Fundamental studies of superconductors using scanning magnetic imaging

In this review I discuss the application of scanning magnetic imaging to fundamental studies of superconductors, concentrating on three scanning magnetic microscopies-scanning SQUID microscopy (SSM), scanning Hall bar microscopy (SHM) and magnetic force microscopy (MFM). I briefly discuss the history, sensitivity, spatial resolution, invasiveness and potential future developments of each technique. I then discuss a selection of applications of these microscopies. I start with static imaging of magnetic flux: an SSM study provides deeper understanding of vortex trapping in narrow strips, which are used to reduce noise in superconducting circuitry. Studies of vortex trapping in wire lattices, clusters and arrays of rings and nanoholes show fascinating ordering effects. The cuprate high-T-c superconductors are shown to have predominantly d-wave pairing symmetry by magnetic imaging of the half-integer flux quantum effect. Arrays of superconducting rings act as a physical analog for the Ising spin model, with the half-integer flux quantum effect helping to eliminate one source of disorder in antiferromagnetic arrangements of the ring moments. Tests of the interlayer tunneling model show that the condensation energy available from this mechanism cannot account for the high critical temperatures observed in the cuprates. The strong divergence in the magnetic fields of Pearl vortices allows them to be imaged using SSM, even for penetration depths of a millimeter. Unusual vortex arrangements occur in samples comparable in size to the coherence length. Spontaneous magnetization is not observed in Sr2RuO4, which is believed to have p(x) +/- ip(y) pairing symmetry, although effects hundreds of times bigger than the sensitivity limits had been predicted. However, unusual flux trapping is observed in this superconductor. Finally, unusual flux arrangements are also observed in magnetic superconductors. I then turn to vortex dynamics: imaging of vortices in rings of highly underdoped cuprates places limits on spin-charge separation in these materials. Studies of spontaneous generation of fluxoids upon cooling rings through the superconducting transition provide clues to dynamical processes relevant to the early development of the universe, while studies of vortex motion in cuprate grain boundaries allow the measurement of current-voltage characteristics at the femtovolt scale for these technologically important defects. Scanning SQUID susceptometry allows the measurement of superconducting fluctuations on samples comparable in size to the coherence length, revealing stripes in susceptibility believed to be associated with enhanced superfluid density on the twin boundaries in the pnictide superconductor Co doped Ba-122, and indicating the presence of spin-like excitations, which may be a source of noise in superconducting devices, in a wide variety of materials. Scanning magnetic microscopies allow the absolute value of penetration depths to be measured locally over a wide temperature range, providing clues to the symmetry of the order parameter in unconventional superconductors. Finally, MFM tips can be used to manipulate vortices, providing information on flux trapping in superconductors.