Muon spin rotation studies of electronic excitations and magnetism in the vortex cores of superconductors

The focus of this paper is on recent progress in muon spin rotation (mu SR) studies of the vortex cores in type-II superconductors. By comparison of mu SR measurements of the vortex core size in a variety of materials with results from techniques that directly probe electronic states, the effect of delocalized quasiparticles on the spatial variation of field in a lattice of interacting vortices has been determined for both single-band and multi-band superconductors. These studies demonstrate the remarkable accuracy of what some still consider an exotic technique. In recent years mu SR has also been used to search for magnetism in and around the vortex cores of high-temperature superconductors. As a local probe mu SR is specially suited for detecting static or quasistatic magnetism having short-range or random spatial correlations. As discussed in this review, mu SR experiments support a generic phase diagram of competing superconducting and magnetic order parameters, characterized by a quantum phase transition to a state where the competing order is spatially nonuniform.