Anisotropic reversible mixed-state properties of superconducting carbon-dopedMg(B1−xCx)2single crystals

Abstract

We report on magnetic and torque measurements on carbon-doped $\mathrm{Mg}{({\mathrm{B}}_{1\ensuremath{-}x}{\mathrm{C}}_{x})}_{2}$ single crystals with $x=0.038$, 0.066, and 0.095. One-band Ginzburg Landau (GL) and London theories are applied to derive the reversible parameters: i.e., the upper critical fields ${H}_{c2}$, the coherence lengths $\ensuremath{\xi}$, the penetration depths $\ensuremath{\lambda}$, the anisotropy $\ensuremath{\gamma}$, the lower critical fields ${H}_{c1}$, and the GL parameter $\ensuremath{\kappa}$ for fields parallel and perpendicular to the crystallographic $ab$ plane. Due to the persistence of two-band superconductivity in the investigated doping range, these parameters turn out to depend not only on temperature, as in the case of one-band superconductors, but also on field. Therefore, the evaluation was carried out separately for two field regions: first for fields near ${H}_{c1}$ and second close to ${H}_{c2}$. In general, the upper critical field increases and the anisotropy decreases upon carbon doping. All further reversible parameters are significantly modified as well. These modifications are compared for single crystals with different carbon concentration.