Local probes of magnetic field distribution

A wealth of information relating to the magnetic properties of superconductors can be gained from bulk measurements, e.g. magnetisation, transport and heat capacity, yet it is virtually impossible to interpret such data fully without a microscopic picture of vortex structures. Consequently, a range of complementary magnetic imaging techniques has been developed over the years to determine the local magnetic induction in superconducting samples. These can be broadly broken down into those techniques which are sensitive to the stray fields near the sample surface and those which probe the distribution throughout the bulk of the superconductor. The majority of techniques (e.g., Bitter decoration, magneto-optical imaging, scanning SQUID, Hall probe and magnetic force microscopies) fall into the first category and differ from one another predominantly in the available sensitivity and spatial resolution as well as the ease of use. Since these techniques measure magnetic fields directly, the relevant minimum lengthscale is the magnetic field penetration depth (lambda) and the large value of this parameter (~100-200 nm) in high-temperature superconductors (HTS) limits the identification of discrete vortices to rather low fields (<10 mT). At higher fields vortex resolution is lost yet local field profiles representing an average over many closely spaced fluxons are still of enormous value [1, 2]. Scanning tunneling microscopy is also a surface technique but, rather than being sensitive to the stray magnetic fields, it probes the local electronic structure of the superconductor. The location of a vortex can be identified by the reduced (or absent) gap at its core and the small size of the core (~xi~1.5 nm) in HTS allows the locations of discrete vortices to be established up to much higher fields (>10 T). Neutron diffraction, muon spin rotation and transmission electron microscopy belong to the second category of techniques which probe the field distribution throughout the bulk of the superconductor. The first two methods average over a large ensemble of vortices and yield key information about their long range order as well as precise data on microscopic field distributions. Transmission electron microscopy is unique in being a bulk measurement with very high spatial resolution and the ability to resolve discrete vortices within the same constraints as those for the surface field imaging techniques. The strengths and weaknesses of the different techniques are presented in the following sub-sections and an indication given of the type and usefulness of information which one obtains.