Experimental Setup

The $\mu$SR experiments were carried out using both the M15 and M20B positive surface muon beam lines at TRIUMF. The measurements were taken using the LAMPF spectrometer, which consists of three orthogonal pairs of Helmholtz coils plus an array of counters to detect the decay positrons. These coils can be used to either apply a transverse magnetic field to the sample or to cancel out the external magnetic fields in a ZF-$\mu$SR experiment. To perform $\mu$SR experiments on such small crystals, the momentum of the incoming muons was reduced by about $4$% so that sufficient muons stopped in the sample, rather than passing through. However, this also increases the contribution to the background signal from muons that are stopped upstream in the cryostat windows etc. To counteract this problem, the sample was sandwiched between a thin muon counter and the veto counter all contained inside a $^{4}He$ gas-flow cryostat, as shown in Fig. 3.3. A silver mask with a hole slightly smaller than the area of the sample was placed in front of the muon counter. Muons stopping in the mask do not pass through the muon counter and hence are logically excluded. While these muons still decay into positrons that are not logically excluded, we found that their contribution to the ``uncorrelated'' background signal was less than 10% of the good muon-decay count rate. Furthermore, with this experimental arrangement the $\mu$SR spectra contained no observable ``correlated'' background signal. To determine the value of the magnetic penetration depth, TF-$\mu$SR spectra with $\sim 20$ million muon decay events were recorded.