Muon Spin Rotation, Relaxation, and Resonance: Applications to Condensed Matter

Description

Primarily intended for postgraduate students and researchers in the fields of condensed matter science, chemical physics and material science, who plan to use the muon spin rotation, relaxation amd resonance (µSR) techniques, this book combines for the first time a detailed discussion of the physical information contained in the measured polarisation functions with real-life examples taken from the literature. It is divided in three main parts. The first part presents some typical results of the application of µSR and explains the basic principles involved. The second part is the core of this book. It presents a comprehensive discussion of the measured polarisation functions. In the third part we analyse in four chapters selected examples taken from the following fields: diffusion properties of muon and muonium, magnetism, superconductivity, and muonium centres in materials. The book is completed by an epilogue and eight appendices. Cover Contents Preface List of important symbols Numerical values of fundamental constants PART I: BASIC PRINCIPLES 1 A short survey of μSR research 1.1 Basic principles of the μSR techniques 1.2 A flavour of µSR: examples of experimental results References 2 Recording data and extracting the polarisation functions 2.1 A brief history of the muon 2.2 μSR experimental setups 2.3 Principles of μSR data treatment References PART II: POLARISATION FUNCTIONS 3 Basics of muon and muonium polarisation functions 3.1 Muon polarisation function 3.2 Muonium polarisation function References 4 Miscellaneous techniques 4.1 Radio-frequency μSR spectroscopy 4.2 Avoided-level-crossing spectroscopy 4.3 Stroboscopic technique 4.4 Lattice steering 4.5 β-detected NMR technique 4.6 Experiments with negative muons References 5 The magnetic field at the muon site 5.1 The interaction energies at the muon site 5.2 The long-range dipole field at the muon site 5.3 Frequency shift in paramagnets or diamagnets 5.4 Local field in magnets References 6 Muon polarisation functions: field distribution approach 6.1 Characteristics of field distributions 6.2 Static field distributions in a perfect crystal 6.3 Time-dependent field distributions in a perfect crystal 6.4 Field distributions in a partially disordered crystal 6.5 Polarisation functions for two field sources 6.6 Static field distributions and material parameters References 7 Muon polarisation functions: quantum approach 7.1 Analytical methods 7.2 Numerical methods References 8 Muonium polarisation functions 8.1 Atomic properties of muonium 8.2 Isotropic muonium state 8.3 Anisotropic muonium state 8.4 Muonium centres in matter References PART III: CONDENSED MATTER APPLICATIONS 9 Muon and muonium centre diffusion 9.1 Diffusion constant and site transfer rate 9.2 Diffusion of a light interstitial particle 9.3 Diffusion and polarisation functions 9.4 Examples References 10 Investigation of magnetic materials 10.1 Static properties 10.2 Dynamical properties 10.3 Examples 10.4 Complementarity of μSR and other techniques References 11 Investigation of superconductors 11.1 Theoretical background for data analysis 11.2 Examples References 12 Muonium centres in materials 12.1 Inferring muonium centres from silicon studies 12.2 Shallow muonium states 12.3 Quasi-static neutral muonium states 12.4 Muonium state formation 12.5 Different species of muonium centres 12.6 Muoniated free radicals References 13 Epilogue: trends for the future References APPENDICES Appendix A: Handling experimental data A.1 From positron counts to time asymmetry spectra A.2 Oscillating spectra References Appendix B: Polarisation functions: a summary Appendix C: Mathematical concepts and formulae C.1 Tensors C.2 Operators C.3 Spin operators C.4 Rotation operators C.5 Pauli operators C.6 Statistical thermodynamics C.7 Distributions C.8 Linear transforms C.9 Density of states C.10 Some integrals and other formulae References Appendix D: Laboratory and crystal reference frames D.1 Mathematical background D.2 Components of the local field D.3 Longitudinal and transverse relaxation rates D.4 Field variances D.5 Lorentz field D.6 Knight shift D.7 Implications of the muon site symmetry D.8 Implications of the Hamiltonian symmetry References Appendix E: Translational symmetry and Fourier transform E.1 Lattices and unit cells E.2 Reciprocal space and lattice Fourier transform References Appendix F: Correlation functions and linear response theory F.1 Generalised susceptibility F.2 Correlation, static susceptibility, and spectral-weight functions F.3 Green functions References Appendix G: Nuclear data relevant to μSR References Appendix H: f and 3d electronic shell data References Index A B C D E F G H K L M N O P Q R S T V