μSR studies of the vortex state in type-II superconductors

The authors present a review of recent muon spin rotation (μSR) studies of the vortex state in type-II superconductors. There are significant gaps in our understanding of this unusual phase of matter, especially in unconventional superconductors, for which the description of the vortex structure is a subject of great controversy. The μSR technique provides a sensitive local probe of the spatially inhomogeneous magnetic field associated with the vortex state. For the case of a regular vortex lattice, the magnetic penetration depth λ and the coherence length ξ can be simultaneously extracted from the measured internal field distribution. The penetration depth is directly related to the density of superconducting carriers in the material, and measurements of its variation with temperature, magnetic field, and impurities can provide essential information on the symmetry of the order parameter. The coherence length measured with μSR is the length scale for spatial variations of the order parameter within a vortex core. A primary goal of this review article is to show that measurements of these fundamental length scales are fairly robust with respect to the details of how the field distribution is modeled. The reliability of the results is demonstrated by a comparison of the μSR experiments with relevant theories and with other experimental techniques. The authors also review μSR measurements that have focused on the study of pinning-induced spatial disorder and vortex fluctuation phenomena. The μSR technique has proven to be a powerful tool for investigating exotic vortex phases, where vortex transitions are directly observable from changes in the μSR line shape. Particular emphasis is given to μSR experiments performed on high-temperature superconductors since high-quality single crystals have become available.