Using synchrotron X-rays and neutron diffraction we disentangle spin-lattice order in highly frustrated ZnCr2O4 where magnetic chromium ions occupy the vertices of regular tetrahedra. Upon cooling below 12.5 K the quandary of anti-aligning spins surrounding the triangular faces of tetrahedra is resolved by establishing weak interactions on each triangle through an intricate lattice distortion. The resulting spin order is however, not simply a Néel state on strong bonds. A complex co-planar spin structure indicates that antisymmetric and/or further neighbor exchange interactions also play a role as ZnCr2O4 resolves conflicting magnetic interactions. PACS numbers:While tetrahedral atomic clusters are a natural consequence of close packing, they are particularly inconvenient for antiferromagnetically interacting spins. This is because no spin configuration can simultaneously satisfy all six antiferromagnetic interactions amongst spins on the vertices of a tetrahedron [1,2,3,4,5]. The consequence of such "geometrical frustration" is deep suppression of magnetic order and a range of temperatures where spins remain fluctuating despite interactions that far exceed thermal energies [6,7]. Indeed for spins on a lattice of corner-sharing tetrahedra, it appears there is no conventional order in the quantum limit (S = 1/2, T = 0) [5]. Because they entail higher energy spin configurations, geometrically frustrating lattices however typically do not survive in the low temperature limit. Instead a compromise between spin and lattice energy is reached through a first order phase transition that freezes the spin liquid and distorts the lattice [8,9,10,11,12,13]. Such phase transitions challenge conventional theories of magnetism because they involve strongly correlated spins and the collapse of the rigid lattice approximation [14,15,16].A case in point is ZnCr 2 O 4 . At room temperature, it has a cubic F d3m crystal structure where Cr 3+ (S = 3/2) ions form a network of corner-sharing tetrahedra [9]. The Curie-Weiss temperature is -390 K indicating strong antiferromagnetic frustration, yet chromium spins remain in a cooperative paramagnetic phase down to T C = 12.5 K [6,9]. There, a first order phase transition from a cubic paramagnet to a tetragonal antiferromagnet signals the end of distinct spin and lattice degrees of freedom. Tetragonal strain energy alone does not account for the difference between magnetic energy gain and overall latent heat and this was a first indication of a more comprehensive rearrangement of the lattice [9]. Subsequently X-ray superlattice peaks were detected at ( 2 ) c type reflections (see Fig. 1 (a)) [17]. This indicates that below T N the tetragonal lattice has I4m2 symmetry and a √ 2 × √ 2 × 2 chemical unit cell [18]. Theoretical efforts to understand the nature of the phase transition have focused on magneto-elastic couplings that involve symmetric isotropic nearest neighbor (NN) exchange interactions [14,15,16].Here we report a combined synchrotron X-ray and magnetic neutron diffraction study ...
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