Anisotropies of the lower and upper critical fields in MgB$_2$ single crystals

Abstract

The temperature dependence of the London penetration depth ($λ$) and coherence length ($ξ$) has been deduced from Hall probe magnetization measurements in high quality MgB$_2$ single crystals in the two main crystallographic directions. We show that, in contrast to conventional superconductors, MgB$_2$ is characterized by two different anisotropy parameters ($Γ_λ= λ_c/λ_{ab}$ and $Γ_ξ= ξ_{ab}/ξ_c$) which strongly differ at low temperature and merge at $T_c $. These results are in very good agreement with recent calculations in weakly coupled two bands suprerconductors (Phys. Rev. B, 66, 020509(R) (2002).

4 pages, 4 figures