  The Heisenberg nearest neighbour antiferromagnet on the pyrochlore (3D)
lattice is highly frustrated and does not order at low temperature where
spin-spin correlations remain short ranged. Dzyaloshinsky-Moriya interactions
(DMI) may be present in pyrochlore compounds as is shown, and the consequences
of such interactions on the magnetic properties are investigated through mean
field approximation and monte carlo simulations. It is found that DMI (if
present) tremendously change the low temperature behaviour of the system. At a
temperature of the order of the DMI a phase transition to a long range ordered
state takes place. The ordered magnetic structures are explicited for the
different possible DMI which are introduced on the basis of symmetry arguments.
The relevance of such a scenario for pyrochlore compounds in which an ordered
magnetic structure is observed experimentally is dicussed.
