Are there Anti-Magnets ?

An anti-magnet would be something that is always repelled by a magnet.
This property is known as "Diamagnetism" and it is found in several substances.
A form of the element Carbon, called Graphite, is repelled by a magnet.
The metal Bismuth is also strongly diamagnetic.
A very thin wafer of pure graphite will float above a strong magnetic field.
Neodymium Supermagnets are powerful enough to make the graphite float.
A specially prepared type of graphite called "Pyrolytic Graphite" will float twice as high as regular pure graphite.
The strongest field is produced when four magnets are brought together on a flat piece of steel, and they are arranged
NS
SN
where N is the North face up and S is the South face up.
This is a stable arrangement of the magnets,and they will attract each other into this arrangement. The attractive forces will be very strong so it is best to slide the magnets across the metal plate towards their final position with great care.

I have found that pieces of graphite 50 thousandths of an inch thick become "weightless" and below 20 thousandths of an inch thick float well.
( this is about the thickness of the cardboard of a cerial box )
Pyrolytic graphite is expensive, but an equally thick wafer floats higher.

Bismuth is more diamagnetic than graphite, but it is a brittle metal and is much more dense than graphite. If a thin wafer could be made, it would still be too heavy to float.

It is better to float the Neodymium Supermagnet above the Bismuth, blocks of graphite can be used this way as well.

The usual arrangement is to use two blocks of the diamagnetic material and two magnets. The blocks of diamagnetic material should have flat faces. The flat faces are arranged facing each other, one above and one below the magnet to be floated, with about one tenth of an inch clearance above and below the floating magnet.
The other magnet is above the upper block and it's height is adjustable. This is often around two inches above the floating magnet. The "lifter" magnet is usually larger than the "floater" magnet and needs careful adjustment.

The "lifter" magnet attracts the "floater" magnet but as it approaches the Bismuth or Graphite upper face, it is repelled down. If the "floater" magnet drops too low it is repelled back up by the lower face. The "floater" magnet is free to bob and spin freely between the diamagnetic faces.