2.2 Experimental setup for the $\mu$SR technique

 In order to perform $\mu$SR measurements, one has to visit a facility which produces many muons. Currently, there are five such `meson factories' available in the world (see Table 1). The heart of these facilities is a particle accelerator which provides a particle beam with an kinetic energy of a few hundred mega electron volts (MeV). For this high energy regime, there are two types of accelerators available, namely, the cyclotron and the synchrotron. The time structure of the muon beam reflects the accelerator type of the facility and it determines the details of the $\mu$SR setup.

In the synchrotron-based facilities (KEK and RAL), muons come in a pulse, with a spread of $\sim$50 ns and a pulse-to-pulse interval of $\sim$20 ms. Since the muon arrival time (t=0) is known from the timing signal of the synchrotron, $\mu$SR measurements are performed by taking the time spectra of decay positrons relative to the muon pulse. The timing resolution of this `pulse-$\mu$SR' method is limited by the muon pulse-width ($\sim$50 ns), but the experimental time window is virtually infinite ($\sim 20\ {\rm ms}\gg \tau_\mu=2.2\ \mu$s). The long experimental time window makes this method convenient for measurements of slow muon spin relaxation. The pulse-$\mu$SR method is also convenient to introduce extreme conditions, such as high-magnetic fields [30] and optical radiations [31,32], using a pulse magnets/lasers synchronized to the muon pulse.

The cyclotron-based facilities (TRIUMF and PSI) provide a continuous muon beam. As a result, one needs a muon counter on the beam path right before the sample, so that one knows a muon arrival time (t=0). The timing resolution of this `continuous-beam' $\mu$SR method is theoretically infinitesimally small; with carefully tuned electronics and small counters, sub-nanosecond resolution ($\Delta t<1$ ns) may be achieved [33]. The experimental time window is typically $\sim$12 $\mu$s, which is limited by the random background and the pile-up of second muon arrival (see section 2.2.3).

Since all the data in this thesis were obtained at TRIUMF, I will explain more details of the continuous-beam $\mu$SR method in the following sections.

 

Name (location) Accelerator Muons/cm²/sec (pulse width)

$$\sim 3\times 10^6$$ PSI (Switzerland) cyclotron

$$\sim 2\times 10^6$$ TRIUMF (Canada) cyclotron

$$\sim 1\times 10^6$$ LAMPF (U.S.A) synchrotron

$$\sim 1\times 10^6$$ RAL (U.K.) synchrotron

$$\sim 3\times 10^4$$ KEK (Japan) synchrotron