We report on specific heat, high magnetic field transport and ac−susceptibility measurments on magnesium diboride single crystals. The upper critical field Hc2 for magnetic fields perpendicular and parallel to the Mg and B planes is presented for the first time in the entire temperature range. A very different temperature dependence has been observed in the two directions which yields to a temperature dependent anisotropy with Γ ∼ 5 at low temperatures and about 2 near Tc. A peak effect is observed in the susceptibility measurments for µ0H ∼2 T parallel to the c−axis and the critical current density presents a sharp maximum for H parallel to the ab−plane.

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Superconducting QUantum Interference Device (SQUID) microscopy has excellent magnetic field sensitivity, but suffers from modest spatial resolution when compared with other scanning probes. This spatial resolution is determined by both the size of the field sensitive area and the spacing between this area and the sample surface.In this paper we describe scanning SQUID susceptometers that achieve sub-micron spatial resolution while retaining a white noise floor flux sensitivity of ≈ 2µΦ 0 /Hz 1/2 .This high spatial resolution is accomplished by deep sub-micron feature sizes, well shielded pickup loops fabricated using a planarized process, and a deep etch step that minimizes the spacing between the sample surface and the SQUID pickup loop. We describe the design, modeling, fabrication, and testing of these sensors. Although submicron spatial resolution has been achieved previously in scanning SQUID sensors, our sensors not only achieve high spatial resolution, but also have integrated modulation coils for flux feedback, integrated field coils for susceptibility measurements, and batch processing. They are therefore a generally applicable tool for imaging sample magnetization, currents, and susceptibilities with higher spatial resolution than previous susceptometers.PACS numbers: 85.25.Dq,07.55.-w

The superconducting phase diagram of MgB 2 was determined from magnetization, magnetotransport, and single-crystal specific-heat measurements. A zero-temperature in-plane coherence length of 9.4 nm is determined. The superconducting anisotropy ␥ increases from a value around 2 near T c to above 4.5 at 22 K. For Hʈc a pronounced peak effect in the critical current occurs at the upper critical field. Evidence for a surface superconducting state is presented for Hʈc that might account for the widespread in reported values of ␥.