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

TL;DR

This study uses ${}^{11}$B NMR to investigate the anisotropy and penetration depth in MgB$_2$, revealing distinct anisotropic behaviors of the upper critical field and penetration depth at low temperatures.

Contribution

It provides the first detailed NMR-based analysis showing different anisotropies for the upper critical field and penetration depth in MgB$_2$ at low temperatures.

Findings

Anisotropy of the upper critical field $\gamma_{H}$ is 5.4 at low temperature.

Penetration depth $\lambda$ is approximately 1152 Å.

Anisotropy of the penetration depth $\gamma_{\lambda}$ is close to one at low temperature.

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, $\gamma_{H}$, 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 $\lambda$ was determined to be $1,152\pm50$ {\AA}, and the anisotropy of the penetration depth, $\gamma_{\lambda}$, 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.