## Materials and Methods  
### Preparation of the \(Fe_{58.1}Co_{24.9}B_{16}Si_{1}\) Amorphous Alloy  
Previous studies have shown the influence of the elemental composition on the performance of Fe-Co-B amorphous alloys [18; 20; 25]. Considering the soft magnetic properties of the alloy, an optimized composition of Fe\({}_{58.1}Co_{24.9}B_{16}Si_{1}\) was used to fabricate the amorphous materials as follows. Fe\({}_{58.1}\)Co\({}_{24.9}\)B\({}_{16}Si_{1}\) alloy ingots were prepared by a high-frequency induction melting technique. A mixture of high-purity metals (99.9 mass% pure Fe, Co) and metalloids (99.9 mass% Si and 99.5 mass% B) was melted in a pure argon gas atmosphere after evacuation up to 10\({}^{-3}\) Pa. The ingots were repeatedly smelted five times to ensure the even composition of the alloy. Then, the fabricated Fe\({}_{58.1}\)Co\({}_{24.9}\)B\({}_{16}Si_{1}\) alloy ingots were used to prepare an amorphous ribbon 4-7 mm in width and 10 \(\upmu\)m in thickness by a single-roller melt spinner. The melt was overheated to approximately 150 \({}^{\circ}\)C above its liquidus temperature and ejected from a quartz crucible through a rectangular orifice by the overpressure of argon (approximately 20 KPa) onto the surface of a smooth cold-rolled copper wheel with a diameter of 550 mm and a circumferential velocity of 50 m/s, which was sufficient to prevent the material from crystallizing. High-resolution transmission electron microscopy (HRTEM) was used to determine the amorphous nature of the alloy. Figure 1a,b shows the photograph and HRTEM image of the as-spun Fe\({}_{58.1}\)Co\({}_{24.9}\)B\({}_{16}\)Si\({}_{1}\) ribbon. As shown in Figure 1b, a clearly random arrangement of atoms can be noticed. The selected area electron diffraction (SAED) pattern in the inset of Figure 1b shows a classical diffuse diffraction ring without spots. Such features are well known for amorphous materials. In previous works, [PERSON] et al. [18] and [PERSON] et al. [25] investigated the effect of heat treatment on the soft magnetic properties of Fe-Co-B alloys, and they found that an annealing temperature of 595 K can significantly improve the soft magnetic performance of this material. Based on this, the fabricated amorphous ribbon was annealed at 595 K for 1 h to achieve the soft magnetic properties. The magnetizing force versus magnetic flux density (H-B) measurements were carried out by using a vibrating sample magnetometer (VSM) to determine the soft magnetic behavior of our ribbon. As shown in Figure 1c, the fabricated ribbon clearly exhibited an increased magnetic intensity (\(B_{\rm s}\)) after annealing. Generally speaking, the saturation magnetic intensity of materials usually remains the same if the chemical composition does not change. To further explore this problem, X-ray diffraction (XRD) with Cu K\({}_{\rm a}\) radiation was utilized to determine the inner structure of the ribbon before and after annealing. As can be observed from Figure 1d, the presence of a broad halo without sharp peaks suggests the amorphous nature of this ribbon before heat treatment. However, an \(\alpha\)-Fe crystallization trend can clearly be found in the ribbon after annealing. In a previous study, [PERSON] et al. [26] indicated that the \(\alpha\)-Fe nano-crystal may improve the soft magnetic properties of soft magnetic material owing to the high saturation intensity of \(\alpha\)-Fe. Consequently, the \(\alpha\)-Fe crystallization in our material after annealing may be the main reason contributing to the increasing saturation magnetic intensity of the ribbon. After annealing, the prepared ribbon shows a coercivity (\(H_{\rm c}\)) of less than 0.2 Oe and a high saturated magnetic intensity (\(B_{\rm s}\)) of 1.74 T. Such a \(B_{\rm s}\) value is much higher than that of traditional commercially used permalloy (0.6-1 T) or the commercial Co-based (0.77-1.1 T) and Fe-based (1.5 T) amorphous ribbon.