Muon Spin Relaxation Studies of Unconventional Superconductors: First-Order Behavior and Comparable Spin-Charge Energy Scales

Since the late 1980s, the muon spin rotation and relaxation (μSR) method has been extensively applied to studies of unconventional superconductors, including high-Tc cuprate, ruthenate, FeAs, organic, and heavy-fermion systems. With its unique sensitivity to static magnetic order in both long-range ordered and random spin systems, μSR has played a leading role in determining magnetic phase diagrams and elucidating the evolution from the parent antiferromagnetic state to the superconducting state in these systems. The extremely high sensitivity of μSR to small static magnetic fields allowed studies of time-reversal symmetry breaking in the superconducting state of Sr2RuO4 and several other systems and in the pseudogap region of cuprate systems. μSR measurements of the London penetration depth and the superfluid density led to a unique characterization of the pairing symmetry and energy scales of superconducting charges. In this paper, we review the historical developments and recent progress ofμSR studies in unconventional superconductors which revealed, among others, scaling of the superfluid density and Tc, comparable spin and charge energy scales, phase separation between superconducting and non-superconducting volumes, and first-order quantum evolution at phase boundaries. We discuss these results in terms of quantum criticality, crossover from Bose Einstein to BCS condensation, and the influence of competing states via inelastic soft modes. 8.1 Brief History and Technical Overview of μSR In high intensity proton accelerator facilities, such as TRIUMF in Vancouver and Paul Scherrer Intsitut in Switzerland, positive pions are produced by collisions of a proton beam and a meson production target (usually made of carbon or beryllium). Within a very short life time, a positive pion decays into a positive muon and muon neutrino. Since the π+ is a spin-less particle, the muon spin should be polarized by Y.J. Uemura (B) Department of Physics, Columbia University, New York, NY 10027, USA e-mail: [email protected] © Springer-Verlag Berlin Heidelberg 2015 A. Avella and F. Mancini (eds.), Strongly Correlated Systems, Springer Series in Solid-State Sciences 180, DOI 10.1007/978-3-662-44133-6_8 237