Figure 4.1 shows a typical muon-spin
precession signal in the normal and vortex states of YBa_{2}Cu_{3}O_{6.95}
obtained by applying a magnetic field parallel to the -axis.
For convenience these signals are displayed in a reference frame
rotating at about 3 MHz below the average muon Larmor precession frequency
in the vortex lattice. A damped signal
results from the inhomogeneous distribution of magnetic field
in the sample. The undamped signals arising from individual
muons precessing in different local static fields
combine to give a signal which decays over time.
Above *T*_{c} where flux penetrates the sample uniformly,
there is only a slight damping of the signal which is attributed mainly
to the random local fields of nuclear dipolar moments.
On the other hand,
below *T*_{c} the strongly damped signal is primarily due to the inhomogeneous
field distribution of the vortex lattice.

Figure 4.2 shows the
finite Fourier transforms of the time spectra in Fig. 4.1.
The real amplitude of the Fourier transform represents a good approximation
to the internal field distribution.
Above *T*_{c} the SR line shape is symmetric with some broadening due to
the nuclear dipolar moments (see top panel of Fig. 4.2).
Below *T*_{c} the observed line shape is primarily due to the
vortex lattice. The sharp peak at 67.3 MHz is attributed to the
residual background signal from muons which miss the sample.

Figure 4.3 shows a general theoretical field distribution corresponding to a triangular vortex lattice. The sharp cutoff at low fields is due to the minimum in the field distribution which occurs at the center of the triangle formed from three adjacent vortices. The peak is due to the saddle point midway between two adjacent vortices. The long tail is due to the region around the vortex core, and the high-field cutoff is due to the maximum field at the center of the core. As shown in the bottom panel of Fig. 4.2, the sharp features expected from the vortex lattice are smeared in the Fourier transform of the measured muon precession signal. This is primarily due to the broadening effects associated with the Fourier transform (which were discussed in the previous chapter). The measured line shape also contains broadening effects due to the nuclear dipolar moments, fluctuations in the temperature and magnetic field, demagnetization effects associated with the sample geometry and disorder in the vortex lattice caused by pinning.