Introduction to Muon Spin Spectroscopy: Applications to Solid State and Material Sciences (Lecture Notes in Physics, 961)

✍ Scribed by Alex Amato, Elvezio Morenzoni

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 544
• Category: Library

✦ Synopsis

This textbook serves as a comprehensive introduction to muon spin spectroscopy (µSR), offering a detailed exploration of how polarized positive muons can be employed as local probes to investigate material properties at the microscopic level. It provides a self-contained tutorial that begins by explaining the extraction of physical information from a µSR experiment and then proceeds to present illustrative examples in the fields of condensed matter physics, materials science, and nanoscience.
The book focuses on major applications of µSR, including the study of magnetism, superconductivity, and semiconducting materials in both bulk and thin film samples. In addition, two chapters delve into the applications of negative muons, emphasizing their role in elemental materials analysis and introducing fundamental particle physics aspects of muon science. Supplementary material, conveniently summarized in several appendices, covers essential basic concepts.For further exploration, an extensive list of references is provided, enabling readers to deepen their knowledge in specific areas.
To facilitate understanding and mastery of the subject, the textbook offers exercises and solutions. It caters to advanced undergraduate, graduate and PhD level students, researchers who intend to utilize the µSR technique or seek a comprehensive understanding of µSR results for their research, as well as to established practitioners.

✦ Table of Contents

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