Bismuth Hall effect sensors with active sizes in the range 0.1µm - 2µm have been fabricated by electron beam lithography and lift-off techniques for applications in scanning Hall probe microscopy (SHPM). The key figures of merit of the sensors have been systematically characterised as a function of device size. The miniumum detectable field of 100nm probes at room temperature is found to be Bmin=0.9mT/Hz0.5, with scope for more than a factor of ten reduction by using higher Hall probe currents. This is significantly lower than in similar samples fabricated by focussed ion beam (FIB) milling of continuous Bi films, suggesting that the elimination of FIB damage and Ga+ ion incorporation through the use of lift-off techniques leads to superior figures of merit. A number of ways in which the T=300K performance of our sensors could be improved still futher are discussed. High resolution scanning Hall probe microscopy (SHPM) with semiconductor 2DEG Hall probe devices has been used to search for novel phases of vortex matter in single crystals of the high temperature superconductor Bi2Sr2CaCu2O8+. In the crossing lattices regime of these highly anisotropic superconductors under tilted magnetic fields two orthogonal types of flux structure are formed known as Josephson and pancake vortices (JVs and PVs). SHPM has been used to study interacting JV-PV matter with very high in-plane fields. The spacing of JV chains has been systematically quantified as a function of both in-plane and out-of-plane fields. Surprisingly, it is found that the JV chain spacing is not solely a function of the in-plane field, as previously assumed, and the effective anisotropy, γ_eff, is shown to depend strongly on the out-of-plane field strength. Moreover, for a fixed in-plane field the JV stack spacing shows pronounced sawtooth-like oscillations as a function of the out-of-plane field. These measurements are giving us unique new insights into the properties of crossing vortex lattices in highly anisotropic cuprate superconductors at high Josephson vortex stack densities.

The high degree of modification through chemical substitution afforded by the perovskite crystal structure and its related counterparts allows a systematic study of structure-property relationships critical to understand the wide variety of exotic phenomena observed in these materials where the spin, charge, orbital, and lattice degrees of freedom are highly correlated. From the multiple phenomena observed in these materials, which includes multiferroicity, catalytic activity, and high temperature superconductivity, this study is concerned with a material that displays colossal magnetoresistance (CMR), La₂₋₂xSr₁₊₂xMn₂O₇; this is a naturally bilayered manganite that exhibits CMR at a paramagnetic to ferromagnetic transition that coincides with an insulator to metal transition. The strong correlation between different degrees of freedom in the material leads to considerable variation in its magnetic properties due to doping even in the small range studied of 0.32 [less than or equal to] x [less than or equal to] 0.4, where the easy axis of magnetization changes from the c-axis to the ab plane. Magnetic force microscopy (MFM) was used for this part of the work, to visualize the local variation of the out of plane (c-axis) magnetization or magnetic microstructure of La₂₋₂xSr₁₊₂xMn₂O₇ for 0.32 [less than or equal to] x [less than or equal to] 0.4 at the exposed ab surface and its evolution due to an applied magnetic field at 4 K. For the x = 0.32 composition, which is close to the out of plane to in plane magnetization transition, a strong preferred magnetization direction within the ab plane or magnetocrystalline anisotropy was observed. The stray magnetic field of the MFM tip perturbs the magnetic microstructure of low coercivity materials like diluted magnetic semiconductors, making it unsuitable for the study of such materials. For this reason, as part of this project a scanning Hall probe microscope (SHPM), a magnetic imaging technique complementary to MFM that uses a Hall sensor that provides a magnetically non-invasive calibrated measurement of the stray fields at the surface of a sample with good resolution (~ 1 [micrometer]), was designed. The construction of a compact cryogenic variable-temperature (77 - 300 K) SHPM, highlighting its features, is described. / text