Reply to "Threefold error in the reported zero-field cooled magnetic moment of single crystal $La_2SmNi_2O_7$ (arXiv: 2602.23240)"

TL;DR

This paper defends the original superconducting phase fraction calculations against critique, clarifying the correct background subtraction, demagnetization correction, and sample homogeneity, reaffirming the validity of their results.

Contribution

The authors provide a detailed rebuttal to critique, emphasizing proper demagnetization correction and sample quality, reaffirming their original superconducting phase fraction findings.

Findings

Background upturn is from background, not paramagnetic Meissner effect

Demagnetization correction must consider actual measured moment

Sample is a homogeneous high-quality single crystal

Abstract

We respond to the critique by Aleksandr V. Korolev and Evgeny F. Talantsev on the superconducting phase fraction ($f$) calculations in Li et al. Nature 649, 871-878 (2026). First, the weak upturn in the low-temperature tail of our data has been confirmed to originate from the background, and the paramagnetic Meissner effect is absent in our case; thus, field-cooled (FC) data can be used for superconducting phase fraction calculations. Second, demagnetization effect must be calculated based on the actual measured moment as a function of $f$, which has been well-established and routinely employed in the superconductivity community. In contrast, Korolev and Talantsev treated the demagnetization field as a constant; thus, their calculation underestimates $f$ by a factor of $(1-N\chi_{meas})(1-N)$. This factor is close to 1/3, given $N$ = 0.849, $\chi_{meas}$ = -1.313 in our study, which explains the origin of their deviated result (nearly three times smaller than our results). Third, our sample is a homogeneous high-quality bulk single crystal, evidenced by various techniques, making the existence of multiple discrete superconducting regions highly unlikely. We conclude that the superconducting phase fraction calculations reported in Li et al. Nature 649, 871-878 (2026) are not invalidated by the analyses presented in Korolev et al. arXiv: 2602.23240 (2026).