Magnetic Resonators : Feedback with Magnetic Field and Magnetic Cavity

The phase-locking of multiple spin-torque nano oscillators(STNOs) is considered the primary vehicle to achieve sufficient signal quality for applications. This book highlights the resonator's design and its need for feedback for phase locking of STNOs. STNOs can act as sources of tunable microwaves after being phase-locked together. External feedback from a coplanar waveguide placed above an STNO helps ensures coherent single domain oscillations. STNOs placed within magnonic crystal cavities also demonstrate coherent oscillations. Arrays of such cavities provide a route to scale power levels from such nano-oscillators. The book presents numerical and micromagnetics to validate the design. Contents 7 Abbreviations 9 Notations 9 List of Figures 11 List of Tables 15 1 Introduction 16 1.1 Magnonic Crystals 16 1.1.1 Magnon-Based Computing 18 1.1.2 Magnetoelectronics and Magnon Spintronics 20 1.1.3 STNO Configurations 20 1.1.4 STNO Device Principle 22 1.1.5 Mutual Synchronization of STNOs Through Electrical Coupling 23 1.2 Landau–Lifshitz–Gilbert–Slonczewski Equation 24 1.2.1 Plane Wave Method 25 1.2.2 Micromagnetics 28 1.3 Summary 31 References 32 2 Spin-Wave Excitation Patterns Generated by Spin-Torque Nano-Oscillators 34 2.1 Approximate Model 34 2.2 Micromagnetic Simulations 37 2.2.1 Forward Volume Spin Waves 39 2.2.2 Backward Volume and Surface Spin Waves 41 2.2.3 Multiple NC STNOs 41 2.3 Summary 43 References 44 3 Coherent Spin-Wave Oscillations Through External Feedback 45 3.1 Spintronic Oscillator with Magnetic Field Feedback 45 3.1.1 Quasi-Static Simulations 46 3.1.2 Magnetization Dynamics 48 3.1.3 Simulation Results 50 3.2 Electrical Analogy 57 3.3 Summary 59 References 59 4 Magnonic Spectra in 2D Antidot Magnonic Crystals with Line Defect 60 4.1 Plane Wave Method 60 4.1.1 Convergence 66 4.2 Eigenmodes 66 4.3 Micromagnetic Simulations 68 4.3.1 Magnonic Spectra 69 4.3.2 Antidot Magnonic Crystal Waveguide 70 4.3.3 Dispersion Analysis of an MC3 Cavity 70 4.4 Summary 72 References 73 5 Sustaining Spin-Wave Oscillations Through Internal Feedback 74 5.1 Nanocontact STNO in MC Cavity 75 5.1.1 Design Methodology 76 5.1.2 Spin-Wave Dynamics with MCC-End Fire Antenna 77 5.1.3 Current-Induced Oersted Field in a Micromagnetic Simulation 79 5.1.4 Quality Factor Calculation 82 5.2 Phase Locking of Nanocontact STNOs—Broad Side Antenna 84 5.2.1 Symmetric Array of NC STNOs 89 5.2.2 Asymmetric Array of NC STNOs 91 5.2.3 Detuning of SWs in NC STNOs in MC Cavity 92 5.3 Summary 96 References 98 6 Summary and Future Work 100 6.1 Future Work 102 References 102 Publications 104