Anisotropies of the lower and upper critical fields in MgB2 single crystals

Effect of two length scales on the properties of MgB(2) for arbitrary applied magnetic field

Experiments carried out on the intermetallic superconducting material MgB(2) have shown anomalous magnetic field dependence of upper critical field, small angle neutron scattering form factor, specific heat, critical current etc. Similarly, scanning tunnelling microscopy (STM) experiments on vortex structures have shown unusually large vortex core size and two different magnetic and spatial field scales. Also, whereas the specific heat measurements and isotope shift experiments have shown Bardeen-Cooper-Schrieffer-like (BCS-like) behaviour, the temperature dependences of the penetration depth experiments have shown non-BCS-like behaviour. These anomalous behaviours have been attributed to the multiband superconductivity of this material and the nature of the local spatial behaviour of the magnetic induction and the order parameter components having two length scales. We report an analytical investigation of the effect of two length scales on the temperature and the applied magnetic field dependence of several properties of MgB(2), such as, the penetration depth, single vortex and vortex lattice structure, vortex core radius, reversible magnetization, critical current, small angle neutron scattering form factor and the shear modulus of the vortex lattice within the framework of two-order parameter Ginzburg-Landau theory. We solve the corresponding nonlinear Ginzburg-Landau equations numerically exactly using an iterative method for arbitrary applied field H(c1) < H < H(c2), the Ginzburg-Landau parameter and vortex lattice symmetry. This enables us to compute the local spatial behaviour of the magnetic induction and the order parameters accurately for arbitrary applied field and a wide range of temperature. Comparison of the analytical results with experiments on MgB(2) gives very good agreement.

Anisotropy of the Sommerfeld coefficient in magnesium diboride single crystals

The anisotropic field dependence of the Sommerfeld coefficient gamma has been measured down to B-->0 by combining specific heat and Hall probe magnetization measurements in MgB2 single crystals. We find that gamma(B,theta) is the sum of two contributions arising from the sigma and pi band, respectively. We show that gammasigma(B,theta)=B/Bc2(theta) where Bc2(theta)=Bc2ab/sqrt[sin2theta+Gamma2cos2theta] with Gamma approximately 5.4 (theta being the angle between the applied field and the c axis) and gammapi(B,theta)=gammapi(B)=B/Bpi(B). The "critical field" of the pi band Bpi is fully isotropic but field dependent increasing from approximately 0.25 T for B< or =0.1 T up to 3 T approximately Bc2c for B-->3 T. Because of the coupling of the two bands, superconductivity survives in the pi band up to 3 T but is totally destroyed above for any orientation of the field.

Temperature-dependent anisotropy of the penetration depth and coherence length of MgB2

We report measurements of the temperature-dependent anisotropies (gamma(lambda) and gamma(xi)) of both the London penetration depth lambda and the upper critical field of MgB2. Data for gamma(lambda)=lambda(c)/lambda(a) was obtained from measurements of lambda(a) and lambda(c) on a single crystal sample using a tunnel diode oscillator technique. gamma(xi)=H(perp)c(c2)/H(||c)(c2) was deduced from field-dependent specific heat measurements on the same sample. Gamma(lambda) and gamma(xi) have opposite temperature dependencies, but close to T(c) tend to a common value (gamma(lambda) similar or equal to gamma(xi)=1.75 +/- 0.05). These results are in good agreement with theories accounting for the two-gap nature of MgB2.