Fig. 3: Magnetic characterization and inductance enhancement to the RuMi inductors.

a, b Hysteresis loops of the magnetic structures formed by a 300-nm thick Py films (a) and 6 stacks of 50 nm Py/5 nm Ta laminates (b) in the RuMi inductors before rolling, measured with the magnetic field applied perpendicular (x-axis) or parallel (y-axis) to the rolling direction. Insets: MFM images of the corresponding films. Scale bars, 500 nm. c, d Electromagnetic finite element simulation results of the cross-sectional magnetic field distribution at 0.5 GHz with an excitation of 1 V for a 6-cell RuMi inductor with 2.4 mm rolling length, (c) before and (d) after integrating 6 stacks of Py/Ta laminates. Scale bar, 50 μm. Insets: magnified views highlighting the field distribution between spiral layers. The white curved regions (rolled conductors) are omitted for clarity. Scale bar, 5 μm. e, f Measured and simulated inductance (e) and Q-factor (f) versus frequency of the same 6-cell, 2.4-mm-long RuMi inductor with or without the integrated magnetic laminates. Inset: measurement setup showing the GSG test structure. Scale bar, 200 μm. Source data are provided as a Source Data file.