An Introduction to Micromagnetics in the Dynamic Regime / Jacques Miltat ; Gonçalo Albuquerque ; André Thiaville |
Macrospin Dynamics / 1: |
Foundations of Magnetization Precession / 1.1: |
Link to Classical Mechanics and Electromagnetism / 1.2: |
Introducing Damping / 1.3: |
Viewing a Soft Thin Film as a Macrospin / 2: |
Energy Functional / 2.1: |
Asymptotic Solution Transverse Susceptibility in a Experiment / 2.2: |
The Dynamical Astro?d and "No-Ringing" Critical Curves / 2.3: |
Magnetization Dynamics Within a Lagrangian Formalism / 2.4: |
Magnetization States at Submicron Sizes / 3: |
Main Contributions to the Energy Density Functional in the Continuum Approximation / 3.1: |
Energy Minimization / 3.2: |
Applications to Rectangular Platelets with a 2: 1 Aspect Ratio / 3.3: |
Magnetization Dynamics in the Continuum Approximation / 4: |
The Landau-Lifshitz-Gilbert Equation of Magnetization Motion / 4.1: |
A Transverse Susceptibility Experiment in the Continuum Approximation / 4.2: |
Energy Dissipation Versus Damping / 4.3: |
Reversal of the "S" State: An Example / 4.4: |
Conclusion / 5: |
Suggestions for Further Reading / 6: |
Appendix / 7: |
References |
Nonlinear Spinwaves in One- and Two-Dimensional Magnetic Waveguides / Andrei N. Slavin ; Sergei O. Demokritov ; Burkard Hillebrands |
Introduction |
Basics of Nonlinear Spinwave Phenomena in Magnetic Films |
Two-Dimensional Films and Quasi-One-Dimensional Waveguides |
The Space- and Time-Resolved Brillouin Light-Scattering Spectrometer |
Experimental Results |
Effect of the Antenna Aperture / 5.1: |
Spatial Self-Focusing: Spatial Solitons / 5.2: |
Spatiotemporal Self-Focusing: Spinwave Bullets / 5.3: |
Collisions of Spinwave Solitons and Bullets / 5.4: |
Numerical Modeling of Nonlinear Spinwave Propagation |
Conclusions |
Sergey O. Demokritov |
Preparation of Patterned Magnetic Structures |
Spin-Wave Spectrum of Magnetic Wires and Dots |
The Brillouin Light Scattering Technique |
Arrays of Wires |
Arrays of Dots |
Stroboscopic Microscopy of Magnetic Dynamics / Mark R. Freeman ; Wayne K. Hiebert |
Historical Overview |
Experimental Details |
Pulsed Optical Source |
Transient Magnetic Excitation |
Microscope and Polarization Imaging |
System Operation |
New Opportunities in Optical Imaging / 2.5: |
Discussion of Representative Results |
Relaxation,Resonance,and Small Angle Excitation |
Dynamic Reversal and Large-Angle Excitation |
Magnetic Device Characterization and Nonrepetitive Processes |
Summary and Prospects |
Solid Immersion Lens and Confocal Microscopy |
Alternative Time-Resolved Magnetic Microscopies |
Dynamics of Magnetization Reversal: From Continuous to Patterned Ferromagnetic Films / Jacques Ferre |
Experimental Techniques |
Overview of Field-Induced Magnetization Dynamics |
Experimental Facts |
Magnetic Aftereffect |
Dynamics the Hysteresis Loop |
Reversal Processes |
The Nucleation Process |
Domain Wall Motion |
Numerical Simulations |
General Considerations |
Micromagnetic Simulations |
Monte Carlo Simulations in a Nonhomogeneous Film |
Simulations in a 2-D Random-Field Ising Model |
Limitations of Simulations / 5.5: |
Motion of an Interface in a Disordered Medium / 5.6: |
Magnetisation Reversal Dynamics in a Quasi-Perfect Ultrathin Film |
Domain Nucleation / 6.1: |
Domain Wall Propagation / 6.2: |
Magnetisation Reversal Dynamics in Nanostructures |
General Remarks / 7.1: |
Magnetisation Reversal in Small Elements / 7.2: |
Magnetisation Reversal in Noncoupled Dot Arrays / 7.3: |
Magnetisation Reversal in Coupled Dot Arrays / 7.4: |
Small Amplitude Dynamics of Nonhomogeneous Magnetization Distributions: The Excitation Spectrum of Stripe Domains / Ursula Ebels ; Liliana D. Buda ; Kamel Ounadjela ; Phillip E.Wigen8: |
Basics of Ferromagnetic Resonance |
The Uniform FMR Mode |
FMR Technique |
Applications of FMR |
Coupled Oscillations |
General Conditions for the Observation of FMR Modes |
High Pumping Power: Nonlinear Excitations and Chaos / 2.6: |
Co(0001) Stripe Domains: Static Properties and Experimental Excitation Spectrum |
General |
Q Factor and Flux-Closure Caps |
Static Properties of the Co(0001) Stripe Domains |
Pumping Scheme / 3.4: |
The Experimental Excitation Spectrum of Co(0001) / 3.5: |
Fundamental Modes of Stripe Domains |
Acoustic and Optic Domain Resonance Modes |
Bloch Domain Wall Resonance |
Wall Excitations of Stripe Domains with Flux-Closure Caps |
Summary |
Appendix: Domain Wall Dynamics |
Landau-Lifschitz-Gilbert Equation in Polar Coordinates |
Domain Wall Resonance |
Steady-State Motion / 6.3: |
Frequency Domain Magnetic Measurements from Kilohertz to Gigahertz / John F. Gregg |
Time-Domain and Frequency-Domain Measurements |
Resonant and Nonresonant Phenomena |
The Magnetic Susceptibility x(w) |
Resonant Structures |
The Concept of Self-Oscillating Detectors |
Beating Miller Capacitance; the Cherry and Hooper Pair |
Practical Robinson Limiters |
Cavities |
Cryogenic Operation / 9: |
Resonator Design / 10: |
Construction of High-Performance Resonators for 300 kHz-200 MHz / 10.1: |
Cavity Resonator Sensitivity / 10.2: |
Thin Film Samples / 11: |
Parameter Matrices for High-Frequency Circuit Analysis / 12: |
Magnetic Modulation Techniques / 13: |
Ultrasonic Spectrometers / 14: |
Practical Construction and PCB Layout / 15: |
Skin Depth Considerations / 16: |
Practical Applications / 17: |
Laser-Induced Ultrafast Demagnetization: Femtomagnetism, a New Frontier? / Guoping Zhang ; Wolfgang Hubner ; Eric Beaurepaire ; Jean-Yves Bigot |
Historical View of Magnetization (Theory) |
Heisenberg Model (Insulators) |
Itinerant Theory (Metals) |
Simple Theory for Spin-Lattice Relaxation: Picosecond Timescales |
Theory for Ultrafast Spin Dynamics: Femtosecond Timescales |
Theoretical Formalism |
Results: Linear Optical and Magneto-Optical Responses |
Results: Nonlinear Optical and Magneto-Optical Responses |
Results: Intrinsic versus Extrinsic |
Our Explanations: Spin and Charge Dephasing |
Nonequilibrium Heating in Metals |
Heating Metals with Ultrashort Laser Pulses |
Three-Temperature Model of Ferromagnets |
Ultrafast Spin Dynamics: Experimental Review |
Magneto-Optical Response |
Experimental Apparatus |
Experimental Studies: Electrons and Spin Dynamics in Ferromagnets |
Discussion |
The Micromagnetics of Magnetoresistive Random Access Memory / Jian-Gang Zhu ; Youfeng Zheng |
The Pseudospin-Valve Design |
The Magnetic Tunneling Junction Design |
The Vertical Magnetoresistive Random Access Memory |
Micromagnetic Modeling and Computational Method |
Contributions to the Total Energy Density |
The Landau-Lifschitz Equation of Motion |
Comparison of Simulated DomainStructures with Experimental Observations |
Comparison with Images Obtained from Differential Phase-Contrast Microscopy |
Simulated Domain Configurations in Thin Film Elements of Various Shapes |
Magnetic Switching of Memory Elements in the Pseudospin-Valve and the Magnetic Tunneling Junction Designs |
Switching of a Thick Rectangular Magnetic Film Element |
Switching of a Thin Rectangular Magnetic Film Element |
Switching of Elements with Tapered Ends |
The Critical Need for Controlling the Tapered Ends |
The Vertical Magnetoresistive Random Access Memory (VMRAM) |
Design Concept |
Ultimate Area Density Limitation and Magnetic Switching Speed |
Read-Back Signal Level |
Ring Versus Disk Shaped Elements and Fabrication Tolerance |
Challenges and Promises |
Reference |
Index |
Fast Switching of Mesoscopic Magnets / Thomas Schrefl ; Josef Fidler ; Rok Dittrich ; Dieter Suess ; Werner Scholz ; Vassilios Tsiantos ; Hermann Forster |
The Equation of Motion |
Small Magnetic Particles |
Finite-Element Micromagnetics |
Magnetization Reversal in Thin-Film Co Elements |
Polycrystalline Co Elements |
Switching in a Rotational Field |
Switching of Perpendicular Discrete Media |
Effects of Nonzero Temperature |
Langevin Micromagnetics |
Switching Dynamics at Nonzero Temperature |
Spin Damping in Ultrathin Magnetic Films / Douglas L. Mills ; Sergio M. Rezende |
Ferromagnetic Resonance in Ultrathin Ferromagnetic Films. Phenomenology |
The Landau-Lifshitz Equation and the Ferromagnetic Resonance Response of Ultrathin Ferromagnetic Films Frequency Dependence of Line Width in FMR and BLS |
Comments on Extensions of Landau-Lifshitz Phenomenology |
Brief Comments on Experimental Data |
Extrinsic Contributions to the Line Width: The Two-Magnon Mechanism |
Historical Comments |
The Nature of Spin Waves in Ultrathin Ferromagnetic Films |
Two-Magnon Scattering and the FMR Response of Ultrathin Ferromagnetic Films |
Experimental Evidence for the Role of Two Magnon-Processes in the Microwave Response of Ultrathin Ferromagnets |
Concluding Remarks |
Magnetization Dynamics Investigated by Time-Resolved Kerr Effect Magnetometry / Jürgen Fassbender |
Numerical Simulations of Magnetization Dynamics within the Stoner Model |
Model |
Magnetization Dynamics in Static Magnetic Fields |
Magnetization Dynamics in Pulsed Magnetic Fields |
Time-Resolved Kerr Magnetometer Setup |
Magnetization Dynamics in Ferrite Films |
Control of Magnetization Dynamics |
Spin-Wave Propagation |
Calculation of the Magneto-Optic Response |
High Speed Switching and Rotational Dynamics in Small Magnetic Thin Film Devices / Stephen E. Russek ; Robert D. McMichael ; Michael J. Donahue ; Shehzaad Kaka |
Introduction to High-Speed Magnetic Devices |
Background |
Magnetic Devices |
Single-Domain Modeling |
Micromagnetic Simulations of High-Speed Device Dynamics |
NIST Object Oriented MicroMagnetic Framework (OOMMF) |
Standard Micromagnetic Problems |
Modeling of Magnetic Rotation and Switching |
Modeling of Devices Based on Domain-Wall Motion |
High-Frequency Magnetic Device Measurement |
Rotation and Ferromagnetic Resonance in GMR Devices |
Switching of Small GMR Devices |
Effects of Disorder and Thermal Fluctuations |
Effects of Disorder |
Effects of Thermal Fluctuations |
Engineering High-Frequency Dynamic Properties |
Time-Resolved X-Ray Magnetic Circular Dichroism - A Selective Probe of Magnetization Dynamics on Nanosecond Timescales / Stefania Pizzini ; Jan Vogel ; Marlio Bonfim ; Alain Fontaine |
Synchrotron Radiation Techniques for Magnetism |
X-ray Resonant Magnetic Scattering |
X-ray Magnetic Circular Dichroism |
Time-Resolved X-Ray Magnetic Circular Dichroism (XMCD)Experiments |
Microcoils for High Pulsed Fields |
Magnetization Dynamics Studied With XMCD |
Magnetization Dynamics of Spin Valves and Tunnel Junctions Studied with Time-Resolved XMCD |
Magnetization Dynamics of Tunnel Junctions |
Conlusions and Perspectives |
The Dynamic Response of Magnetization to Hot Spins / Wolfgang Weber ; Stefan Riesen ; Hans C. Siegmann |
Absorption and Spin Motion of Electrons in Ferromagnets |
Experiment |
Samples |
Results |
Magnetic Phenomena Generated by an Exchange Field |
The Torque Acting on Magnetization by Hot Spins |
Precessional Magnetization Reversal |
Ultrafast Magnetization and Switching Dynamics / Theo Rasing ; Hugo van den Berg ; Thomas Gerrits ; Julius Hohlfeld |
Switching by Short Magnetic Field Pulses |
Precessional Dynamics |
Generation of Field Pulses using Photoconductive Switches |
The Experimental Setup |
Field-induced Precession Dynamics / 1.4: |
Coherent Magnetization Reversal by Field-Pulse Shaping |
Experimental Approach for Pulse Shaping |
Excitation by Shaped Magnetic Field Pulses |
Laser-induced Switching of Magnetic Media |
Magneto-Optical Recording - Introduction |
Thermomagnetic Writing - Basics |
Ultrafast Dynamics of Thermomagnetic Writing |
Experimental Procedure |
Femtosecond Laser-induced Dynamics |
Conclusion and Outlook / 3.6: |
Laser-Induced Magnetization Dynamics / Bert Koopmans |
Excitation and Detection Schemes |
Dielectric Response |
Transient Magneto-Optics |
Implementation of Time-Resolved MOKE |
Time-Resolved Magnetization Modulation |
Magnetization-Induced Optical Second-Harmonic Generation |
Photoemission / 2.7: |
Other Approaches / 2.8: |
Transient Magnetic Phenomena |
Charge Dynamics |
Demagnetization |
Some Words on Conservation Laws |
Dichroic Bleaching |
Dependence on Ambient Temperature |
MO Strain Effects |
Laser-Induced Precession / 3.7: |
Studies of Ultrafast Magnetization Dynamics |
Early Work |
Toward Instantaneous Magneto-Optics |
Magnetism or Optics? |
Identification of Optical Artifacts |
Access to Genuine Magnetization Dynamics / 4.5: |
GHz Dynamics / 4.6: |
Conclusions and Outlook / 4.7: |
Precessional Switching of Thin Nanomagnets with Uniaxial Anisotropy / Thibaut Devolder ; Hans Werner Schumacher ; Claude Chappert |
Basic Facts About Precessional Dynamics in Transverse Field |
From Stoner-Wohlfarth Energy Minimization to Precessional Switching |
Definitions: Geometry and Notations |
A Tutorial Example: The Bascule Precession of a Isotropic Thin Film |
Magnetization Trajectory for a Loss-Free Isotropic Film Subjected to a Transverse Field / 2.3.1: |
Switching Speed for a Loss-Free Isotropic Film Subjected to a Transverse Field / 2.3.2: |
Precessional Switching at High Hard-Axis Fields |
"All-Electrical" Experimental Methods |
Evidence of the Quasiperiodic Nature of the Magnetization Motion |
Evidence of Quasiballistic Magnetization Switching Trajectories |
Precessional Switching at Moderate Hard-Axis Fields and Zero Damping |
Classification of the Magnetization Trajectories |
Field-Dominated (Switching) Trajectories / 4.1.1: |
Anisotropy-Dominated (Nonswitching) Trajectories / 4.1.2: |
Characteristic Times Involved in a Precessional Switching Event Near and Below H[subscript k] |
Initial Delay, Slow-Down Time and Maximum Speed Time / 4.2.1: |
Rule of Thumb for the Precession Frequency / 4.2.2: |
Minimal Switching Field, Bifurcation Trajectory and its Intrinsic Noise Sensitivity |
Arbitrary Initial Magnetization and Consequences for Nonmacrospin Samples |
Minimal Reversal Field Versus Minimal Energy Cost |
Perspectives for the Speed Scaling of Precessional MRAM |
Damped Nanomagnets: Relaxation-Dominated Precessional Switching |
Consequences of Finite Damping |
Loss of Energy and of Periodicity / 5.1.1: |
Rise-Time Constraints / 5.1.2: |
Perturbation Treatment of Finite Damping |
Energy Loss Per Unit Cycling of the Trajectory / 5.2.1: |
Number of Trajectories Gone Through Before Bifurcation / 5.2.2: |
Bifurcation Field in the Presence of Finite Damping |
Direct-Write: Biasing the Precession with an Easy-Axis field |
Precessional Switching in Magnetic Random Access Memories |
Magnetization Trajectories for Combined Easy-Axis and Hard-Axis Fields |
Magnetization Trajectories for Nearly Transverse Applied Fields / 6.2.1: |
Magnetization Trajectories for Nearly Antiparallel Appllied Fields / 6.2.2: |
General Case: Lobe Centers and Bounce-Occurrence Criteria / 6.2.3: |
The Dynamical Astroid |
Derivation of the Dynamical Astroid / 6.3.1: |
Smallest Switching Field and Extrema of the Dynamical Astroid Curve / 6.3.2: |
Characteristic Duration of a Precessional Direct-Write Event / 6.4: |
Generalized Initial Delay / 6.4.1: |
Main Rotation Time / 6.4.2: |
Alignment Time / 6.4.3: |
Pause Interval / 6.4.4: |
Precession Frequency for Arbitrary Field Orientation / 6.4.5: |
Strategies for the Cell Writing and Selection in a Practical Memory Array / 6.5: |
The Selectivity and Direct-Write Issues in Precessional MRAM / 6.5.1: |
Optimal Field Synchronization for Jitter Immunity / 6.5.2: |
Size of the Addressing Window / 6.5.3: |
Spin-Wave Excitations in Finite Rectangular Elements / Christian Bayer ; Jorg Jorzick ; Sergej O. Demokritov ; Konstantin Y. Guslienko ; Dmitry V. Berkov ; Natalia L. Gorn ; Mikhail P. Kostylev |
Samples and Experimental Setup |
Longitudinally Magnetized Long Stripes |
Transversely Magnetized Long Stripes |
Rectangular Elements |
Analytical Approach |
Rectangular Magnetic Elements |
Outlook |
Ferromagnetic Resonance Force Microscopy / Philip E. Wigen ; Michael L. Roukes ; Peter C. Hammel |
MRFM Detection of Weakly Interacting Spins (ESR and NMR) |
MRFM in Ferromagnetic Systems |
Magnetostatic Modes |
Linewidths |
Scanning Mode |
Dependence of the Fundamental Mode on Sample Dimensions / 3.3.1: |
Dispersion Relation / 3.3.2: |
Spatial Mapping of Magnetostatic Modes / 3.3.3: |
Hidden Modes / 3.3.4: |
Mapping RF Force Fields / 3.3.5: |
FMRFM in Metal Films |
Torque Measurements in a Uniform Field |
Mechanical Torque on a Thin Film |
Magnetization versus Field (M-H) Loops |
Microresonating Torque Magnetometer ([mu]RTM) |
Bimaterial Micromechanical Calorimeter Sensor for FMR |
Vortex Dynamics / Christian H. Back ; Danilo Pescia ; Matthias Buess |
Time-Resolved Magneto-Optical Microscopy |
Brillouin Light Scattering |
Synchrotron-Based Techniques |
Excitation Schemes |
Pulsed Precessional Motion |
Microwave Excitation |
The Energy Landscape of Confined Magnetic Structures |
Gyroscopic Vortex Motion in Micrometer Sized Ferromagnetic Squares and Disks |
The Modal Spectrum of Permalloy Disks |
Domain-Wall Dynamics in Nanowires and Nanostrips / Andre Thiaville ; Yoshinobu Nakatani |
Types of Samples and Domain Walls |
Wall Types in Nanowires |
Numerical Results / 2.1.1: |
Comparison to 1D Profiles / 2.1.2: |
One-Dimensional Effective Model |
Wall Types in Nanostrips |
Dynamics of a Transverse Wall in a Nanowire |
Analytical Model |
Dynamics of a Transverse Wall in a Nanostrip |
Dynamics of a Bloch-Point Wall in a Nanowire |
Dynamics of a Vortex Wall in a Nanostrip |
General Results for Steady-State Motion of Domain Walls |
Thiele's Equations |
Doring's Kinetic Potential |
Domain-Wall Dynamics in Magnetic Logic Devices / Del Atkinson ; Colm C. Faulkner ; Dan A. Allwood ; Russell P. Cowburn |
Domain-Wall Propagation in Nanowires -Velocity and Dynamics |
Domain-Wall Dynamics in Continuous and Nanostructured Permalloy Films |
Domain-Wall Velocity in Permalloy Thin Films |
Domain-Wall Behavior in Permalloy Planar Nanowires |
Domain-Wall Dynamics in Complex Structures for Magnetic Logic |
Magnetic Logic Circuits |
Domain-Wall Propagation through Corner Structures |
Domain-Wall Propagation through Logic Junction Structures |
Spin-Transfer Torque and Dynamics / Mark D. Stiles |
Quantum Scattering |
Semiclassical Transport |
Boltzmann Equation and Drift-Diffusion Approximation |
Spin Pumping |
Circuit Theory |
Collinear Transport |
Non-Collinear Transport and Torque |
Leads/Reservoirs |
Lateral Inhomogeneity |
Micromagnetics |
Geometry and Energetics |
Landau-Lifshitz-Gilbert Equation |
The Single or Macrospin Approximation |
Onset of Precessional States / 4.3.1: |
Precessional States: Stability Range / 4.3.2: |
Switching and Out-of-Plane Precessional States / 4.3.3: |
Langevin Dynamics |
The Micromagnetic Regime |
Appendix Drift-Diffusion Solution for a Single Interface / A: |
Appendix Precession and Spin Transfer in Phase Space: Melnikov's Method / B: |
Spin- and Energy Relaxation of Hot Electrons at GaAs Surfaces / Torsten Ohms ; Kevin Hiebbner ; Hans Christian Schneider ; Martin Aeschlimann |
Review of Spin-Flip Processes in GaAs |
Optical Orientation of Photoexcited Carriers |
Band-Structure Properties |
Elliott-Yafet Mechanism |
Dyakonov-Perel Mechanism |
Bir-Aronov-Pikus Mechanism |
Spin-Polarization Dynamics |
Theory of Spin-Relaxation Dynamics |
Spin Decay in a Schottky Barrier |
Experiments |
Time- and Spin-Resolved 2PPE |
Experimental Setup |
Experimental Results for GaAs (100) |
Comparison Between Experimental and Theoretical Results |