Strong-coupling multigap superconductivity in the Heusler compound ScAu$_2$Al
ScAu$_2$Al is the Heusler superconductor with the highest reported transition temperature, Tc, close to 5 K. Here, we combine high-resolution ac calorimetry and electrical-transport measurements with first-principles-based Eliashberg calculations. The large specific-heat jump, $ΔC/{γ_nT_c} =$ 2.2, well above the weak-coupling BCS value of 1.43, together with an electron-phonon coupling constant $λ = $1.1, establishes ScAu2Al as a strong-coupling superconductor. The electronic specific heat is described better by a two-gap α model, with $2Δ_S/k_BT_c = $ 4.1 and $2Δ_L/k_BT_c = $ 4.8, than by a single-gap model. The thermodynamic upper critical field follows a conventional WHH-like temperature dependence with $B_{c2}(0) = 0.18$ T, whereas the resistively determined critical field reaches values about three times larger and exhibits a pronounced positive curvature. We attribute the enhanced resistive field scale to superconductivity in disordered grain-boundary and interfacial regions. The experimental results are supported by calculations of the heat capacity and upper critical field within the Eliashberg formalism using Fermi-surface and electron-phonon parameters obtained from first-principles calculations