## 2 Magnetometer Design  
We developed equipment using only available and inexpensive components. This was an important issue in the design of this system. Figure 1a shows a schematic drawing of the designed magnetometer: (1) We used an acrylic plate of 65 \(\times\) 55 mm with 10.5 mm of thickness, two Hall effect sensors were attached to them, (2) two neodymium magnets of the same configuration containing 12.78 mm thick and 19 mm in diameter, (3) all these were on an iron base containing two screws of the same configuration, with approximately 30 mm in diameter and 109 in length, (4) a printed circuit board used to operate the sensor plate details can be seen in Figure 1b, (5) an alignment system consisting of a screw and a spring system, necessary to align the probe Hall to improve the detection of the sample induced field, (6) an aluminum base, (7) a battery set or a power supply system that can supply the sensors with 5 V DC--the output readings are taken by a multimeter. The probe is precisely centered between two neodymium magnets (K&J Magnetics), 19 mm diameter and 12.9 mm length. A magnetic field of up to 0.4 T can be detected. In addition, the homogeneity of the magnetic field applied by the magnets was verified. In this study, we used a 9640 commercial magnetometer (F. W. Bell Inc., Orlando, FL, USA). The probe was built using two Hall effect sensors: One MLX-90215 sensor (Melexis Inc.) with an active sensitivity area of 0.20 \(\times\) 0.20 mm, which has a gain from programming 4.1 to 140 mV/mT, and a voltage that can be adjusted from 0.03 to 4.97 V (this sensor needs to be programmed and calibrated before use), and one AD-AD22151 sensor (Analog Devices, Inc.), which has an active diameter of 300 \(\upmu\)m, with sensitivity ranging from 10 to 110 mV/mT. Differently from the first one, this sensor was designed to vary its sensitivity during operation [12,13]. First, we analyzed the behavior of the sensors in the laboratory environment, using a thermocouple connected to one of the magnets. At the position of the Melexis sensor, no temperature change was detected during the measurement period, even when the magnet got closer to the sensor. For better performance, we used a circuit board developed by [PERSON] and his collaborators (See Figure 1b) [13]. Figure 1b shows the circuit board specifications: R1 is an 18 k\(\Omega\) resistor, R2 is a 1 k\(\Omega\) resistor, R3 is a variable resistor from 0 to 10 k\(\Omega\) (trimmer), C1 and C2 are capacitors, C1 is a 1 \(\upmu\)F power filter and C2 has 0.1 \(\upmu\)F, 1 to 8 refers to the connection pins of the AD22151 sensor (sensor input and output connections). Furthermore, in the space between the magnets, where there is an acrylic plate, the magnetic field applied nearby the probe has high homogeneity and is suitable for the sample holder sizes. The noise of both sensors was analyzed, and we measured noise of approximately 40 \(\upmu\)V, using equipment to analyze the spectrum (SR760 Stanford Research Systems Inc., Culver City, CA, USA). In Figure 2, we can see the probe Hall built on an acrylic structure, with two bands of 56 \(\times\) 56 mm and 6.4 mm thickness. One of the bands is used to assemble the sensors, and the other for the sample holder. The probe components are: (1) Acrylic sample holder, (2) containing a cylindrical cavity of 3.0 mm diameter and 3.0 mm deep, located near one of the ends-in addition to analyzing fine particles, the sample holder can analyze bulk materials, particles and liquid samples (such as magnetic nanoparticles in oil), (3) S1 sensor circuit board (See Figure 2, No. (5)), AD-AD22151 Hall effect sensor (Analog Devices, Inc.), with variable sensitivity, responsible for detecting the sample induced magnetic field on the \(y\)-axis, we can select the sensitivity using a switch attached to the multimeter, (4) S2 MLX  
Figure 1: (**a**) Schematic figure of the magnetometer built with all components, two magnets, and an acrylic plate (probe Hall) in the center with two Hall effect sensors assembled on an iron base.