Anisotropy and Penetration Depth of MgB$_{2}$ from ${}^{11}$B NMR

Abstract

The ${}^{11}$B NMR spectra in polycrystalline MgB$_2$ were measured for several magnetic fields (1.97 T and 3.15 T) as a function of temperature from 5 K to 40 K. The composite spectra in the superconducting state can be understood in terms of anisotropy of the upper critical field, $γ_{H}$, which is determined to be 5.4 at low temperature. Using Brandt's algorithm\cite{Brandt} the full spectrum, including satellites, was simulated for the temperature 8 K and a magnetic field of 1.97 T. The penetration depth $λ$ was determined to be $1,152\pm50$ Å, and the anisotropy of the penetration depth, $γ_λ$, was estimated to be close to one at low temperature. Therefore, our findings establish that there are two different anisotropies for upper critical field and penetration depth at low temperatures.