Temperature dependent anisotropy of the penetration depth and coherence length in MgB$_2

Abstract

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 MgB${}_2$. 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. ${\gamma }_{\xi }=H_{c2}^{\parallel c}/H_{c2}^{\perp c}$ 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 (${\gamma }_{\lambda }\simeq {\gamma }_{\xi }=1.75\pm 0.05$). These results are in good agreement with theories accounting for the two gap nature of MgB${}_2$

4 pages with figures (New version)