Order Parameter of ${\mathrm{MgB}}_2$: A Fully Gapped Superconductor

We have measured the low-temperature specific heat $C\left(T\right)$ for polycrystalline ${\mathrm{MgB}}_2$ prepared by high pressure synthesis. $C\left(T\right)$ below 10 K vanishes exponentially, which unambiguously indicates a fully opened superconducting energy gap. However, this gap is found to be too small to account for $T_c$ of ${\mathrm{MgB}}_2$. Together with the small specific heat jump $\Delta C/{\gamma }_n{T}_c=1.09\mathrm{}$, scenarios such as anisotropic $s$-wave or multicomponent order parameter are called for. The magnetic field dependence of $\gamma \left(H\right)$ is neither linear for a fully gapped $s$-wave superconductor nor $H^{1/2}$ for nodal order parameter. It seems that this intriguing behavior of $\gamma \left(H\right)$ is associated with the intrinsic electronic properties other than flux pinning.