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Next: 3 The SR Technique Up: 2 The Characteristic Length Previous: 2.4 The GL Penetration

2.5 Measuring the Characteristic Length Scales

In the Meissner state, $\lambda$ can be measured by excluded volume techniques (such as microwave cavity perturbation), inductive methods and far infrared reflectivity. The latter is a surface measurement which can determine the absolute value of $\lambda$.In the vortex state, $\mu$SR, nuclear magnetic resonance (NMR) or small angle neutron scattering can be used to measure the magnetic field inhomogeneity due to the vortex lattice in the bulk of the sample, from which an absolute value of $\lambda$ can be obtained.

In contrast, there are few direct measurements of $\xi$.Estimates of its magnitude can be obtained from the contribution of fluctuations to measured quantities such as the specific heat, susceptibility or conductivity. Scanning tunneling microscopy (STM ) can be used to measure the vortex-core radius r0 at the sample surface, which provides an estimate of $\xi$ [*]. However, the coherence length is most often determined indirectly from measurements of the upper critical field, Hc2. At this field the vortices begin to overlap and the superconductor undergoes a first order phase transition into the normal state. Since the radius of a normal vortex core is about the size of the coherence length, then at Hc2 there is a direct relationship with $\xi$. In particular, from GL theory  
 \begin{displaymath}
\xi (T) = \sqrt{\frac{\Phi_0}{2 \pi H_{c2} (T)}} \, .\end{displaymath} (69)
In the high-Tc materials, Hc2 is extremely large (e.g. on the order of 102 T in YBa2Cu3O7 at $T \! = \! 0$) and is therefore difficult to measure accurately. Measurements are generally limited to temperatures near Tc where Hc2 is considerably smaller ($H_{c2} \! \rightarrow \! 0$ as $T \! \rightarrow \! T_c$). However, near Tc thermal fluctuations of the vortex lines can depin or melt the solid 3D vortex-lattice into a vortex liquid phase. Rather than Hc2, what is often measured is the transition of the ordered 3D vortex solid into a vortex fluid phase, in which many of the vortices are free to move independently of each other. The phenomenon is analogous to the way in which thermal vibrations of water molecules cause ice to melt into water. The problem of thermal fluctuations is most serious in short coherence length superconductors with high transition temperatures. This is because fluctuation effects become important when the thermal energy kB T exceeds the condensation energy $\xi_{a} \xi_{b} \xi_c H_c^2/ 8 \pi
\! \propto \! (T \! - \! T_c)^{1/2}$[43]. Here, $\xi_{a} (T) \xi_{b} (T) \xi_c (T)$ is the minimum volume occupied by the fluctuation and Hc is the thermodynamic critical field. In the high-Tc materials, thermal fluctuations are mainly responsible for the large variation in reported values of $\xi$ determined from Hc2 measurements. A more appropriate way to determine $\xi$ is to perform measurements deep in the superconducting state, well away from the strong fluctuation regime. This can be achieved with $\mu$SR, a bulk technique which is described next.


next up previous contents
Next: 3 The SR Technique Up: 2 The Characteristic Length Previous: 2.4 The GL Penetration