1.1.2 The idea of the measurements in this thesis

 The three spin systems introduced above (spin Peierls, even-leg-number spin-ladder and the Haldane system) are characterized by (1) a non-magnetic ground state and (2) a finite energy gap between the ground state and the first excited state. Up to now, numerous experiments have been performed to detect the energy gap in model materials of these spin gap systems, and some of these have successfully found the gap.

The experiments presented in this thesis investigate other feature of the spin gap systems: the absence of an internal magnetic field in the ground state. As the main experimental technique, I have utilized the Positive Muon Spin Rotation/Relaxation ($\mu$SR) technique [6,7,28], which is the most sensitive microscopic probe currently available for small and/or dilute magnetic moments. For example, it is straight forward for the $\mu$SR technique to detect the nuclear dipolar fields which originate from nuclear magnetic moments as small as $\sim10^{-3}\mu_{\rm B}$ ($\mu_{\rm B}$ denotes the electron Bohr magneton) [6]. The high sensitivity to dilute moments is seen in investigations of dilute spin glass alloys [7]; static moments as dilute as $\sim$0.1% are easy to investigate with the $\mu$SR technique. These two experiments have shown that $\mu$SR is the most sensitive probe to confirm the absence/presence of magnetic order in a spin system.

Another favorable feature of $\mu$SR is that one may investigate spin fluctuations around the muon with the help of spin relaxation theories in solids. In some of the spin gap materials, non-magnetic ion and/or charge doping to the system has been performed, and it was found that the doping induces moments from the sea of singlet pairs. This thesis presents $\mu$SR measurements of these doped systems as well, in order to clarify the fluctuations of the induced moments.

The structure of this thesis is as follows: the following two chapters (Chapter 2 and 3) introduce the $\mu$SR technique and the spin relaxation theories, which are necessary to understand the experimental results. The subsequent three chapters are devoted to spin-ladder materials Sr_n-1Cu_n+1O_2n (Chapter 4), a Haldane material Y₂BaNiO₅ (Chapter 5) and a spin-Peierls material CuGeO₃ (Chapter 6). Concluding remarks are given in Chapter 7.