## 3 Experimental Setup: Methods and Procedures
### Investigation of Mechanical and Magnetic Properties of Samples
The samples were then ground and polished with a Struers TegraPol-15 polisher and etched with G + HF + HNO\({}_{3}\) (G: glycerine; HF: hydrofluoric acid; HNO\({}_{3}\): nitric acid). The microstructure was examined with an NEOPHOT 32 microscope (Zeiss AG, Oberkochen, Germany) and documented with NIS Elements 4 (Nikon Corporation, Minato, Tokyo, Japan). Microhardness was measured using a Zwick/Roell ZH\({}_{\text{u}}\) tester (Zwick-Roell Ltd., Ulm, Germany) with a 0.5 kp load (HV 0.5) and a 10 s load time. Hardness changes from annealing were measured with a handheld Vickers tester (HV 10) using a 10 kp load. Magnetic properties were tested using a BT 42i force sensor (CMA, Amsterdam, The Netherlands), with data analysed using Coach 6.7 software (CMA). The setup for investigating the prepared samples' weak magnetic fields (intrinsic magnetic fields) consists of a defined measuring apparatus. The samples were measured in a highly controlled environment within a chamber specifically engineered to shield against electromagnetic interference (EMI). This setup ensured that external factors did not compromise the accuracy of the results. A single-axis sensor (AFF755B, Sensitec GmbH, Mainz, Germany) was used to detect weak magnetic fields. The AFF755B is an exceptional low-noise magnetic field sensor that leverages the advanced anisotropic magneto-resistive (AMR) effect. Featuring a sophisticated Wheatstone bridge with an integrated flip coil for offset correction, this sensor dramatically reduces the temperature coefficient of the offset (Figure 2a). It is expertly designed for the detection of very weak magnetic fields (below 20 \(\upmu\)G or 2 nT) including the Earth's magnetic field [23]. In a \(3\times 3\) matrix arrangement, nine such sensors were used to perform the experiments. This configuration was used for the aim to sense the magnetic field simultaneously and the investigated surface at specific points. Figure 2b illustrates the situation when the measuring probe and the material under investigation were positioned. Figure 3a shows the positioning of the individual sensors within the designed probe, and Figure 3b shows how the data from each sensor were acquired: a 9:1 multiplexer was used, allowing for quasi-parallel data acquisition from all nine sensors. The following procedures were implemented during signal acquisition: The outputs from all sensors were normalized due to the sequential acquisition and processing of multiplexed data. At the same time, the offset of individual sensors was suppressed. A 2D visualization was used to visualize the results, and a continuous magnetic field map was created based on the values from all sensors. Spline interpolation was used to improve the resolution or accuracy of the mapping. The following procedure was followed in the given case of a matrix arrangement of sensors. Each sensor has a defined location \((x_{i},y_{i})\) in  
Figure 3: Magnetic field array probe: (**a**) schematic arrangement of sensors; (**b**) manipulation of proper probe signals using multiplexer. Figure 2: The internal circuitry of the AFF755B AMR sensor used in the measurements: (**a**) SO8 housing and a sensor calibration curve; (**b**) the designed and realized probe using a matrix arrangement of the AMR sensors [26]. the plane and detects the value of the magnetic field strength \(B\) (\(x_{i},y_{i}\)) at that position. The nodal values are obtained from each sensor:  
\[B_{ij}=B\left(x_{i},y_{i}\right)\text{, for }i,j=1,2,3, \tag{1}\]  
where \(x_{i},y_{i}\) are the coordinates of the nodes, and \(B_{i,j}\) are the measured values. Subsequently, a 2D spline interpolation is implemented.