## 3 Results  
The X-ray diffraction (XRD) patterns are displayed in Figure 1. From the results in Figure 1, the Co\({}_{40}\)Fe\({}_{40}\)V\({}_{10}\)B\({}_{10}\) demonstrated diffracted peaks in all Co\({}_{40}\)Fe\({}_{40}\)V\({}_{10}\)B\({}_{10}\) thin films, indicating that there are distinct phases including CoFe (110) at about 20 with 46\({}^{\circ}\), V (110) at 20 with 48\({}^{\circ}\), FeB (130) at 20 with about 54\({}^{\circ}\), and the signal CoFe (200) at 20 with 57\({}^{\circ}\). The XRD intensities increased from 10 nm up to 30 nm and then drastically decreased for the 40 nm film. It can be reasonably concluded that the 40 nm is not a homogeneous and discontinuous film, thus inducing a weak crystalline peak. Apparently, a distinct high crystalline XRD peak occurred at 30 nm. According to [PERSON]'s formula (1), the average grain size (D) can be estimated by measuring the full width of the half-height width (FWHM, B) of the 30-nm diffraction peak. [PERSON]'s formula is [28; 29],  
\[\mathrm{D}=\mathrm{k}\lambda/\mathrm{Bcos}\theta \tag{1}\]  
where k (0.89) is [PERSON]'s constant; \(\lambda\) is the X-ray wavelength of the Cu K\({}_{\alpha 1}\) line; B is the FWHM of the 30-nm diffraction peak; and \(\theta\) is the half angle of the diffraction peak. This formula shows that D is proportional to 1/B, so the smaller B corresponds to larger grains. The 30 nm of the Co\({}_{40}\)Fe\({}_{40}\)V\({}_{10}\)B\({}_{10}\) thin film has a smaller B and can induce larger grains to be deposited. The composition of the CoFeVB alloy films was determined. The composition data for CoFeVB films by FESEM equipped with an EDX spectrometer was shown in Table 1. The corresponding EDX patterns of the Co\({}_{40}\)Fe\({}_{40}\)V\({}_{10}\)B\({}_{10}\) films are shown in Figure 2. However, the B content could not be measured in the EDX measurement, because the boron atom is too light. According to the result, it was found that the 40 nm film was not a homogeneous composition. Non-uniform composition is caused by the multi-directional and multi-angle scattering of the sputtered atoms [30; 31]. Figure 1: X-ray diffraction patterns of the Co\({}_{40}\)Fe\({}_{40}\)V\({}_{10}\)B\({}_{10}\) films. Figure 3 presents the low-frequency alternate-current magnetic susceptibility (\(\chi_{\rm ac}\)) results in the CoFeVB films. When the thickness increased from 10 nm to 40 nm, \(\chi_{\rm ac}\) decreased sharply with the increase in frequency. According to Equation (2) [29; 32; 33; 34; 35],  
\[\rm{H_{c}=P_{c}D^{6}K_{1}^{4}/\mu_{0}M_{s}A^{3}}, \tag{2}\]  
where \(\rm{P_{c}}\) is the order constant of unity; \(\rm{D}\) is the grain size; \(\rm{K_{1}}\) is the magneto-crystalline anisotropy; \(\mu_{0}\) is the free space permeability; \(\rm{M_{s}}\) is the saturation magnetization; \(\rm{A}\) is the exchange stiffness constant; and \(\rm{H_{c}}\) is the coercivity. By Equation (2), it can be reasonably concluded that \(\rm{H_{c}}\) is proportional to crystalline grain size \(\rm{D^{6}}\) and demonstrates that large grain size distribution has a higher \(\rm{H_{c}}\). The lowest \(\chi_{\rm ac}\) was detected at 30 nm due to the large grain distribution and high coercivity, which enhanced the spin coupling strength [17; 36; 37]. The range of the external field (\(\rm{H_{ext}}\)) used was not sufficient to rotate the spin state, consequently, the spin sensitivity was reduced and the \(\chi_{\rm ac}\) value was decreased. Figure 4 shows the maximum \(\chi_{\rm ac}\) value associated with the thickness of the CoFeVB. For CoFeVB films with a thickness of 20 mm, the maximum \(\chi_{\rm ac}\) value of \(1.96\times 10^{-2}\) was obtained. When the thickness increased from 10 to 20 nm, the maximum \(\chi_{\rm ac}\) was increased from \(1.5\times 10^{-2}\) to \(1.96\times 10^{-2}\). In addition, the maximum \(\chi_{\rm ac}\) decreased from \(1.96\times 10^{-2}\) to \(1.31\times 10^{-2}\) as the thickness ranged from 20 to 40 nm. The results show that the spin sensitivity is the strongest at the optimal resonance frequency (\(\rm{f_{res}}\)).