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Abstract. Low-temperature powder neutron diffraction measurements are performed in the ordered magnetic state of the pyrochlore antiferromagnet Gd 2 Sn 2 O 7 . Symmetry analysis of the diffraction data indicates that this compound has the ground state predicted theoretically for a Heisenberg pyrochlore antiferromagnet with dipolar interactions. The difference in magnetic structures of Gd 2 Sn 2 O 7 and of nominally analogous Gd 2 Ti 2 O 7 is found to be determined by a specific type of third-neighbor superexchange interaction on the pyrochlore lattice between spins across empty hexagons.Frustration or inability to simultaneously satisfy all independent interactions [1] has become an important theme in condensed matter research, coupling at the fundamental level a wide range of phenomena, such as high-T c superconductivity, the folding of proteins and neural networks. Magnetic crystals provide one of the simplest stages within which to explore the influence of frustration, particularly when it arises as a consequence of lattice geometry, rather than due to disorder. For this reason, geometrically frustrated magnetic materials have been the objects of intense scrutiny for over 20 years [2]. Particular interest has been focussed on kagomé and pyrochlore (see Fig. 1) geometries of vertex-sharing triangles and tetrahedra respectively. Model materials with their structures display a wide range of exotic low-temperature physics, such as spin ice [3], spin liquids [4], topological spin glasses [5], heavy fermion [6], and co-operative paramagnetic ground states [7]. Research into these systems was spawned from studies of the archetypal geometrically frustrated system-the Heisenberg pyrochlore antiferromagnet, which in the classical limit was shown theoretically to possess a disordered ground state. Raju and co-workers found that the Heisenberg pyrochlore antiferromagnet with dipolar interactions has an infinite number of degenerate spin configurations near the mean-field transition temperature, which are described by propagation vectors [hhh] [8]. Later, Palmer and Chalker showed that quartic terms in the free energy lift this degeneracy and stabilize a four-sublattice state with the ordering vector k = (0 0 0) (the PC state) [9].Among various pyrochlore materials Gd 2 Ti 2 O 7 and Gd 2 Sn 2 O 7 are believed to be good realizations of Heisenberg antiferromagnets. Indeed, the Gd 3+ ion has a half-filled 4f -shell with nominally no orbital moment. A strong intrashell spin-orbit

We attempt to solve the magnetic structure of the gadolinium analogue of 'spin-ice', using a mixture of experimental and theoretical assumptions. The eventual predictions are essentially consistent with both the Mössbauer and neutron measurements but are unrelated to previous proposals. We find two possible distinct states, one of which is coplanar and the other is fully three-dimensional. We predict that close to the initial transition the preferred state is coplanar but that at the lowest temperature the ground-state becomes fully three-dimensional. Unfortunately the energetics are consequently complicated. There is a dominant nearest-neighbour Heisenberg interaction but then a compromise solution for lifting the final degeneracy resulting from a competition between longer-range Heisenberg interactions and direct dipolar interactions on similar energy scales.