Polarized and unpolarized neutron diffraction studies have been carried out on single crystals of the coupled spin tetrahedra systems Cu2Te2O5X2 (X=Cl, Br). A model of the magnetic structure associated with the propagation vectors kCl ~ -0.150,0.422,1/2 and kBr ~ -0.172,0.356,1/2 and stable below TN=18 K for X=Cl and TN=11 K for X=Br is proposed. A feature of the model, common to both the bromide and chloride, is a canted coplanar motif for the 4 Cu2+ spins on each tetrahedron which rotates on a helix from cell to cell following the propagation vector. The Cu2+magnetic moment determined for X=Br, 0.395(5)muB, is significantly less than for X=Cl, 0.88(1)muB at 2K. The magnetic structure of the chloride associated with the wave-vector k differs from that determined previously for the wave vector k~0.150,0.422,1/2 [O. Zaharko et.al. Phys. Rev. Lett. 93, 217206 (2004)].
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