## Materials and Methods
### Fabrication of the Micro-Fluxgate Sensor  
The fabrication of the micro-fluxgate sensor was performed on a circular glass wafer. Figure 2a-h shows the MEMS-based fabrication process of the microsensor as follows: (a) A Cr-Cu seed layer was sputtered onto the glass substrate as conductive layer for electroplating, and a positive photoresist was spun on the seed layer, which was then patterned by ultraviolet lithography with a template of the bottom coil. Then, a 20-\(\upmu\)m-thick Cu film was electroplated in the photoresist mold to act as the bottom coil. (b) After the bottom coil was completed, the positive photoresist was spun and patterned with a template of vias. A vertical Cu cylinder was electroplated in the photoresist mold to act as the Cu vias to connect the top coil. Then, the seed layer was removed by reactive ion etching after the photoresist was eliminated with acetone. (c) Polyimide was spun onto the wafer and baked at 250 \({}^{\circ}\)C in vacuum for 2 h for solidification; here, polyimide was used for electrical insulation in order to isolate the magnetic core from the bottom Cu coil. Then, the polyimide was etched by reactive ion etching to expose the Cu vias. Then, another Cr-Cu seed layer was deposited onto the surface and a Fe-Co-B-based magnetic core (\(\mathrm{Fe}_{\mathrm{S}\mathrm{S}\mathrm{1}}\mathrm{Co}_{\mathrm{2}\mathrm{ }\mathrm{4}}\mathrm{9}\mathrm{B}_{\mathrm{16}}\mathrm{Si}_{\mathrm{1}}\)) with a thickness of 10 \(\upmu\)m was attached onto the wafer by epoxy AB glue. (d) Because of the present processing of MEMS technology, how to fabricate an amorphous core with a particular size and shape is often a difficult problem to resolve. In this work, chemical wet etching was adopted in the fabrication of the Fe-Co-B-based amorphous magnetic core. In order to pattern the magnetic core, a photoresist model was made on the surface of the ribbon and patterned with the shape of the sensor core. Then, chemical wet etching (etching solution: 1 HNO\({}_{\mathrm{3}}\):2 HCl:4H\({}_{\mathrm{2}}\)O\({}_{\mathrm{2}}\):8H\({}_{\mathrm{2}}\)O, in volume ratio) was used to remove the excess ribbon uncovered with the positive photoresist, and the Fe-Co-B amorphous ribbon was etched into a long rectangular shape for use as the magnetic-sensitive core of our sensor. The epoxy dispergator was then utilized to remove the residual glue. (e) After eliminating the photoresist, a new positive photoresist was spun and patterned with the template of vias. The Cu vias were then electroplated to reach a height over the magnetic  
Figure 1: (**a**) Photograph of the fabricated Fe–Co–B ribbon; (**b**) transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) image of the Fe–Co–B alloy ribbon; the selected area electron diffraction (SAED) pattern is shown in the inset; (**c**) magnetizing force vs. magnetic flux density (H–B) hysteresis loops for the Fe–Co–B alloy ribbon in the as-spun and annealed (595 K, 1 h) states, the inset shows the partial enlargement for \(-1\)–\(1\) Oe; (**d**) XRD pattern of the melt-spun and annealed Fe–Co–B alloy ribbon. core. (f) Afterwards, the Cr-Cu seed layer was removed by reactive ion etching after eliminating the photoresist, and polyimide was spun on the wafer again and baked at 250 \({}^{\circ}\)C in vacuum for 2 h to isolate the sensor core from the top coils. Then, the polyimide was etched by reactive ion etching to expose the Cu vias. (g) A second layer of magnetic core and vertical vias was fabricated using the same sequence of lithography, electroplating, and polyimide discussed above in Figure 2c-f. (h) After fabrication of the sensor core and coating the Cr-Cu seed layer on the wafer again, the positive photoresist was spun onto the seed layer and patterned with the template of the top Cu coil. A Cu film with a thickness of 20 \(\upmu\)m was then electroplated in the photoresist mold to form the top Cu coil. Finally, the whole sensor was obtained after removing the photoresist and seed layer.