This type of PCB actuator has garnered interest as a manipulation platform for small scale manufacturing. Kevin Lynagh has written an excellent summary of the prior art on his blog page.
The Wikipedia article on Diamagnetism describes the phenomena with the following:
"Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field. Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic."
Pyrolytic graphite is a material that has been treated to produce a uniform and planar crystal structure. This structure exhibits uniquely strong diamagnetic properties, and can be used to produce stable levitation.
Below is a picture of the sample of graphite I was able to source from a seller on eBay.
I found it difficult to visualize some of the theory explained in previous publications, so I created a simple visualization of the magnetic action of the device.
The Python package magpylib was used to calculate 3D static magnetic fields of line currents and permanent magnet actutator. Used in combination with matplotlib, I was able to produce the following magnetic field projections.
The first test circuit board ended up having multiple problems (grounding issues + inadequate driver current limit), however the traces/coils on the top half could still be interfaced via plated through-hole contacts.
Below is a close-up image showing the details of the edges of the perpendicular trace patterns.