## 1 Introduction  
Magnetism detection and measurement have been an essential function in many application fields for years [1]. Among all the magnetic sensing methods, the application of the fluxgate principle constitutes one of the most important and well-developed detection techniques [2]. As a classical weak magnetic field measurement technology, fluxgate sensors have been attracting great interest worldwide because of their high sensitivity, high resolution, high temperature stability, low noise, and low offset drift [3]. However, traditional fluxgate sensors are fabricated by winding coils mechanically around magnetic cores, thus resulting in numerous drawbacks of the measuring systems based on conventional fluxgate sensors, such as large size, great weight, and high power consumption, which limits the application of conventional fluxgate sensors in many areas where compact size and portability are always in demand [4; 5]. In the past few years, with the development of information technology and portable electronic equipment, there has been an urgent demand for miniaturized fluxgate sensors in these modern applications [6]. Recently, significant progress hasbeen made in complementary metal-oxide-semiconductor (CMOS)- and microelectromechanical system (MEMS)-based microsensor manufacturing techniques with the rapid development of microelectronics technology [7; 8]. Micro-fluxgate sensors fabricated by CMOS and MEMS technology show great potential in many application fields such as parallel robot applications [9], small satellite positioning [10], portable global positioning system (GPS) positioning equipment [11], detection of biomagnetic nanoparticles [12], and global navigation satellite systems [13] because of their small size, light weight, good integration of signal processing circuits, and so on. However, because of the limitation of device dimensions and the saturation magnetizing principle of operation, micro-fluxgate sensors also have several problems, including a low signal-to-noise ratio, relatively poor sensitivity, and a narrow linearity range [14]. Although the signal-to-noise ratio can be compensated for by some additional methods, such as structural optimization or residence time difference technology (RTD) [15], the linearity range and sensitivity, which are severely affected by the core material of the fluxgate sensor [16], are key factors to determining the application performance of the sensor. So far, permalloy is the most traditional soft magnetic material, and it is widely used as the magnetic core material of fluxgate sensors. However, because of its poor high-frequency performance and relatively low saturation induction density, permalloy is far from being satisfactory as the magnetic core material of micro-fluxgate sensors, which are needed in order to meet urgent demand for the development of information technology and portable electronic equipment. In order to facilitate the uninterrupted development of fluxgate sensors toward wider measuring ranges and higher sensitivities, magnetic core materials with better magnetic performance are needed. To meet this need, amorphous soft magnetic alloys have been developed [17]. As compared to traditional soft magnetic materials, amorphous alloys possess many advantages such as higher permeability, high saturation induction density, and low consumption [17]. Among a variety of amorphous materials, Fe-Co-B amorphous alloys have attracted the attention of researchers in recent years because of their superior soft magnetic properties [18]. As compared to most commercially used Fe-based or Co-based amorphous alloys, Fe-Co-B amorphous materials not only possess the high magnetic induction and high saturation magnetic field strength of Fe-based amorphous alloys [19] but also the low coercivity and low magnetostriction of Co-based amorphous materials [20]. Moreover, because of the excellent high-frequency performance of Fe-Co-B amorphous alloys [21], they are considered a better choice for use as magnetic core materials in high-frequency magnetic sensors.