Scanning Hall probe microscopy of magnetic vortices in very underdoped yttrium-barium-copper-oxide

Since their discovery by Bednorz and Muller in 1986, high-temperature cuprate superconductors have been the subject of intense research. Despite this effort, agreement on the mechanism of high- Tc has not been reached. Many theories make their strongest predictions for underdoped superconductors with very low superfluid density ns/m*. I implemented a scanning Hall probe microscope (SHPM) and used it to study magnetic vortices in newly available single crystals of very underdoped YBa2Cu3O6+x . These studies have disproved a promising theory of spin-charge separation, measured the apparent vortex size (an upper bound on the penetration depth lambda ab), and revealed an intriguing phenomenon of "split" vortices.; SHPM is a non-invasive and direct method for magnetic field imaging. It is one of the few techniques capable of submicron spatial resolution coupled with sub-phi0 (flux quantum) sensitivity, and it operates over a wide temperature range. Chapter 2 introduces the variable temperature scanning microscope and discusses the scanning Hall probe set-up and scanner characterizations. Chapter 3 details my fabrication of submicron GaAs/AlGaAs Hall probes and discusses noise studies for a range of probe sizes, which suggest that sub-100 nm probes could be made without compromising flux sensitivity.; The subsequent chapters detail SHPM (and SQUID) studies of very underdoped YBa2Cu3O6+x crystals with T c ≤ 15 K. Chapter 4 describes two experimental tests for visons, essential excitations of a spin-charge separation theory proposed by Senthil and Fisher. We searched for predicted hc/ e vortices and a vortex memory effect with null results, placing upper bounds on the vison energy inconsistent with the theory. Chapter 5 discusses imaging of isolated vortices as a function of Tc. Vortex images were fit with theoretical magnetic field profiles in order to extract the apparent vortex size. The data for the lowest Tc 's (5 and 6.5 K) show some inhomogeneity and suggest that lambda ab might be larger than predicted by the Tc ∝ ns(0)/m* Uemura relation for underdoped cuprates. Finally, Chapter 6 examines observations of apparent "partial vortices" in the crystals. My studies of these features indicate that they are likely split pancake vortex stacks. Collectively these magnetic imaging studies deepen our knowledge of cuprate superconductivity, especially in the important regime of low superfluid density.