Muon Spin Rotation, Relaxation, and Resonance: Applications to Condensed Matter (International Series of Monographs on Physics, 147)

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 1 Contents 6 Preface 10 List of important symbols 12 Numerical values of fundamental constants 17 PART I: BASIC PRINCIPLES 18 1 A short survey of μSR research 20 1.1 Basic principles of the μSR techniques 22 1.2 A flavour of μSR: examples of experimental results 31 References 46 2 Recording data and extracting the polarisation functions 50 2.1 A brief history of the muon 50 2.2 μSR experimental setups 51 2.3 Principles of μSR data treatment 58 References 60 PART II: POLARISATION FUNCTIONS 62 3 Basics of muon and muonium polarisation functions 64 3.1 Muon polarisation function 65 3.2 Muonium polarisation function 70 References 72 4 Miscellaneous techniques 73 4.1 Radio-frequency μSR spectroscopy 74 4.2 Avoided-level-crossing spectroscopy 79 4.3 Stroboscopic technique 83 4.4 Lattice steering 86 4.5 β-detected NMR technique 86 4.6 Experiments with negative muons 88 References 89 5 The magnetic field at the muon site 91 5.1 The interaction energies at the muon site 91 5.2 The long-range dipole field at the muon site 97 5.3 Frequency shift in paramagnets or diamagnets 110 5.4 Local field in magnets 113 References 114 6 Muon polarisation functions: field distribution approach 116 6.1 Characteristics of field distributions 117 6.2 Static field distributions in a perfect crystal 118 6.3 Time-dependent field distributions in a perfect crystal 132 6.4 Field distributions in a partially disordered crystal 143 6.5 Polarisation functions for two field sources 160 6.6 Static field distributions and material parameters 162 References 178 7 Muon polarisation functions: quantum approach 181 7.1 Analytical methods 182 7.2 Numerical methods 208 References 214 8 Muonium polarisation functions 216 8.1 Atomic properties of muonium 216 8.2 Isotropic muonium state 217 8.3 Anisotropic muonium state 224 8.4 Muonium centres in matter 231 References 242 PART III: CONDENSED MATTER APPLICATIONS 244 9 Muon and muonium centre diffusion 246 9.1 Diffusion constant and site transfer rate 246 9.2 Diffusion of a light interstitial particle 250 9.3 Diffusion and polarisation functions 256 9.4 Examples 256 References 261 10 Investigation of magnetic materials 264 10.1 Static properties 265 10.2 Dynamical properties 282 10.3 Examples 340 10.4 Complementarity of μSR and other techniques 359 References 364 11 Investigation of superconductors 371 11.1 Theoretical background for data analysis 372 11.2 Examples 407 References 412 12 Muonium centres in materials 416 12.1 Inferring muonium centres from silicon studies 417 12.2 Shallow muonium states 420 12.3 Quasi-static neutral muonium states 423 12.4 Muonium state formation 424 12.5 Different species of muonium centres 426 12.6 Muoniated free radicals 429 References 432 13 Epilogue: trends for the future 435 References 437 APPENDICES 438 Appendix A: Handling experimental data 440 A.1 From positron counts to time asymmetry spectra 440 A.2 Oscillating spectra 443 References 449 Appendix B: Polarisation functions: a summary 450 Appendix C: Mathematical concepts and formulae 452 C.1 Tensors 452 C.2 Operators 454 C.3 Spin operators 454 C.4 Rotation operators 455 C.5 Pauli operators 455 C.6 Statistical thermodynamics 456 C.7 Distributions 457 C.8 Linear transforms 459 C.9 Density of states 460 C.10 Some integrals and other formulae 461 References 467 Appendix D: Laboratory and crystal reference frames 468 D.1 Mathematical background 468 D.2 Components of the local field 469 D.3 Longitudinal and transverse relaxation rates 470 D.4 Field variances 471 D.5 Lorentz field 472 D.6 Knight shift 473 D.7 Implications of the muon site symmetry 475 D.8 Implications of the Hamiltonian symmetry 477 References 478 Appendix E: Translational symmetry and Fourier transform 479 E.1 Lattices and unit cells 479 E.2 Reciprocal space and lattice Fourier transform 480 References 483 Appendix F: Correlation functions and linear response theory 484 F.1 Generalised susceptibility 484 F.2 Correlation, static susceptibility, and spectral-weight functions 485 F.3 Green functions 488 References 490 Appendix G: Nuclear data relevant to μSR 491 References 496 Appendix H: f and 3d electronic shell data 497 References 500 Index 501 A 501 B 501 C 501 D 501 E 501 F 501 G 502 H 502 K 502 L 502 M 502 N 502 O 502 P 502 Q 503 R 503 S 503 T 503 V 503 Intended for graduate students and researchers who plan to use the muon spin rotation and relaxation techniques. A comprehensive discussion of the information extracted from measurements on magnetic and superconductor materials. The muonium centres as well as the muon and muonium diffusion in materials are discussed. Alain Yaouanc, Pierre Dalmas De Réotier. Includes Bibliographical References And Index.