Contents

• Contents
• 1 General introduction
  • 1.1 Antiferromagnetic spin systems without Néel order
    • 1.1.1 An overview of singlet ground state systems
    • 1.1.2 The idea of the measurements in this thesis
• 2 The muon spin rotation/relaxation ($\mu$SR) technique
  • 2.1 The basics
  • 2.2 Experimental setup for the $\mu$SR technique
    • 2.2.1 Production of a muon beam
    • 2.2.2 $\mu$SR spectrometer
    • 2.2.3 Electronics and data handling
    • 2.2.4 Counter/muon spin geometries
• 3 Spin relaxation theories
  • 3.1 Gaussian Kubo-Toyabe theory [#!Toyabe66!#,#!KuboToyabe67!#,#!HayanoPRB79!#]
  • 3.2 Lorentzian theory [#!UemuraPRB85!#]
  • 3.3 A minor correction to the Lorentzian theory
  • 3.4 Summary of the Kubo-Toyabe theories
• 4 Spin-ladder system
  • 4.1 Introduction
  • 4.2 Spin-ladder material Sr_n-1Cu_n+1O_2n
  • 4.3 $\mu$SR measurements
    • 4.3.1 The 3-leg ladder material (n=5)
    • 4.3.2 The 2-leg ladder material (n=3)
  • 4.4 Summary
• 5 Haldane system
  • 5.1 Introduction
    • 5.1.1 Haldane's prediction
    • 5.1.2 The Valence-Bond-Solid Hamiltonian
    • 5.1.3 Physical Hamiltonians
    • 5.1.4 Experimental evidence for Haldane's conjecture
  • 5.2 Haldane material Y₂BaNiO₅
    • 5.2.1 Susceptibility measurements
    • 5.2.2 $\mu$SR measurements
    • 6.2.4 Discussion
  • 5.3 Summary
• 6 Spin-Peierls system
  • 6.1 Introduction
    • 6.1.1 Theories
    • 6.1.2 Organic spin Peierls materials
  • 6.2 Spin-Peierls material CuGeO₃
    • 6.2.1 Previous measurements
    • 6.2.2 Non-magnetic ion doping
    • 6.2.3 $\mu$SR measurements
    • Discussion
  • 6.3 Summary
• 7 Concluding remarks
• A Appendix
  • A.1 Extended Lieb-Shultz-Mattis Theorem [#!ALLMP86!#]
  • A.2 The 10/3 effect [#!AndersonRMP53!#,#!KuboTomitaJPSJ54!#]
  • A.3 Relaxation function in Néel state with randomness
• References