Specific Heat of Mg11B2 : 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, $\ensuremath{\Theta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1050\mathrm{K}$, the coefficient of the normal-state electron contribution, ${\ensuremath{\gamma}}_{n}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2.6\mathrm{mJ}{\mathrm{mol}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}2}$, and a discontinuity in the zero-field specific heat of $133\mathrm{mJ}{\mathrm{mol}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$ at ${T}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}38.7\mathrm{K}$. The estimated value of the electron-phonon coupling parameter, $\ensuremath{\lambda}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.62$, could account for the observed ${T}_{c}$ only if the important phonon frequencies are unusually high relative to $\ensuremath{\Theta}$. 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.