Many
common materials such as water, wood, plants, animals, diamonds, fingers,
etc. are usually considered to be non-magnetic but in fact, they are
very weakly diamagnetic. Diamagnets repel, and are repelled by a strong
magnetic field. The electrons in a diamagnetic material rearrange
their orbits slightly creating small persistent currents which oppose
the external magnetic field. Two of the strongest diamagnetic materials
are graphite and bismuth.
The forces created by
diamagnetism are extremely weak, millions of times smaller than the
forces between magnets and such common ferromagnetic materials as
iron. However, in certain carefully arranged situations, the influence
of diamagnetic materials can produce startling effects such as levitation.
It was proved in 1842
that it is impossible to stably levitate any static array of magnets
by any arrangement of fixed magnets and gravity. However, the addition
of diamagnetic materials makes such levitation possible. The July
22 Nature paper,
Magnetic Levitation at your fingertips, describes two configurations
where diamagnetic materials are used to stabilize the levitation of
a magnet in the field of a fixed lifting magnet.
In the first configuration,
the magnet is levitated by a vertical superconducting solenoid electromagnet
at a point where it is vertically stable but horizontally unstable.
This means that the floating magnet wants to move off center and hit
the walls of the solenoid. If a diamagnetic bismuth liner is added
to the inside wall of the solenoid, it repels the magnet overcoming
the horizontal instability and produces stable levitation of the magnet.

In the second configuration,
the magnet is levitated at a point far below the electromagnet where
it is stable horizontally, but vertically unstable. Diamagnetic plates
are put above and below the magnet to stabilize the vertical motion.
In this case, human fingers were used as the stabilizing diamagnetic
plates, accomplishing for real what magicians do by illusion.
If a stronger diamagnetic
material such as graphite is used for vertical stabilization, the
levitation can be accomplished with common permanent magnets in a
small hand held device. This type of levitator may find use as a frictionless
bearing and is a candidate to replace servo levitators for some applications.
Earlier A. Geim has demonstrated
the suspension
of living things such as frogs in a strong magnetic field. The
diamagnetic repulsion of the living tissue exactly balances gravity
throughout the body. This makes it feasible to investigate the effects
of weightlessness on small bodies without going into space.
Here are some new pictures
of the levitation of pieces of graphite by permanent magnets. More
details and another configuration coming soon.

Details about
the planar magnet array above and other interesting configurations
can be seen at
Meredith Lamb's website.
A new, long
technical paper on Diamagnetic Stabilization of Magnet Levitation
is available
here.
A shorter published technical
paper is available
here.
Martin Simon, Department
of Physics and Astronomy, UCLA
Andre Geim, High Field Magnet Laboratory, University of Nijmegen,
The Netherlands
A description of this
work and much more about levitation can be found at
Andre Geim's website.
Another magnetic levitator
which gets around Earnshaw's Theorem in a different way is the levitron.
This link takes you to an explanation of Spin-stabilized
magnetic levitation.