Specific Heat of ${\mathrm{Mg}}^{11}{B}_2$: Evidence for a Second Energy Gap

Measurements of the specific heat of ${\mathrm{Mg}}^{11}{\mathrm{B}}_2$ from 1 to 50 K, in magnetic fields to 9 T, give the Debye temperature, $\Theta =1050\mathrm{}\mathrm{K}$, the coefficient of the normal-state electron contribution, ${\gamma }_n=2.6\mathrm{}\mathrm{mJ}{\mathrm{mol}}^{-1\mathrm{}}{\mathrm{K}}^{-2\mathrm{}}$, and a discontinuity in the zero-field specific heat of $133\mathrm{mJ}{\mathrm{mol}}^{-1\mathrm{}}{\mathrm{K}}^{-1\mathrm{}}$ at $T_c=38.7\mathrm{}\mathrm{K}$. The estimated value of the electron-phonon coupling parameter, $\lambda =0.62\mathrm{}$, could account for the observed $T_c$ only if the important phonon frequencies are unusually high relative to $\Theta$. At low $T$, there is a strongly field-dependent feature that suggests the existence of a second energy gap, about 4 times smaller than the major gap.