Author Correction: Ultra-low core loss in Fe-enriched soft magnetic ribbons enabled by nanostructure and high-frequency domain engineering

Some ribbons supplied by an industry partner, including NANOMET and HiB-NANOPERM, were mistakenly assumed to be commercially available.In reality, these samples are still under development for commercialization and should not be compared with the other commercial materials.Moreover, HiB-NANOPERM is provided in the amorphous state and refers to materials that undergo ultra-high-speed annealing.Although the material composition in our original paper was the same, the annealing process had not been optimized.The plotted points referred to as NANOMET were similar.Therefore, the terminology of HiB-NANOPERM and NANOMET were not appropriately applied to these materials.To ensure a fair comparison and to focus only on commercially available materials, the corresponding data have been removed from the revised Fig. 5b.For better clarity, the annealing history of the commercially available samples, whether or not they were subjected to annealing, is clearly indicated in the updated Fig. 5b.Some alloys such as FT-3 and 2605HB1M are supplied in an amorphous state.FT-3, known commercially as FINEMET, requires post-annealing to induce nanocrystallization before evaluation.This distinction has now been made explicit.The updated Fig. 5b presents a clearer comparison that benchmarks our alloys more accurately against established commercial grades.For reference, catalogue values for FT-3M (in the shape of cut core), 2605S-3A, and 2605SA1 are also included where data under comparable measurement conditions (f = 10 kHz, B = 1.0 T) are available 1,2 .These alloys exhibit relatively low core loss values, though within a smaller saturation magnetization range.We have, to the best of our knowledge, included representative commercially available materials tested under comparable measurement conditions.Several literature reports also highlight compositions with notably low losses 3,4 , such as Fe 73.5 Cu 1 Nb 3 Si 15.5 B 7 (~31 W/kg, 0 M s = 1.23 T, s = 0.5 10 -6 ), Fe 85 Nb 6 B 9 (~34 W/kg, 0 M s = 1.67 T, s 0), Fe 90 Zr 7 B 3 (~45 W/kg, 0 M s = 1.63 T, s = -1.1 10 -6 ), and Fe 89 Hf 7 B 4 (~35 W/kg, 0 M s = 1.59 T, s = -1.2 10 -6 ), core loss values reported under identical conditions (10 kHz, 1 T) and characterized by rather small magnetostriction values, an approach for reducing core loss recently demonstrated by experiment and theory 4 , but not the strategy adopted in the present work.In addition, the Fe 87 B 13 alloy 4 demonstrates a higher saturation magnetization of 0 M s = 1.92 T with a core loss of ~83 W/kg and a saturation magnetostriction value of ~12 10 -6 .These results indicate performance that surpasses the empirical limits typically reported for commercial alloys.However, since their commercial viability has not yet been established, these compositions were excluded from Fig. 5b.In this study, we evaluated core loss using a Single Sheet Tester (SST, Iwatsu SY-8219 and SY-956).However, the SST would be affected by stress induced by the measuring yoke contacting the sample during measurement, and the upper limit of frequency is 20 kHz.To further validate the potential of our findings, we fabricated a ring-shaped single plate sample.The ring sample was inserted in a case, and the core loss of the ring sample was carefully examined using a BH analyzer (Iwatsu SY-8218 and SY-951).The broadband core loss data of Supplementary Fig. 6 were obtained in this way.The ring samples were prepared by femtosecond-laser cutting on the amorphous precursors, producing rings with an outer diameter of 30 mm and an inner diameter of 20 mm.A ring sample of FINEMET FT-3 was also fabricated, annealed under ideal conditions after cutting, and the core loss of both samples was measured under identical conditions (10 kHz and 1 T).These results confirm that the materials developed in this study