Antiferromagnetic materials, by forming magnetic domain couples of the same magnitude in antiparallel direction, nullify each other resulting in zero magnetic moment.
Similarly, ferrimagnetic materials exhibit the same behavior but the domains have varying magnitude that results in a finite net magnetic moment
Where are they applied?
In a sentence(s!) : Ferro , antiferro and ferro refer to the microscopic interactions between atomic moments . As a rule of thumb the energies of these interactions are reflected in the transition temperatures and the magnetic fields needed to align microscopically atomic moments. These interactions are basically QM and are quite different from the mechansms of domain formation in ferro and ferri . The latter are macroscopic orderings of blocks of atomic moments which serve to reduce the macroscopic field energy of the entire sample . So a relatively weak B field will align / rotate macroscopic domains , to get a net polarisation, in say Fe or Ni .On the other hand a B field several orders larger would be needed to align the atomic moments in MnF2 ( an almost ideal antiferro,).
A very well-known material with ferrimagnetic order is magnetite, probably the most ancient magnetic material which was practically used. It is also one of the few materials with finite macroscopic polarization which is intrinsically biocompatible. Notfew organisms (from bacteriae to birds) are able to synthesize it.
Antiferromagnets are being used in artificial magnetic devices, usually in combination with ferromagnets. Here, one can find the phenomenon of exchange bias, which is being used e.g. in so-called "spin valves".
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