## 3 Experimental Setup: Methods and Procedures
### Investigation of Mechanical and Magnetic Properties of Samples
For each row of sensors (constant \(y_{i}\)), a spline function is created on the \(x\)-axis:  
\[B_{\text{j}}\left(x\right)=S\left(x;x_{1},x_{2},x_{3},B_{1,j},B_{2,j},B_{3,j}\right) \tag{2}\]  
where \(S(x)\) is a spline function, and at the same time, based on the interpolated values for \(x\) (\(B_{\text{j}}\left(x\right)\)), a spline interpolation is performed for the \(y\)-axis for a particular \(x_{\text{k}}\):  
\[B\left(x,y\right)=S\left(y;y_{1},y_{2},y_{3},B\left(x,y_{1}\right),B\left(x,y_ {2}\right),B\left(x,y_{3}\right)\right) \tag{3}\]  
The resulting 2D spline interpolation, a continuous function \(B\left(x,y\right)\), is obtained by combining the interpolations in both axes. This function describes the magnetic field over the entire sensor area. The measurement probe was powered by a constant 5 V DC voltage source, drawing approximately 145 mA of current during the measurement process. This configuration ensures stable operation and consistent data acquisition, which is crucial for the high-fidelity analysis of the material's magnetic behaviour. Figure 4 shows the measurement setup for performing intrinsic magnetic field measurements, which consists of the following main components: 1: lock-in amplifier; 2: XYZ stage controller; 3: synchronization and electronic circuit (MUX) device; 4: designed and realized AMR array probe; 5: XYZ positioning system; and 6: precision PTFE table. The Signal Recovery DSP 7280 lock-in amplifier (Ametek, Inc., Berwyn, PA, USA) is a selective voltmeter used to filter out valuable signals. The filtered signal from the AMR probe was then transmitted to the analogue input of the acquisition card and processed using LabVIEW 2024 QlVirtual instrumentation software (National Instruments, Austin, TX, USA). A program block was created in the virtual instrumentation environment to manipulate the signals, store data, and execute other necessary actions. This interface also produced control commands for a three-axis linear manipulator to which the probe was connected. The measurement was conducted in an electromagnetic-shielded space using a linear three-axis manipulator (Velmex Inc., New York, NY, USA) attached to the sensor. The manipulator arm utilizes stepper motors and a threaded rod, providing a resolution of 1.1 \(\upmu\)m on each axis, enabling precise positioning. This setup allows for the construction of a spatial map of the magnetic field near the samples under investigation. The scanning procedure in the region of interest (ROI) involved positioning the sample in the centre of a 50 mm \(\times\) 50 mm area. The samples' magnetic field was scanned using a technique called raster scanning. Data from the sensor were recorded as the sensor moved in the \(y\)-axis direction, with 1000 readings taken for each scan line. The spacing between individual scanning lines was fixed at \(\Delta x\) = 0.5 mm. This means that 100 scan lines were recorded for each scan setup of one sample area, representing one complete scan cycle. After each cycle, the sensor was returned to the initial (reference) position. All examined samples were subjected to a non-contact investigation, with a focus on the repeatability of each measurement. Each sample was measured from both of its identical sides (faces), which were labelled as L (left side) and R (right side). The experimental measurement conditions from both opposite surfaces were essentially the same. The probe was consistently positioned above the sample at a fixed distance from the sample surface, \(h\) = 1.0 mm. The data were collected using a PXI 6255 digital acquisition card (DAQ) (National Instruments, Austin, TX, USA), with a sampling frequency of \(f_{\rm s}\) = 10 kHz.