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 on a very small scale. In a sense, the graphite becomes a magnet with the same polarity as the field facing.
The essential concept of this project is a small permanent magnet actuator which slides (or levitates!) around on an active planar base. This base is made of a printed circuit board with serpentine traces forming two loops on both the top and bottom layers. A way to think about this winding configuration is to imagine cutting open a stepper motor along its axis and unrolling it onto a plane. In a similar sense, the actuator can be controlled in much the same way as a set of two-phase stepper motors.
Below is an illustration of the proposed layer stack-up within the actuator bed.
I found it difficult to visualize some of the theory explained in previous literature on this design, 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 the design which was simplified into line currents. Used in combination with matplotlib, I was able to produce these magnetic field projections.
The first board layout had the capability interface with cheap A4988 drivers, but I didn't have high hopes that they would be able provide enough power and so it was loosely designed and quickly abandoned. Header pins/wires can be soldered to holes at the bottom where the phases are labelled on the silkscreen.
Below is a close-up image showing the details of the edges of the perpendicular trace patterns.
Below is a picture of the sample of graphite I sourced from a suspiciously cheap vendor on eBay. Although it was listed as "pyrolytic", I am sure the material is low-grade in terms of its magnetic properties.