## 3 Results and Discussion
### MBN Measurements  
Figure 5 shows two important aspects associated with the surface and the corresponding MBN. The first is related to the valuable heterogeneity in MBN with respect to the sheet width. In particular, the regions near the sheet edge emit much higher MBN in the RD. Moreover, the opposite sites (A and B) are also different, and the MBN for side B in the RD is much higher than that for side A. The MBN in the TD is lower, and the heterogeneity in the MBN distribution is less pronounced. The remarkable heterogeneity in MBN (especially for RD) is due to the different degrees and the extent of decarburization in the different regions [31]. Higher MBN is related to more developed decarburizing, and vice versa. The second aspect is associated with the differences between MBN before and after demagnetization; see Figures 5-7. MBN in the RD exhibits magnetized values that are significantly lower than those after demagnetization. This difference is more pronounced for the regions emitting lower MBN. Furthermore, this behavior is only minor in the TD. The physical explanation for this effect is based on the presence of remnant magnetization originating from the manufacturing process (probably the heterogeneity in plastic deformation, as previously reported [27]). The motion of DW motion in ferromagnetic bodies spreads through the matrix in the form of avalanches [32; 33]. The neighboring regions (or grains) are magnetically coupled [34; 35; 36], and the change in magnetization in a certain region triggers a similar process in the neighboring ones. As soon as a certain region contains remnant magnetization, DWs in this region can be remarkably attenuated or fully hindered, being magnetically coupled to the regions containing remnant magnetization. In other words, the presence of unpinned DWs produced during manufacturing (remnant magnetization) attenuates DWs in the magnetically coupled neighboring regions. Figure 4: HV0.1 profiles for the positions emitting different MBN in the RD. Figure 5 also demonstrates the anisotropy in the remnant magnetization, since the influence of demagnetization prevails in the RD as contrasted with the TD due to the alignment of DWs in the RD. Preferential alignment of the DWs in certain directions favors the MBN in this direction and attenuates the MBN when the altered magnetic field is reversed [22]; see Figure 6 (the consecutive MBN bursts are different before demagnetization). Apart from other aspects, MBN is also a function of DWs' speed motion \(v_{p}\) in m.s\({}^{-1}\) (see Equation (1)). \[v_{p}=\frac{dM}{dt}=(H-H_{c})^{q} \tag{1}\]  
Figure 5: MBN along the sheet width; (**a**) MBN in RD—side A, (**b**) MBN in RD—side B, (**c**) MBN in TD—side A, (**d**) MBN in TD—side B.  
Figure 6: Four consecutive MBN bursts before and after demagnetization—side A: (**a**) before demagnetization—MBN 302 \(\pm\) 32 mV and (**b**) after demagnetization—MBN 850 \(\pm\) 5 mV. where \(M\) is the magnetization, \(H\) is the altered magnetic field, and \(H_{c}\) is the magnetic field necessary for the initiation of DW motion (exponent \(q\) is about \(\approx\)0.5) [10; 37]. Due to the presence of remnant DW alignment, \(H_{c}\) in the direction of DW alignment will be less compared with the reversed field, which in turn results in a different MBN. Furthermore, very high STDV (standard deviation) and asymmetry can be found in consecutive MBN bursts; see Figure 6.  
The influence of demagnetization on MBN is more pronounced in the regions emitting lower MBN after demagnetization; see Figure 7 as well as Supplementary Materials. These regions are mostly related to the less developed decarburizing and the harder matrix in terms of its mechanical and corresponding magnetic hardness. The \(PP\) and MBN are very often closely related when a high MBN is related to a low \(PP\), and vice versa [11; 38]. The magnetic field necessary to unpin DWs in regions of higher dislocation density is usually higher due to the stronger opposition of dislocation tangles to irreversible DW motion [11].