Superconductivity mediated by a soft phonon mode: Specific heat, resistivity, thermal expansion, and magnetization of Y B 6

The superconductor $\\mathrm{Y}{\\mathrm{B}}_{6}$ has the second highest critical temperature ${T}_{c}$ among the boride family $M{\\mathrm{B}}_{\\mathrm{n}}$. We report measurements of the specific heat, resistivity, magnetic susceptibility, and thermal expansion from $2\\phantom{\\rule{0.3em}{0ex}}\\text{to}\\phantom{\\rule{0.3em}{0ex}}300\\phantom{\\rule{0.3em}{0ex}}\\mathrm{K}$, using a single crystal with ${T}_{c}=7.2\\phantom{\\rule{0.3em}{0ex}}\\mathrm{K}$. The superconducting gap is characteristic of medium-strong coupling. The specific heat, resistivity, and expansivity curves are deconvolved to yield approximations of the phonon density of states $F(\\ensuremath{\\omega})$, the spectral electron-phonon scattering function ${\\ensuremath{\\alpha}}_{\\mathit{tr}}^{2}F(\\ensuremath{\\omega})$, and the phonon density of states weighted by the frequency-dependent Gr\\uneisen parameter ${\\ensuremath{\\gamma}}_{G}(\\ensuremath{\\omega})F(\\ensuremath{\\omega})$, respectively. Lattice vibrations extend to high frequencies $g100\\phantom{\\rule{0.3em}{0ex}}\\mathrm{meV}$, but a dominant Einstein-like mode at $\\ensuremath{\\sim}8\\phantom{\\rule{0.3em}{0ex}}\\mathrm{meV}$, associated with the vibrations of yttrium ions in oversized boron cages, appears to provide most of the superconducting coupling and gives rise to an unusual temperature behavior of several observable quantities. A surface critical field ${H}_{\\mathrm{c}3}$ is also observed.