This project is an AC Susceptometer designed to characterize the magnetic properties of materials from ~1KHz - ~1MHz. The core of the device is a custom coil assembly featuring a large outer driving solenoid (76 mm diameter, 54 turns) and a differential inner pickup pair (45 mm diameter, 86 turns each).

We drive the outer coil with a function generator to create an oscillating magnetic field (20uT RMS at low frequencies). The pickup coils are wound in opposition so that, in free space, the induced voltages theoretically cancel out. We use a Lock-in Amplifier (LIA) referenced to the drive signal to demodulate the output, allowing us to extract signals buried in noise.
The measurement relies on Faraday’s Law of Induction. When a sample is placed inside one of the pickup coils, its magnetic susceptibility chi modifies the local magnetic flux, breaking the symmetry of the coil pair. This imbalance induces a net voltage. By analyzing the signal components in-phase X and out-of-phase Y with the drive, we can determine the complex susceptibility of the material. The in-phase component corresponds to the real susceptibility X', indicating magnetization, while the quadrature component X'' relates to energy dissipation. This allows us to observe magnetic phase transitions and loss mechanisms that DC measurements might miss.
We are able to get qualitative measurements but we are unable to verify the quantitative accuracy of most measurements due to the lack of calibration samples within an order of magnitude of most of our ferrite samples. Additional corrections prevent us from precisely comparing samples of different geometries.
Results:
We measured the susceptibility of 6 samples:
- Dy2O3 Powder
- Fe2O3 Powder
- Ferrofluid
- Ferrites
- Barium Hexaferrite
- Type 77 Ferrite
- Type 78 Ferrite
The signal from our Dysprosium Oxide (Dy2O3) calibration standard is extremely weak—hovering at just a few microvolts below 10 kHz, which is barely indistinguishable from our 6 uV noise floor. It also appears to be inaccurate to compare samples of different volumes. We compared the Dy2O3 powder against an Iron Oxide (Fe2O3) sample with 5x the volume. Based on standard molar susceptibility values, density, and volume, the Fe2O3 signal should be roughly one-third the strength of the Dy2O3. However, experimental data shows the Fe2O3 magnitude is 5x stronger—a ~15x deviation from prediction. The results for the samples are below:
Material | Dysprsium | Fe2O3 | BaM | Ferrofluid | 77 Ferrite | 78 ferrite |
Volume (cm^3) | 3.534 | 18.65 | 5 | 18.65 | 8.96 | 10.77 |
Weight (g) | 7.7264 | 28.1353 | 98.69 | |||
Susceptibility (cm^3/mol) | 89,600·10−6 | 3586.0x10−6 | ||||
volume susceptibility | 0.00186 | 0.00063 | 2.5 | 2000 | 2300 | |
Relative Signal Strength (Permeability * volume) compared to Dy2O3 | 1 | 0.34042 | 1,347 | 1,077,584 | 1,239,222 | |
Measured relative signal strength at 10KHz | 1 | 5 | 280 | 1,300 | 2,700 | 6,000 |
The ordering is accurate except for the iron oxide which is inaccurate likely due to the volume correction error.

The baseline is also quite large, 6 uV, this may be due to poor common ground noise from our outlet, em radiation noise or other sources. At higher frequencies the parasitic capacitance between the driving and pickup coils becomes significant, this limits the frequency range of the device.


Andrew Ferguson
Dan Berard
mircemk