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

Abstract

We report measurements of the temperature dependent anisotropies ($γ_λ$ and $γ_ξ$) of both the London penetration depth $λ$ and the upper critical field of MgB$_2$. Data for $γ_λ=λ_c/λ_a$ was obtained from measurements of $λ_{a}$ and $λ_c$ on a single crystal sample using a tunnel diode oscillator technique. $γ_ξ=H_{c2}^{\parallel c}/H_{c2}^{\bot c}$ was deduced from field dependent specific heat measurements on the same sample. $γ_λ$ and $γ_ξ$ have opposite temperature dependencies, but close to $T_c$ tend to a common value ($γ_λ\simeq γ_ξ=1.75\pm0.05$). These results are in good agreement with theories accounting for the two gap nature of MgB$_2$