3.3 The Rotating Reference Frame

It is often convenient to fit the measured asymmetry spectrum in a ``rotating reference frame'' (RRF). To do this, one multiplies the complex muon polarization $\tilde{P}(t)$ by a function $e^{i \omega_{RRF} t}$. The RRF frequency $\omega_{RRF}$ is chosen to be slightly lower than the average Larmor-precession frequency $\overline{\omega}_{\mu}$ of the muon in the sample. There are two important benefits from this procedure. The first is that the quality of the fit can be visually inspected. The precession signal viewed in this rotating reference frame has only low frequency components on the order of $\overline{\omega}_{\mu} - \omega_{RRF}$, where $\overline{\omega}_{\mu}$is the average precession frequency in the lab frame. Second and most important, it allows the data to be packed into much fewer bins, greatly enhancing the speed of fitting.

Further details of the $\mu$SR technique may be found elsewhere (e.g. see Refs. [47,46,49,50]). The essential point is that the muon accurately probes the local distribution of magnetic fields in the bulk of the superconductor. The resulting $\mu$SR line shape contains considerable information. Of particular interest, are the magnetic penetration depth $\lambda$, the coherence length $\xi$ and the vortex-lattice structure. Unfortunately, the $\mu$SR line shape also contains information not generally wanted--such as the effects of flux lattice disorder and additional fields such as those due to nuclear dipolar moments. Furthermore, extracting quantities such as $\lambda$ and $\xi$ from the data requires some modelling of the internal field distribution. This is the major difficulty in employing the $\mu$SR technique.