Addendum: Magnetic field screening in hydrogen-rich high-temperature superconductors

In our paper 1 , we studied the magnetic response of H 3 S and LaH 10 superconductors to an applied magnetic field using Superconducting Quantum Interference Device (SQUID) magnetometry. Prof. Hirsch, in his Matters Arising entitled “On the Author Correction to “Magnetic field screening in hydride superconductors” Nat Commun 15, 8144 (2024)” and in the Comment 2 , questioned the averaging procedure applied to the magnetization data and raised broader doubts about the superconducting nature of high- T c hydrides. We accept that the original publication did not sufficiently describe the data processing steps, specifically the smoothing, averaging, and filtering procedures applied to the measured magnetic moment M(H appl ,T) datasets used to determine the penetration field H p . Due to the SQUID magnetometer’s dual current source configuration, magnetization measurements on our micrometer-scale samples exhibit an increased noise level above approximately 30 mT. To extract values of H p from these high-noise datasets, we applied standard mathematical smoothing/filtering techniques. In addition, here we describe an alternative method to determine H p without any data processing, based on a methodology commonly used for extracting critical currents in superconductors 3 from V(I) datasets. This approach was recently shown to be effective for DC magnetization data 4 . The H p values of the present analysis are consistent with those published in our original work 1 . We emphasize that the Comment 2 concerns the secondary matter of estimating Ginzburg-Landau parameter, not the fundamental evidence for superconductivity in hydride superconductors. Our full raw magnetization datasets – featuring both virgin and hysteretic M(H appl ,T) curves – clearly show characteristic superconducting behavior below T c , and the absence of hysteresis above it. These datasets are openly accessible via the Open Science Framework ( https://osf.io/7wqxb/ ), allowing independent evaluation of our analysis.