Introduction to Muon Spin Spectroscopy : Applications to Solid State and Material Sciences

• Record Nr.: UNISA996587860803316
• Autore: Amato Alex
• Pubbl/distr/stampa: Cham : , : Springer International Publishing AG, , 2024; ©2024
• ISBN: 3-031-44959-2
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (544 pages)
• Collana: Lecture Notes in Physics Series ; ; v.961
• Altri autori (Persone): MorenzoniElvezio
• Disciplina: 539.72114
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface -- Contents -- Physical Constants, Symbols and Abbreviations -- Values of Important Physical Constants (Grouped by Subject) -- Important Symbols -- Acronyms and Abbreviations -- 1 Fundamentals -- 1.1 The Muon as Elementary Particle -- 1.2 A Brief History of the Muon -- 1.3 Atmospheric Muons -- 1.4 Pion: The Parent Particle -- 1.4.1 Pion Properties -- 1.4.2 Pion Production Reactions -- 1.4.3 The Pion Decay -- 1.5 Muon Properties -- 1.6 The Muon Decay -- 1.6.1 Kinematics -- 1.6.2 Differential Positron Emission -- 1.6.3 Decay of a Muon Ensemble -- 1.7 Muon Magnetic Moment and Spin Precession -- 1.7.1 Muon Magnetic Moment -- 1.7.2 Muon Spin Precession -- 1.8 Muon Beams -- 1.8.1 Proton Accelerators -- 1.8.2 Example of a Proton Accelerator for muSR -- 1.8.3 Surface and Decay Muon Beams -- 1.8.4 Beam Optics and Beamline Elements -- Exercises -- References -- 2 Muon Implantation and Thermalization in Matter -- 2.1 Energy Loss of Particles in Matter -- 2.1.1 Energy Loss by Ionization: Classical Approach -- 2.1.2 Energy Loss: Bethe Formula -- 2.2 Range and Slowing Down Time -- 2.2.1 Range of Muons -- 2.2.2 Thermalization Time -- 2.2.3 Multiple Scattering -- 2.3 Muon States in Matter -- Exercises -- References -- 3 muSR Technique -- 3.1 Key Features of the muSR Technique -- 3.2 The muSR Signal -- 3.3 Experimental Setup -- 3.3.1 Continuous Beam -- 3.3.2 Muon-On-Request Setup -- 3.3.3 Pulsed Beam -- 3.4 Measurement Geometries -- 3.4.1 Zero Field and Longitudinal Field Geometry -- 3.4.2 ; Transverse Field Geometry -- Exercises -- References -- 4 Polarization Functions -- 4.1 Static Internal Fields -- 4.1.1 Single Valued Field -- 4.1.1.1 Single Crystal -- 4.1.1.2 Polycrystal -- 4.1.2 Continuous Field Distributions -- 4.1.2.1 Gaussian Distribution -- 4.1.2.2 Lorentzian Distribution -- 4.1.2.3 Stretched and Gaussian-Lorentzian Kubo-Toyabe Functions.; 4.1.3 Generalizations of the Kubo-Toyabe Functions -- 4.2 Polarization Functions for Applied External Fields -- 4.2.1 Longitudinal Field -- 4.2.2 Transverse Field -- 4.2.3 Some Special Polarization Functions -- 4.3 Dynamical Effects -- 4.3.1 The Strong Collision Approximation -- 4.3.1.1 The Muon Spin Polarization -- 4.3.1.2 Dynamical Effects for Gaussian Distributions in a Longitudinal Field -- 4.3.1.3 Dynamical Effects for Gaussian Distributions in a Transverse Field -- 4.3.1.4 Dynamical Effects for Lorentzian Fields -- 4.3.2 Stretched Exponential Function -- 4.4 A Quantum Mechanical Approach to the Muon Spin Relaxation -- 4.4.1 Redfield Expressions -- 4.4.2 Spectral Density -- Exercises -- References -- 5 Study of Magnetism -- 5.1 Local Magnetic Field in Magnetic Materials -- 5.1.1 The Muon-Electron Interaction -- 5.1.2 Hyperfine Contributions in a Solid -- 5.1.3 Demagnetizing and Lorentz Fields -- 5.1.4 Examples of Local Field Determination -- 5.2 Magnetic Volume Fraction and Magnetic Transitions -- 5.2.1 Examples -- 5.3 Magnetic Fluctuations -- 5.3.1 Examples -- 5.4 Incommensurate Magnetic Structures -- 5.5 Dynamics of Spin Glasses -- 5.6 Magnetic Response in the Paramagnetic or Diamagnetic State: The Knight-Shift -- 5.6.1 Paramagnetism of the Conduction Electrons: Fermi Contact Term Knight-Shift -- 5.6.1.1 Pauli Susceptibility -- 5.6.2 Knight-Shift in Materials with Local Moments -- 5.6.2.1 The Dipolar Field Contribution -- 5.6.2.2 The RKKY-Enhanced Contact Field Contribution -- 5.6.2.3 The Total Knight-Shift -- 5.6.3 Determination of the Muon Stopping Site -- 5.6.4 Angular Dependence of the Knight-Shift -- 5.6.5 Nonlinear Knight-Shift Versus Susceptibility -- 5.7 Depolarization Created by Nuclear Moments -- 5.7.1 Classical Calculation -- 5.7.1.1 The TF Case -- 5.7.1.2 The ZF Case.; 5.7.2 Influence of the Quadrupolar Interaction on the Nuclear Dipolar Width -- Exercises -- References -- 6 Study of Superconductivity -- 6.1 Concepts of Superconductivity -- 6.1.1 The Two Characteristic Length Scales of Superconductors -- 6.1.1.1 The Magnetic Penetration Depth -- 6.1.1.2 The Coherence Length -- 6.1.2 Type-I and Type-II Superconductors -- 6.1.3 The Intermediate State -- 6.1.4 Energy Gap and Symmetry of the Pairing State -- 6.1.4.1 Multiple Superconducting Gaps -- 6.2 Vortex State of a Type-II Superconductor -- 6.2.1 Principle of a muSR Experiment in the Vortex State -- 6.2.2 Local Field in the Vortex State -- 6.2.2.1 Field Generated by an Isolated Vortex -- 6.2.2.2 Field Distribution from the London Model -- 6.2.3 Coherence Length and Applied Magnetic Field Dependence -- 6.2.4 Anisotropy of the Magnetic Penetration Depth -- 6.3 Analysis of the muSR -- 6.3.1 Models of Data Analysis -- 6.3.1.1 Single Gaussian Analysis -- 6.3.1.2 Multi-Gaussian Analysis -- 6.3.1.3 Full Model Analysis -- 6.3.1.4 Model Comparison -- 6.4 Interplay of Magnetism and Superconductivity -- 6.5 Study of Vortex Matter -- 6.5.1 Vortex Pinning -- 6.6 Spontaneous Magnetic Field in Superconductors -- 6.7 Study of the Intermediate State -- Exercises -- References -- 7 Muonium -- 7.1 Introduction -- 7.2 Muonium Ground State and Hyperfine Interaction -- 7.2.1 Ionization Energy -- 7.2.2 Isotropic Hyperfine Interaction -- 7.2.3 Hyperfine Splitting in an External Field -- 7.3 Time Evolution of the Muon Polarization in the Muonium State -- 7.3.1 Introduction -- 7.3.2 Longitudinal (and Zero) Field -- 7.3.3 Transverse Field -- 7.3.4 Nuclear Hyperfine Interaction -- 7.3.5 ; Isotropic Muonium in Solids -- 7.4 Anisotropic Muonium -- 7.5 Shallow Muonium -- 7.6 Muon-Polaron Complexes -- Exercises -- References.; 8 Investigations of Thin Films and Heterostructures with Low-Energy Muons -- 8.1 Introduction -- 8.2 Generation of Low-Energy Muons -- 8.2.1 Use of Degraders -- 8.2.2 Laser Resonant Ionization of Muonium -- 8.2.3 Moderation in Thin Layers of Cryosolids -- 8.3 The Low-Energy Muon Apparatus at PSI -- 8.4 Stopping Profiles of Low-Energy Muons in Thin Films -- 8.5 Examples -- 8.5.1 Magnetic Field Profiling at the Surface of Superconductors -- 8.5.1.1 Strong Type-II Superconductors -- 8.5.1.2 Nonlocal Superconductors -- 8.5.2 Heterostructures -- 8.5.3 Studies of Dynamics -- 8.5.4 Thin Films -- Exercise -- References -- 9 Use of Negative Muons: μ-SR and Elemental Analysis -- 9.1 Negative Muon Beams -- 9.2 Implantation of Negative Muons in Matter -- 9.2.1 Muonic Atoms -- 9.3 mu-SR -- 9.3.1 ``Conventional'' mu-SR -- 9.3.2 X-ray Triggered mu-SR -- 9.4 Elemental Analysis -- 9.4.1 Principle -- 9.4.2 Typical Spectra -- 9.4.3 Depth Dependence -- 9.4.4 Capture Probability -- 9.4.5 Determining the Isotopic Ratio -- 9.4.6 Examples -- 9.4.7 Characteristics and Comparison with Other Techniques -- Exercise -- References -- 10 Particle Physics Aspects -- 10.1 Muon Decay and Lepton Numbers -- 10.2 Theory of the Muon Decay -- 10.3 Calculation of the Muon Decay -- 10.3.1 Energy Distribution of the Decay Electron -- 10.3.2 Decay of a Polarized Muon -- 10.3.3 Decay via Intermediate Vector Boson Exchange -- 10.4 Muon Lifetime and Determination of the Fermi Constant -- 10.5 Muon Magnetic Anomaly -- 10.5.1 Experiment -- 10.5.2 Theory -- Exercises -- References -- 11 Conclusions and Outlook -- References -- A Magnetic Moment and Spin -- A.1 Magnetic Moment and Angular Momentum -- A.2 Spin Angular Momentum -- A.2.1 Spin Operators -- A.2.2 Spin 1/2 States and Pauli Matrices -- B Magnetic Multipoles -- C Derivation of the TF Abragam Formula -- D Demagnetizing Field.; E Units of Hyperfine Constants -- F Density Matrix -- F.1 Pure Quantum Mechanical State -- F.2 Mixed Quantum Mechanical State -- F.3 Time Evolution of an Operator -- F.4 Density Matrix of a Spin 1/2 Particle -- F.5 Density Matrix of Muonium -- G Relativistic Concepts -- G.1 Useful Relations of Relativistic Quantum Mechanics -- G.2 Dirac Equation -- G.2.1 Properties of the -Matrices -- G.2.2 Free Particle Solutions of the Dirac Equation -- G.3 Dirac Field Operators -- G.4 Fermi's Golden Rule and Lorentz Invariance -- References -- Solutions of the Exercises -- References -- Index.