Extended Data Fig. 4: S21 dip due to surface effect of ferrite.

a. Photonic band structure of bulk ferrite. b. Photonic band structure of surface ferrite. c. Comparison between simulated and experimental scattering parameters after surface ferrite modification. The saturation magnetization of the surface layer is determined by the dip frequency, which equals the Larmor frequency (\({\omega }_{0}^{{\prime} }\)) of the surface ferrite, being higher than the bulk Larmor frequency (ω0). The Larmor resonance linewidth (ΔH’) of the surface layer is determined by the spectral width of the transmission dip. The thickness of the surface layer is determined by the depth of the S21 dip. The details of the modeling are in Supplementary Section VI.