Dzyaloshinski-Moriya interactions in the kagome lattice

The kagome lattice exhibits peculiar magnetic properties due to its strongly frustated crystallographic structure, based on corner-sharing triangles. For nearest neighbor antiferromagnetic Heisenberg interactions there is no Neel ordering at zero temperature both for quantum and classical spins. We show that, due to the peculiar structure, antisymmetric Dzyaloshinski-Moriya interactions (D (.) (S-i x S-j)) are present in this lattice. In order to derive microscopically this interaction we consider a set of localized d-electronic states. For classical spins systems, we then study the phase diagram (T, D/J) through mean field approximation and Monte-Carlo simulations and show that the antisymmetric interaction drives this system to ordered states as soon as this interaction is non-zero. This mechanism could be involved to explain the magnetic structure of Fe-jarosites. (C) 2002 Elsevier Science B.V. All rights reserved.