Nearly twofold overestimation of the superconducting volume fraction in pressurized Ruddlesden-Popper nickelates

The detection of the DC diamagnetic state in pressurized Ruddlesden-Popper nickelates remained an unsolved experimental problem until recent experiments in which Zhu et al.$^1$ measured the DC diamagnetic responses in zero-field cooled (ZFC) mode in pressurized La4Ni3O10. Zhu et al.$^1$ reported that the ratio of the measured ZFC magnetic moment to the Meissner magnetic moment of the sample (and this ratio was termed the superconducting volume fraction$f$) reaches 81-86%. We regard outstanding experimental results$^1$; however, our calculations based on the reported experimental datasets$^1$ using the standard procedure showed the ratio to be 51-59%. Upon our request, Zhu et al.$^1$ provided detailed explanations and the equation they used to calculate$f$. To our knowledge, the procedure$^1$ and equation$^1$ for calculating $f$ have never been mentioned or described before, including in Ref.$^1$. Here we argue that the proposed equation$^1$ and procedure$^1$ are incorrect, and that this equation$^1$ results in multiple overestimations of the superconducting volume fraction in the sample. This overestimation error affects all superconducting volume fractions $f$ in Ruddlesden-Popper nickelates reported to date$^{1-4}$. Therefore, we describe the error we discovered in this paper.