On the estimating the superconducting volume fraction from the internal magnetic susceptibility
Zhang et al. [1] reported zero-field cooling (ZFC) and field cooling (FC) data for Pr₄Ni₃O₁₀ single crystals under high pressure, confirming bulk superconductivity in Ruddlesden-Popper nickelates and estimating a superconducting volume fraction f = 0.85 using the amplitude of the internal susceptibility χ_internal. This paper questions the key assumption of that method, namely f = |χ_internal|, and demonstrates through a counterexample that even when the calculated |χ_internal| for a sample reaches 0.82, the actual superconducting volume fraction f may be below 0.10. The authors point out that the calculation of the demagnetizing factor N depends on the distribution of non-superconducting regions within the sample, and the homogeneity assumption does not hold—if 90.2% of the volume is non-superconducting phase, the measured susceptibility can still match the original results as long as the geometry alters the demagnetizing factor. Therefore, χ_internal alone cannot uniquely determine f, and this approach requires reexamination across the entire field of superconductivity research.