Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions

The Heisenberg nearest-neighbor antiferromagnet on the pyrochlore (three-dimensional) lattice is highly frustrated and does not order at low temperature where spin-spin correlations remain short ranged. Dzyaloshinsky-Moriya interactions (DMI's) 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's (if present) tremendously change the low-temperature behavior of the system. At a temperature of the order of the DMI's a phase transition to a long-range-ordered state takes place. The ordered magnetic structures are explicited for the different possible DMI's 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 discussed.