Fig. 3: Soft magnetic properties of the URPCs and their comparison with those of other amorphous PCs.

a Hysteresis loops of the URPCs and cold-compacted PCs. The insets show schematic diagrams of the magnetic ___domain structures of the two PCs. b Histograms of the porosity and volume resistivity of the two PCs. c Optical images of the small-size and large-size toroidal URPCs with complex geometries resembling the Chinese character “工”. d Permeabilities of the two PCs with the small-size and large-size at frequencies of 1–30 MHz. e Pcv of the two PCs with the small-size (non-transparent mode) and large-size (semi-transparent mode). f DC bias performance of the two PCs with the small-size and large-size. g Comparison of the soft magnetic properties of the two PCs, with values for cold-compacted PCs normalized to 100. h Histogram comparison of the soft magnetic properties of the URPCs and various amorphous PCs reported thus far, with the value of permeability, DC bias, and low core loss of cold-compacted PCs normalized to 100. Noted that, Although the soft magnetic properties of the large-size samples show a slight decline relative to the small-size ones in (d–f), they still maintain excellent overall performance, indicating the inapparent impact of sample size on soft magnetic properties.