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Nat Commun
Nat Commun
Nature Communications
2041-1723
Nature Publishing Group UK London

39294110
52327
10.1038/s41467-024-52327-0
Matters Arising
On the Author Correction to “Magnetic field screening in hydride superconductors”
Hirsch J. E. jhirsch@ucsd.edu

grid.266100.3 0000 0001 2107 4242 Department of Physics, University of California, San Diego, La Jolla, CA 92093-0319 USA
18 9 2024
18 9 2024
2024
15 814414 9 2023
15 8 2024
© The Author(s) 2024
2024
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pmcarising from V.S. Minkov et al. Nature Communications 10.1038/s41467-022-30782-x (2022)

Reference1 reported measurements of diamagnetic moment versus magnetic field for sulfur hydride and lanthanum hydride under pressure in its Fig. 3a, b respectively, claiming that they provide evidence that the samples are superconducting and allow to infer the value of the lower critical magnetic fields as function of temperature. Reference2 explained that several linear transformations were used in obtaining the data shown in Fig. 3a, b of ref. 1 from the measured data shown in Figs. 3e and S10, and 3f and S11 of ref. 1 respectively, including subtraction of a significant diamagnetic background. Here we show that those statements are contradicted by facts. This calls into question the claim of ref. 1 that Fig. 3a, b of ref. 1 are evidence for superconductivity in these materials.

From the deviation of linear dependence of magnetic moment on magnetic field for LaH10 under pressure shown in Fig. 1, reproduced from Fig. 3b of ref. 1, the authors extracted values of critical field versus temperature. As the Author Correction to ref. 1 recently published2 explains, the data shown in Fig. 1 are not measured data. Rather, they were obtained from measured data by a set of linear transformations. Reference2 explains that linear transformations would "not affect the onset of the deviation of the M(H) virgin curve from the linear dependence” on magnetic field.Fig. 1 Magnetic moment of LaH10 under pressure versus magnetic field, from Fig. 3b of ref. 1.

We have added the straight red line connecting the origin with the magnetic moment at field 100 mT for the curve for temperature 80K (blue points).

The latter statement is correct. It necessitates that the transformation is truly linear, if the transformation is not linear the statement is clearly invalid. For the virgin curve, one point is fixed at the origin, since there is no magnetization for zero applied field. In Fig. 1 we have connected the origin and the point for the T = 80 K curve for LaH10 at field H = 100 mT by a straight red line. Note that all the points for the magnetic moment for T = 80 K for fields between 0 and 100 mT fall below the straight red line.

The data for Fig. 1 were obtained from measured data shown in Fig. 3f of ref. 1. In Fig. 2 we show a portion of those data. The three blue curves correspond to T = 80 K, as the blue points in Fig. 1. The middle blue curve is the virgin curve, starting with zero moment at zero field. We have connected that point with the moment at field H = 100 mT by a straight red line.Fig. 2 Magnetic moment of LaH10 under pressure versus magnetic field, from Fig. 3f of ref. 1.

The center blue curve is the virgin curve for temperature 80 K. We have added a straight red line connecting the origin with the magnetic moment at field 100 mT for the virgin curve for temperature 80 K (blue points). The numbers on the bottom axis give the magnetic field in mT.

It can be seen in Fig. 2 that some of the measured points fall below the straight red line and some fall above. This is different from the blue points in Fig. 1, that are all below the straight red line connecting the points at zero field and 100 mT field.

Given any linear transformation of the data points in Fig. 2, we can redraw the red line so that it passes through the transformed points at 0 mT and 100 mT, and again some of the data points will fall below the new straight line and some above. Thus, the blue points in Fig. 1 could not have originated from a linear transformation nor from a set of linear transformations applied to the blue points in Fig. 2, as ref. 2 claimed. If the transformation used to obtain the curve shown in Fig. 1 from the curve shown in Fig. 2 was nonlinear, the procedure used to extract the critical field from the data in Fig. 1 is clearly invalid.

The same is true for magnetization data of H3S shown in Fig. 3a of ref. 1, supposedly derived through linear transformations of the data shown in Figs. 3e and S10 of ref. 1. In Fig. 3 we show data for the hysteresis cycle for H3S at 140 K, from Fig. S10 of ref. 1. We have connected the points for zero magnetic field and 100 mT with a straight red line. It can be seen that about half the points for fields between 30 mT and 100 mT are above the red line and half are below. Instead, the lower left inset in Fig. 3 shows the data derived from these measurements through supposedly linear transformations, reproduced from Fig. 3a of ref. 1. It can be seen that all the green points in the curve lie below the straight red line connecting the points for 0 and 100 mT. It is obvious that those points cannot results from linear transformations performed on the data shown in the main body of the figure. Furthermore, no smoothing of the raw data shown in the main body of Fig. 3 can give rise to the parabolic green curve shown in the inset of Fig. 3. As shown in ref. 3, the same applies to the magnetization data for H3S at temperature T = 100K shown in Fig. 3a, e of ref. 1.Fig. 3 Magnetic moment of H3S under pressure versus magnetic field for temperature 140K, from Fig. S10 of ref. 1.

The center black curve is the virgin curve. We have added a straight red line connecting the origin with the magnetic moment at field 100 mT. The numbers on the bottom axis give the magnetic field in mT. The inset at the lower left shows the magnetic moment from Fig. 3a of ref. 1 at 140 K supposedly obtained after linear transformations, the red line in the inset connects the points at field 0 and 100 mT.

Therefore, the origin of the curves in Fig. 3a, b of ref. 1 is not what the paper and its Author Correction states it is. What the origin of those curves is is unknown. Furthermore, the origin of the data points (circles) on the curves in Fig. 3a, b of ref. 1 and how they were derived from the measured data points is unknown. If the transformations used to obtain them from measured data were nonlinear, as the analysis in this paper indicates, it would not be possible to extract values of critical field from deviations from linearity, as ref. 1 does. More generally, the data shown in Fig. 3a, b of ref. 1 cannot be interpreted as showing physical properties of the samples, since their relation to the measured data is unknown. They certainly cannot be used to infer the values of the critical field shown in Fig. 3c, d of ref. 1, a central result of ref. 1, unless the relation of the curves shown in Fig. 3a, b of ref. 1 with the measured data can be clearly established. In particular, for the lower temperature curves of Fig. 3 a of ref. 1, T = 20 K, 40 K, 60 K, 80 K, crucial to obtain the zero-temperature value of the lower critical field of H3S deduced in the paper, there is no information in ref. 1 nor in ref. 2 about the measured data from which the published data were derived.

To clarify the relation between the information conveyed in Fig. 3a, b of ref. 1 and the measured data, the authors of ref. 1 should release their measured data for examination by readers. We have requested access to those data on January 11, 2023, and repeatedly therafter. The data have not been released to date.

Discussion of other aspects of the magnetization data of ref. 1 and its Author Correction2 and their implications for the question whether or not they provide evidence for superconductivity in these materials is given in refs. 3–5.

Acknowledgements

The author is grateful to F. Marsiglio for collaboration in related work.

Author contributions

The author made all the contributions to this paper.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work.

Competing interests

The author declares no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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References

1. Minkov VS Magnetic field screening in hydrogen-rich high-temperature superconductors Nat. Commun. 2022 13 3194 35680889
Minkov, V. S. Magnetic field screening in hydrogen-rich high-temperature superconductors. Nat. Commun. 13, 3194 (2022).35680889
2. Minkov VS Author correction: magnetic field screening in hydrogen-rich high-temperature superconductors Nat. Commun. 2023 14 5322 37658055
Minkov, V. S. Author correction: magnetic field screening in hydrogen-rich high-temperature superconductors. Nat. Commun. 14, 5322 (2023).37658055
3. Hirsch JE Can linear transformations bend a straight line? comment on “author correction: magnetic field screening in hydrogen-rich high-temperature superconductors Physica. C 2024 616 1354400
Hirsch, J. E. Can linear transformations bend a straight line? comment on “author correction: magnetic field screening in hydrogen-rich high-temperature superconductors. Physica. C 616, 1354400 (2024).
4. Hirsch JE Marsiglio F On magnetic field screening and trapping in hydrogen-rich high-temperature superconductors: unpulling the wool over readers’ eyes J. Supercond. Nov. Magn. 2023 36 1813
Hirsch, J. E. & Marsiglio, F. On magnetic field screening and trapping in hydrogen-rich high-temperature superconductors: unpulling the wool over readers’ eyes. J. Supercond. Nov. Magn. 36, 1813 (2023).
5. Hirsch JE Hysteresis loops in measurements of the magnetic moment of hydrides under high pressure: Implications for superconductivity Physica. C 2024 617 1354449
Hirsch, J. E. Hysteresis loops in measurements of the magnetic moment of hydrides under high pressure: Implications for superconductivity. Physica. C 617, 1354449 (2024).
