Scanning SQUID microscopy of unconventional superconductivity and frustrated magnetism

Scanning SQUID microscopy makes a unique contribution to the study of quantum materials, including unconventional superconductors and frustrated magnets, as it is a scanned probe technique and a highly quantitative magnetic probe. The ability to scan means that we are able to spatially resolve material properties, which is important as the samples tend to be complex lattices comprised of 3 or more elements, sometimes including dopants that are disordered by construction. Materials can never be grown perfectly, and this leads to a variety of possible material defects; additionally, materials that go through phase transitions, such as structural or magnetic transitions, will often have non-trivial domain structure that also leads to spatial variation. By spatially resolving such defects and domain boundaries, we are able to gain an understanding of how and why they interact with the properties under study. Chapters 2 and 3 serve as an introduction to the physics of SQUIDs and the art and science of scanning SQUID microscopy. These are directed primarily towards new students and practitioners, with the goal of reducing the learning curve for the technique, which can be quite challenging to overcome. Chapter 4 covers different measurement techniques that use scanning SQUID microscopy through short descriptions and case studies. The experiments covered include disordered Nb dot arrays, the split superconducting transition of PrOs4Sb12, the anisotropy of the penetration depth in single crystals of x = 1/8 LSCO, and magnetism in oxygen deficient LAO/STO heterostructures. In Chapter 5, I cover the integration of a piezoelectric-based strain cell with scanning SQUID microscopy and its implementation in studying the purported chiral superconductor, Sr2RuO4. The ability to tune anisotropic strain in situ provides a symmetry-breaking field that is compatible with SQUID electronics and promises to have many future applications. In this experiment, we ruled out the existence of a linear cusp in the response of the superconducting transition temperature to the applied anisotropic strain at the level predicted by theory. We do not rule out the possibility that Sr2RuO4 is a chiral order parameter, but it remains an open question why this signature would be smaller than predicted. The next chapter, Ch. 6, covers magnetic susceptibility measurements of bulk samples of x = 1/8. Samples at this doping show a reported bulk superconducting transition temperature much lower than those at both higher and lower dopings; furthermore, a cascade of phase transitions including structural transitions, charge ordering, and spin ordering occur as the temperature is reduced, and the transition to a bulk superconducting state is preceded by a diverging resistivity anisotropy that has led to the proposal of an exotic pair density wave state. We find instead that the superconducting transition in this material is grossly inhomogeneous, occurring at substantially higher temperatures in some regions, such as edges and terraces. This suggests that the resistivity anisotropy may be due to the percolation in two but not three dimensions of superconducting filaments along such defects. Chapter 7 focuses on the classical spin ice Ho2Ti2O7, a canonical example of frustrated magnetism. This work represents the first comprehensive study using scanning SQUID microscopy for magnetic flux noise spectroscopy, which we employed to disentangle the magnetic dynamics in our sample due to defects and theoretically predicted monopole-like excitations. We find that our data qualitatively deviate from simple models for spin ensembles in several ways that are consistent with the expectations for a dilute, low-mobility gas of magnetic monopoles. This technique promises to be essential in future studies of frustrated magnetic systems, including the search for quantum spin liquids. Chapter 8 covers work on engineered, exotic superconducting junctions. With devices comprised of the junction under study with conventional superconducting leads that close on one another to realize a ring structure, we are able to position our SQUID susceptometer over each device to conduct a measurement of the current-phase relationship. We demonstrate that the high transmission states at the surface of 3D topological insulator HgTe give rise to a distinctly non-sinusoidal current-phase relationship that is forward-skewed. The power of this technique is at least in part in our ability to measure many such devices in a single experiment, owing to the non-contact nature of the measurement. In concluding in Chapter 9, I attempt to tie together several overarching themes of my graduate work and give a coherent view of where scanning SQUID microscopy might be headed, including potential avenues for instrumentation development and new imaging modalities. The work contained in this thesis was conducted as part of the Stanford Institute for Materials and Energy Sciences and was funded by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract No. DE-AC02-76SF00515.

Keywords: Applied Physics.
Advisor: Moler Kathryn A. 
Fisher Ian R. (Ian Randal) 
Kivelson Steven