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Electron-phonon coupling constant and BCS ratios in (La,Nd)-H superhydride

Stoichiometric near room-temperature superconductors (i.e., $H_3S$ and $LaH_{10}$) exhibit so high ground state upper critical field, $B_{c2}(0)>100 T$, that the magnetic phase diagram in these materials cannot be measured in non-destructive experiments. However, recently, Semenok et al (arXiv2203.06500) proposed the idea to explore full magnetic phase diagram in NRTS samples in which the superconducting order parameter is suppressed by the magnetic element doping. If the element is uniformly distributed in the material, then the theory of the electron-phonon mediated superconductivity predicts the suppression of the order parameter in three-dimensional s-wave superconductor. Semenok et al (arXiv2203.06500) experimentally proved this idea by substituting La with the magnetic rare earth Nd in the $La_{1-x}Nd_{x}H_{10-y}$. As a result, $T_c$ in the $La_{1-x}Nd_{x}H_{10-y}$ (x=0.09) decreases to Tc~120 K, and the upper critical field decreases to $B_{c2}(T=41 K)=55 T$. While the exact hydrogen content should be further established in the $La_{1-x}Nd_{x}H_{10-y}$ (because similar $T_c$ suppression was observed in hydrogen deficient $LaH_{10-y}$ reported by Drozdov et al (2019 Nature 569 528)), a significant part of the full magnetic phase diagram for $La_{1-x}Nd_{x}H_{10-y}$ (x=0.09) was measured. Here we analyzed reported Semenok et al (arXiv2203.06500) data for $La_{1-x}Nd_{x}H_{10-y}$ (x=0.09) compressed at P=180 GPa and deduced: (a) Debye temperature, $T_θ=1156 K$; (b) the electron-phonon coupling constant, $λ_{e-ph}=1.65$; (c) the ground state superconducting energy gap, $Δ(0)=20.2 meV$; (d) the gap-to-transition temperature ratio, $2Δ(0)/k_BT_c=4.0$; and (e) the relative jump in specific heat at $T_c$, $ΔC/C=1.68$. The deduced values indicate that $La_{1-x}Nd_{x}H_{10-y}$ (x=0.09; P=180 GPa) is moderately strong coupled s-wave superconductor.