  Theoretical predictions of the magnetic anisotropy of antiferromagnetic
materials are demanding due to a lack of experimental techniques which are
capable of a direct measurement of this quantity. At the same time it is highly
significant due to the use of antiferromagnetic components in magneto-resistive
sensor devices where the stability of the antiferromagnet is of upmost
relevance. We perform an ab-initio study of the ordered phases of IrMn and
IrMn3, the most widely used industrial antiferromagnets. Calculating the form
and the strength of the magnetic anisotropy allows the construction of an
effective spin model, which is tested against experimental measurements
regarding the magnetic ground state and the Neel temperature. Our most
important result is the extremely strong second order anisotropy for IrMn3
appearing in its frustrated triangular magnetic ground state, a surprising fact
since the ordered L12 phase has a cubic symmetry. We explain this large
anisotropy by the fact that cubic symmetry is locally broken for each of the
three Mn sub-lattices.
