The quantum pyrochlore antiferromagnet is studied by perturbative expansions and exact diagonalization of small clusters. We find that the ground state is a spin-liquid state: The spin-spin correlation functions decay exponentially with distance and the correlation length never exceeds the interatomic distance. The calculated magnetic neutron diffraction cross section is in very good agreement with experiments performed on Y(Sc)Mn2. The low energy excitations are singlet-singlet ones, with a finite spin gap. PACS number(s): 75.10. Jm, 75.50.Ee, Since Anderson proposed the resonant valence bond (RVB) wave function for the triangular lattice 1 , there has been a lot of attention focused on frustrated lattices, because they might have a spin-liquid-like ground state in two-or three-dimensional lattices. The frustrated systems can be classified into two different categories: structurally disordered systems and periodic lattices. Among the last one the ground state of the S = 1 2 quantum Heisenberg antiferromagnet on the kagomé and pyrochlore lattices is expected to be a quantum spin liquid (QSL). The common point of these two lattices is the high degree of frustration as they both belong to the class of the "fully frustrated lattices." The classical mean field description indicates a pathological spectrum with an infinite number of zero energy modes which prevents any magnetic phase transition and produces an extensive zero temperature entropy 2-4 . The classical critical properties are nonuniversal for both systems 5 . The pyrochlore lattice consists of a 3D arrangement of corner sharing tetrahedra (Fig. 1). All compounds which crystallize in the pyrochlore structure exhibit unusual magnetic properties: Two of them, FeF 3 and NH 4 Fe 2+ Fe 3+ F 6 6 , are known to have a noncollinear long range ordered magnetic structure at low temperature; the other compounds do not undergo any phase transition, but many of them behave as spin glasses, although there is no structural disorder at all. It is remarkable that frustration in a periodic lattice may give rise to ageing and irreversibility so that a conpound such as Y 2 Mo 2 O 7 has been considered as a "topological spin glass" 3,7 . The problem of ordering in the pyrochlore lattice was initiated by Anderson 8 who predicted that only long range interactions are able to stabilize a Néel-like ground state. More recently, mean field studies 9 have confirmed these predictions; from classical Monte Carlo calculations 5,10,11 it was concluded that this system does not order down to zero temperature, but any constraint will induce magnetic ordering 12 . FIG. 1.Description of the pyrochlore lattice as an fcc lattice of tetrahedra. Solid lines connect sites interacting with exchange J, dashed lines with exchange J ′ .The only attempt to describe the quantum S = 1 2Heisenberg antiferromagnet on the pyrochlore lattice has been done by Harris et al. 13 who studied the stability of a dimer-type order parameter and showed that quantum fluctuations play a crucial role. In this Letter, ...

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Due to the particular geometry of the kagomé lattice, it is shown that antisymmetric Dzyaloshinsky-Moriya interactions are allowed and induce magnetic ordering. The symmetry of the obtained low temperature magnetic phases are studied through mean field approximation and classical Monté Carlo simulations. A phase diagram relating the geometry of the interaction and the ordering temperature has been derived. The order of magnitude of the anisotropies due to Dzyaloshinsky-Moriya interactions are more important than in non-frustrated magnets, which enhances its appearance in real systems. Application to the jarosites compounds is proposed. In particular, the low temperature behaviors of the Fe and Cr-based jarosites are correctly described by this model.