Traditionally, the behaviour of the magnetic penetration depth in the vortex state of a superconductor has been determined from the variation of the second moment (i.e. the square of the width) of the SR line shape. The second moment of the local magnetic field distribution n(B) is
Figure 4.6(a) shows the temperature dependence of for a mosaic of three high quality YBa2Cu3O6.95 single crystals. Despite the poor quality of the fits, the Gaussian function appears to effectively model the change in the second moment of the SR line shape. As the temperature is increased, decreases dramatically due to the natural progression towards a symmetric internal field distribution as the penetration depth grows. A serious drawback with this method is its inability to resolve the several phenomena which separately contribute to the width of the SR line shape. For example, one cannot assume that the linear T dependence of at low temperatures necessarily implies that has the same linear dependence. For instance, some of the change in the line width may arise from thermal fluctuations of the vortex lines which result in a narrowing of the SR line shape at higher temperatures. Thus, the magnitude of the linear term in could be different than that of , or worse, could have a different leading term.
Consider Fig. 4.6(b), which shows the temperature dependence of the muon depolarization rate in single crystal YBa2Cu3O6.95 for two different applied magnetic fields. There is a distinct drop in at low T when the applied magnetic field is changed from 0.5 to 1.5 T. Moreover, the term linear in T decreases at the higher field. However, there is no way to determine whether the field dependence of the muon depolarization rate is due to intrinsic or extrinsic effects. We now believe that the field dependence of observed in some of the earlier SR experiments was misinterpreted as being due to an increase in flux-lattice disorder at low magnetic fields. The precise cause of this field dependence will be addressed later on in this report.
There are many other serious limitations or problems associated with using a simple Gaussian analysis. For instance, the shape of the internal field distribution will change when there are variations in the vortex-lattice geometry and at a crossover at low fields where the intervortex spacing L equals . Fitting to a Gaussian function will misidentify these changes in the SR line shape as changes in .This simple analysis is also insensitive to the high-field tail of the measured internal field distribution--so that no information regarding the structure of the vortex cores or the behaviour of can be obtained.