of the SHE. In the oscillator, a skyrmion circulates around the modulation boundary between opposite SHE-torque regions, where the SHE pushes the skyrmion in the opposite direction, toward the modulation boundary. A micromagnetic simulation confirms such oscillations. This SHE-modulation-based skyrmion oscillator is expected to overcome the troubling issues of conventional spin-torque oscillators. As part of recent approaches to search for possible applications of spintronic devices, neuromorphic engineering is also briefly discussed in Chapter 4. A neuron device with integrate-and-fire feature is realized via current-driven DW motion in a wire with a magnetic tunnel junction at the end. With the already proposed idea of a DW synapse device, all-DW-based artificial neural network can be realized. Additionally, miscellaneous analytic equations were derived to help magnetic-parameter measurement and to offer design rules for certain properties. The depinning current from a triangle notch, the equations to measure spin-orbit torque at any initial angle and the equations to measure anisotropy field from magneto optical Kerr effect setup are derived from associated analytic models and explained in Chapter 5. Findings analyzed in this thesis provide the latest understanding of the spin-Hall effect modulated systems and some others. The explained spin dynamics in these systems not only exhibit properties that can better the state-of-the-art applications, but also triggers new possibilities to design in completely unconventional ways.강자성 물질은 정렬된 자화의 상태가 외부 요인에 의해 깨지지 않는 한, 반영구적으로 자기장을 가진다. 이것은 자화가 일종의 비휘발성을 가진다는 것을 의미하며, 이는 자화를 변화시킬 수 있는 적절한 방법이 갖추어진다면, 자성물질을 이용하여 저전력의 저장장치를 구현할 수 있다는 것을 의미한다. 실제로 1980 년대부터 거대 자기 저항 효과 (giant magnetoresistance: GMR)와 스핀 토크 현상 (spin torque)이 발견됨으로써, 자화가 각자 전기적으로 측정되거나, 컨트롤 될 수 있게 되었고, 이로 인해, 물질의 스핀 상태가 본격적으로 전기 소자에 응용되기 시작하였다. 주로 논리 및 메모리 소자에 응용되는 관련 분야에 대한 제반의 연구를 스핀트로닉스 (spintronics: spin electronics)라고 부른다. 스핀트로닉스는 언급하였듯이, 스핀들의 집단 현상에 깊게 관계되어 있기 때문에, 시스템에 주어진 여러 제한 조건들에 의해, 완전히 새로운 현상이 발견될 뿐만이 아니라, 그 조건을 이용함으로써, 원하는 특성을 디자인 할 수 있는 가능성까지 갖추고 있다. 여러 제한조건들 중, 간단한 3층 구조의 강자성 박막이 놀랍도록 복잡한 스핀 동역학을 보이는 것이 알려져 있다. 강자성 물질만이 아닌, 이웃하는 층의 물질과 두께, 경계면의 조건 등에 의해 다양한 자성 특징이 관찰되고 있고, 이 논문 또한 이러한 3층 구조에 전류가 주입되었을 때 나타나는 여러 현상을 밝히고 이용하는 데 핵심을 두고 있다. 3층 구조 필름의 여러 흥미로운 동역학 중에서도, 자성층에 이웃한 물질층에서 일어나는 스핀 홀 효과 (spin-Hall effect: SHE)는 디자인의 용이함에 있어 뛰어난 모습을 보인다. 스핀 홀 효과의 크기와 부호는 이웃층의 물질만이 아닌 두께에 따라 바뀌기 때문에, 이웃층의 두께를 바꾸어주는 것만으로, 자성층에 스핀 홀 효과로 인해 전달되는 스핀 토크의 크기 및 부호를 마음대로 바꾸어 줄 수 있다. 이 기술은 스핀 홀 효과 조정 기술 (spin-Hall effect modulation)으로 불리며, 이 논문은 이 스핀 홀 효과 조정 기술을 이용하여 스핀 홀 효과의 크기 및 부호가 다른 영역을 만들어 준 특수한 시스템들에서 어떤 새로운 스핀 동역학이 관찰 될 수 있는지를 미소자기시뮬레이션 (micromagnetic simulation)과 이론적 분석을 통해 연구하였다. 챕터 2는 전류로 구동되는 자구벽 (domain wall: DW)이 어떻게 스핀 홀 효과 조정 경계면에서 피닝 (pinning) 및 디피닝 (depinning) 되는 지 소개한다. 주어진 조정 경계면에서의 한쪽 방향으로 자구벽을 디피닝 시키는 방법이 소개되며, 이를 이용하여, 자구벽을 흐르는 전류의 부호를 바꾸어주는 것만으로 순차적으로 다음 조정 경계면으로 패스해나갈 수 있는 구조적인 방법을 구현함으로써, 학계의 주요 관심사인 레이스트랙 메모리의 실현에 한 걸음 더 다가간다. 챕터 3는 본 논문의 하이라이트로써, 스핀 토크 진동자의 새로운 컨셉을 기울어진 스핀 홀 효과 조정 경계면에서의 자성 스커미온 (skyrmion)의 동역학을 이용하여 구현한 결과를 소개한다. 진동자 구조 내부에서, 스커미온은 서로 스핀 홀 효과의 부호가 반대인 스핀 홀 효과 조정 영역 사이의 경계면을 따라 돌며, 이는 미소자기시뮬레이션을 통해 확인되었다. 새로운 컨셉인 스핀 홀 효과 조정 스커미온 진동자 (spin-Hall-effect-modulation skyrmion oscillator: SHEM-SO)는 현재까지 제시되어 있는 스핀 토크 진동자들의 모든 결함을 극복할 수 있을 것으로 기대된다. 챕터 4에서는 현재 스핀트로닉스가 새로이 역할을 할 바이오 모방 신경 공학 (neuromorphic engineering)에서 얻은 결과를 간략히 소개한다. 전류 구동 자구벽 움직임과 자기 터널 효과를 이용하여, 적분 및 발사 (integrate and fire) 기능을 구현한 뉴론 장비가 이미 제시되어 있는 자구벽 시냅스 디바이스와 합쳐져, 자구벽만으로 구현 가능한 인공 신경망 구조가 소개된다. 추가적으로, 자기 특성을 측정하거나, 새로운 장비의 디자인 룰을 제공하는 데 도움이 될 수 있는 여러 분석식들을 유도한 결과를 소개한다. 삼각 놋치 구조에서의 디피닝 전류의 식과, 임의의 자화 각도에서 스핀 궤도 토크 (spin-orbit torque)를 측정하는 데 필요한 식과, 광자기 컬 효과 (magneto optical Kerr effect: MOKE) 셋업 상에서 수직 비등방성 자기장 (perpendicular magneto anisotropy field)를 측정하는 데 필요한 식 등을 유도한 결과를 챕터 5에서 간략히 다룬다. 본 논문에 기술되어 있는 발견들은 스핀 횰 효과 조정 시스템에 대한 최신의 이해를 제공한다. 이런 시스템들에서 설명되는 스핀 동역학은, 최신 스핀트로닉스 장비들의 기준을 한 단계 업그레이드할 뿐만이 아니라, 틀에 박힌 스핀트로닉스 소자의 디자인 룰을 타파하고, 온전히 새로운 방식의 접근을 가능케 한다는 점에서 의의를 가진다.Contents Abstract 02 List of Figures 08 1. Introduction 11 1.1 Magnetic anisotropy 13 1.2 Spin torque 14 1.2.1 Spin-transfer torque 14 1.2.2 Spin-orbit torque 17 1.2.3 Spin-Hall effect modulation 19 1.3 Magnetic structures 20 1.3.1 Domain wall 20 1.3.2 Dzyaloshinskii-Moriya interaction 22 1.3.3 Skyrmion 23 1.4 Ferrimagnetism 24 1.5 Micromagnetic simulation 26 2. Domain wall pinning/depinning at the spin-Hall-effect-modulation boundary 29 2.1 Introduction 30 2.2 Pinning at the spin-Hall-effect-modulation boundary 31 2.3 Unstable depinning at the spin-Hall-effect-modulation boundary 33 2.4 Unidirectional depinning at three different spin-Hall-effect-modulation boundaries 35 3. Spin-Hall-effect-modulation skyrmion oscillator 44 3.1 Introduction 45 3.2 Skyrmion motion at the tilted spin-Hall-effect-modulation boundary 47 3.3 Properties of the spin-Hall-effect-modulation skyrmion oscillator 51 3.4 Spin-Hall-effect-modulation skyrmion oscillator in the synthetic ferrimagnetic structure 52 3.5 Conclusion 54 3.6 Supplementary analysis 54 3.6.1 Simulation methods 54 3.6.2 Thiele formula for skyrmion motion near modulation boundary 55 3.6.3 Thiele formula for synthetic ferrimagnets 58 3.6.4 Frequency variation with respect to the angle of the modulation boundary 60 4. Domain wall neuron device 62 4.1 Introduction 63 4.2 Synapse device 66 4.3 Neuron device 67 5. Derivation of miscellaneous analytic equations 70 5.1 The analytic formula on depinning current of magnetic domain walls driven by spin-orbit torques from artificial notches 71 5.1.1 Depinning field/current from a notch 72 5.1.2 1st-order approximation for transverse spin-orbit torque 80 5.2 1st-order equation of equilibrium angle under spin-orbit torque from any initial angle 82 5.3 Optical measurement of magnetic anisotropy field in nanostructured-ferromagnetic thin films 86 6. Conclusion 94 References 96 Publication List 107 Abstract in Korean (국문 초록) 108 Acknowledgments (감사의 글) 111Docto