Using inelastic magnetic neutron scattering we have discovered a localizedspin resonance at 4.5 meV in the ordered phase of the geometrically frustratedcubic antiferromagnet $\rm ZnCr_2O_4$. The resonance develops abruptly fromquantum critical fluctuations upon cooling through a first order transition toa co-planar antiferromagnet at $T_c=12.5(5)$ K. We argue that this transitionis a three dimensional analogue of the spin-Peierls transition.
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