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

Abstract

The temperature dependence of the London penetration depth ($\lambda$) and coherence length ($\xi$) 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 (${\Gamma }_{\lambda }={\lambda }_c/{\lambda }_{ab}$ and ${\Gamma }_{\xi }={\xi }_{ab}/{\xi }_c$) 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

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