SCANNING HALL PROBE MICROSCOPY OF MAGNETIC VORTICES IN VERY UNDERDOPED YTTRIUM-BARIUM-COPPER-OXIDE a dissertation submitted to the department of physics and the committee on graduate studies of stanford university in partial fulfillment of the requirements for the degree of doctor of philosophy Janice Wynn Guikema March 2004 c  Copyright by Janice Wynn Guikema 2004 All Rights Reserved ii [...]... the very underdoped YBCO studies, and finally overviews the preparation of the YBCO crystals 1.1 Scanning magnetic microscopy In this section I discuss and compare the three types of scanning magnetic sensors employed in the Moler Lab Then I introduce basic concepts of the scanning microscopy and discuss the desire for good spatial resolution 1.1.1 Mesoscopic magnetic sensors Scanning magnetic microscopy. .. resolution-limited Scanning Hall probe microscopy of individual vortices and the determination of λ from the images was first demonstrated by Chang et al (1992) for a superconducting thin film Oral et al (1996b) and Davidovi´ et al (1996) also achieved scanning Hall c probe microscopy of single vortices several years later 14 CHAPTER 1 INTRODUCTION probe B h λab c-axis &z 2λab Figure 1.9: Cartoon of a vortex in a layered... cuprates and YBa2 Cu3 O6+x SQUID microscopy of vortices in YBa2 Cu3 O6+x and fits Scanning Hall probe images of hc/2e vortices Hall probe images of a vortex while cooling The Senthil-Fisher ring experiment to test for visons Vortex memory in the YBa2 Cu3 O6+x phase diagram Magnetic flux trapped in a superconducting ring Flux quanta trapped in a ring with Tc = 6.0 K ... 6.10 SQUID images of partial vortices in a YBa2 Cu3 O6.354 crystal Partial and full vortices in very underdoped YBCO Hall probe images containing partial vortices for a range of Tc Partial vortices prefer certain locations Effect of an in- plane field on partial vortex formation Comparison of thermal motion of partial vortices and full vortices Partial vortices coalesced... compromising flux sensitivity 1.2 Vortex imaging In this section I will give a brief review of vortices in superconductors, motivation for why we should image them, and finally an introduction to the vortex imaging experiments on very underdoped YBa2 Cu3 O6+x described in Chapters 4–6 1.2.1 The basics My main use of the scanning Hall probe (and SQUID) microscope has been to image magnetic vortices in superconductors,... deep in the pseudogap in its “normal” state, and the doping level is close to the antiferromagnetic insulating phase For this reason it is important to study very underdoped cuprates to help illuminate the mechanism of the superconductivity Our scanning magnetic microscopy studies of the very underdoped cuprate superconductor YBa2 Cu3 O6+x (YBCO), with x ∼ 6.35, have refuted a promising theory of spin-charge... mediates the binding of the spin and charge, and the vison would have to accompany any hc/2e vortices Their theory predicted the presence of hc/e vortices (2Φ0 ) for low superfluid density and also predicted a vortex memory effect for an underdoped superconducting ring 16 CHAPTER 1 INTRODUCTION Using scanning SQUIDs and Hall probes, we searched for these double vortices and the memory effect in very underdoped. .. for a number of SQUIDs Hall probes have the advantage of being direct magnetic field sensors, because the measured Hall voltage is directly proportional to the perpendicular magnetic field averaged over the Hall cross Figure 1.3 shows a Hall probe response to an applied magnetic field Hall probes are non-invasive, having self-field of only ∼0.4 mG at typical operating currents and sample -probe distances,... regions Spatial resolution of a probe can be a determining factor in its usability for studying magnetic phenomena Figure 1.5 shows images of canted antiferromagnetic domains in the manganese oxide Pr0.7 Ca0.3 MnO3 (sample courtesy of Bernhard Keimer and Diego Casa) that I took with a 2 µm Hall probe However, the magnetic features in the images appear similar in size to the 2 µm probe and thus it is likely... averages of multiple domains over the finite sized Hall 1.1 SCANNING MAGNETIC MICROSCOPY 2 µm 80 G 10 µm 9 Figure 1.5: Images of canted antiferromagnetic domains in Pr0.7 Ca0.3 MnO3 taken with a 2 µm Hall probe The images are spatial resolution limited and the individual domains are not resolved T = 10 K 4 1 0 8 µm (a) Gauss 2 1.9 Φ0 3 8 µm (b) Figure 1.6: Hall probe and SQUID images of many vortices . SCANNING HALL PROBE MICROSCOPY OF MAGNETIC VORTICES IN VERY UNDERDOPED YTTRIUM- BARIUM- COPPER- OXIDE a dissertation submitted to the department of physics and the committee. 72 4.2 SQUID microscopy of vortices in YBa 2 Cu 3 O 6+x and fits . . . . . . . . 76 4.3 Scanning Hall probe images of hc/2e vortices . . . . . . . . . . . . . . 78 4.4 Hall probe images of a vortex. Partial and full vortices in very underdoped YBCO . . . . . . . . . . 120 6.3 Hall probe images containing partial vortices for a range of T c . . . . 121 6.4 Partial vortices prefer certain locations