We report on measurements of the magnetic moment in superconducting MgB2 single crystals. We find µ0H c c2 (0) = 3.2 T, µ0H ab c2 (0) = 14.5 T, γ = 4.6, µ0Hc(0) = 0.28 T, and κ(Tc) = 4.7. The standard Ginzburg-Landau and London model relations lead to a consistent data set and indicate that MgB2 is a clean limit superconductor of intermediate coupling strength with very pronounced anisotropy effects.PACS numbers: 74.25. Ha, 74.60.Ec, 74.70.Ad The recent discovery of superconductivity in MgB 2 [1] has attracted a lot of attention. Especially the rather high transition temperature of nearly 40 K in such a simple compound is of interest for applications, but also for an analysis of the physical mechanism leading to superconductivity. Several experiments indicate a phonon mediated s -wave BCS mechanism [2,3]. Different models are proposed to explain the particular properties of MgB 2 [4,5]. Their correctness has to be checked by experiments, but only a few results are available on single crystals [6,7,8,9,10,11,12].We report in this Letter on magnetization measurements on single crystalline MgB 2 in magnetic fields applied parallel and perpendicular to the uniaxial crystallographic (≡ c) axis. A detailed evaluation allows us to obtain the temperature dependence of the most important reversible mixed state parameters, such as the critical magnetic fields, the characteristic lengths, the Ginzburg-Landau (GL) parameter and the anisotropy. We will show that MgB 2 is a clean limit superconductor of intermediate coupling strength with very pronounced anisotropy effects.Several single crystals of MgB 2 were grown using high pressure cubic anvils. Details of the process will be published elsewhere [13]. Two crystals (sample A:3 ) were investigated by magnetic methods. The transition temperature (T c ) of each sample was obtained from the ac -susceptibility measured in a 1 T quantum interference device (SQUID) magnetometer. Sample A shows an onset of T c at 38 K and a rather broad transition of about 1 K. A linear fit of H c c2 vs. T near T c indicates a "bulk transition temperature" of 37.5 K (see inset of fig. 1a). In sample B we find T c = 38.3 K, ∆ T c = 0.3 K and a "bulk T c " of 38.2 K. A simple analysis [14] of the slope of the magnetic moment after reversing the applied field demonstrates that the size of the domain, in which the supercurrents flow without impedance, is identical to the sample size. Furthermore, a comparison of the calculated and the measured magnetization in the Meissner regime indicates a superconducting volume fraction of about 100 %. The further evaluation of the mixed state parameters did not show significant differences between these two crystals.The measurements of the magnetic moment were carried out in the 1 T and in an 8 T (SHE) SQUID magnetometer (for details, cf. [15]). Fig. 1a shows the upper critical field of MgB 2 for applied fields H a c (H c c2 ) and H a ab (H ab c2 ). H c2 (T ) is determined either from the onset of the superconducting signal in the m(T ) curve ("T c (H a )") or ...

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This paper presents an extensive experimental and theoretical analysis of anisotropy effects in superconducting niobium. It is concluded that anisotropy efFects, especially in the magnetic properties, are clearly discernible and that the theoretical analysis results in a mean-square anisotropy of the electron -phonon interaction of 0.0335 + 0.0035 and of the Fermi velocity of 0.118+ 0.007. These anisotropy parameters are in excellent agreement with previous de Haas - van Alphen experiments.

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