Fig. 1: Specific heat data of Pr₃Cr_10−xN₁₁ under different magnetic fields.

a Temperature dependence of electronic specific heat coefficient C_e/(γ_nT) with different applied magnetic fields are presented in different colors: μ₀H = 0 T (black), μ₀H = 1 T (red), μ₀H = 3 T (blue), μ₀H = 5 T (magenta), μ₀H = 7 T (wine), μ₀H = 9 T (orange). The solid lines are the fits with full-gap-model. The dashed lines indicate T_c for different fields, determined by the middle of the jump. It is worth mentioning that the magenta full-solid dots were measured on an additional sample. To show the difference, the data were named as [5] T. Inset: C/T vs. T² for different applied fields. The solid line is the fit of the normal state data. b Temperature dependence of H_c2 determined from specific heat measurements are shown in orange. Solid lines are the fits of WHH and GL-model (see the text). Dashed line: the Pauli paramagnetic limit. The error bars represent the estimated uncertainty for T_c under corresponding magnetic fields. c–e Sommerfeld coefficient γ(H) of Pr₃Cr_10−xN₁₁ (indicated by purple dots), UTe₂ (indicated by dark-yellow dots)¹⁹, and URhGe (indicated by olive dots)⁵¹. Solid lines: fits of \({\gamma }_{0}(H)/{\gamma }_{0}(0) \sim {e}^{-{H}^{* }/H}\).