## 3 Experimental Setup  
Our experimental setup is shown in Figure 3. The exciting coil (6) and the PM (8) are placed on two sides of the test sample (7). The sample is placed on a stage, and can move in one direction via the controller (2). \(F_{PM}\) represents the force exerted on the PM (8), and it is measured by an LCM system (8, 9 and 10) [20; 21; 22; 23] due to its high sensitivity and quick response. Two components of the force are measured by changing the alignment of the LCM system and then repeating the procedure: One component is perpendicular to the sample surface (z) (Figure 3b), and the other is parallel to the sample and is the same as the direction of the defect movement (x) (Figure 3c).  
The PM is composed of NbFeB with a size of 1 mm \(\times\) 1 mm \(\times\) 1 mm. The cantilever is made of stainless steel (12 CrNi177) with a size of 7 mm \(\times\) 1.2 mm \(\times\) 40 \(\upmu\)m (length \(\times\) width \(\times\) thickness). The sample board is made of copper (\(\sigma\) = 5.9 \(\times\) 10\({}^{7}\) S/m) with a thickness of 1 mm. The sample board contains through-holes of various diameters (0.3-2 mm) to simulate defects. The sample board is placed on a stage that can be controlled to move in the \(x\)-direction at a speed of 2.45 mm/s (with an accuracy of positioning of 0.005 mm, and a range of 25 mm). Note that the slow relative movement between the sample and the magnetic field at this speed induces a negligible eddy current. A precision translation stage is used to adjust the position of the PM to guarantee the same measurement conditions. The distance between the PM and the surface of the testing sample is d = 0.5 mm, which is called lift-off distance.  
During the experiment, a sinusoid current (200 Hz) is applied to the exciting coil, which causes oscillation of the cantilever. The reason for choosing this frequency is to adapt to the LCM system so that the cantilever beam is in a sensitive state. Moreover, a low frequency can provide a better penetration depth, which is 4.6 mm. This oscillation is detected by a Microtrak3 displacement sensor (made by the MTI company, New York, USA), which has a measuring range of \(\pm\)5 mm and a resolution of 1.25 \(\upmu\)m. The error caused by the cantilever's deformation is in a range of 0.05-0.1%, which is  
Figure 3: **(a)** Experimental setup: 1. Computer; 2. Moving stage controller; 3. Oscilloscope; 4. Direct-current power supply; 5. Defect (mimicked by the through-holes); 6. Exciting coil; 7. Test sample; 8. PM; 9. Cantilever; 10. Laser displacement sensor. During the experiment, the test sample moves in the \(x\)-direction while displacement of cantilever is measured; **(b)** Setup for measuring the \(z\)-direction force; **(c)** Setup for measuring the \(x\)-direction force.  
negligible. The test sample moves uniformly in one direction driven by the stage, so that different areas of the sample are scanned by the exciting coil PM system. A MDO3022 Tektronix oscilloscope collects the data from the displacement sensor as the scanned area moves, and thus provides information regarding oscillation as a function of the defect position.  
To better understand the mechanics of our system and interpret the experimental results, numerical simulation work based on the finite element method is performed to study the force acting on the PM. The simulation work is carried out in a commercial software package of COMSOL Multiphysics 5.3 under the following conditions: the exciting coil and PM are aligned to each other (both located at origin in _x-y_ plane) and placed on two sides of the sample conductor as the set of the experiment; the sample contains a defect, which is moving along the x-axis; the parameters (size, position etc.) in the simulation are the same as those in experiments and the amplitude of the force acting on the PM is calculated as the defect moves.