Frustrated systems are ubiquitous and interesting because their behavior is difficult to predict. Magnetism offers extreme examples in the form of spin lattices where all interactions between spins cannot be simultaneously satisfied. Such geometrical frustration leads to macroscopic degeneracies, and offers the possibility of qualitatively new states of matter whose nature has yet to be fully understood. Here we have discovered how novel composite spin degrees of freedom can emerge from frustrated interactions in the cubic spinel ZnCr2O4. Upon cooling, groups of six spins self-organize into weakly interacting antiferromagnetic loops whose directors, defined as the unique direction along which the spins are aligned parallel or antiparallel, govern all low temperature dynamics. The experimental evidence comes from a measurement of the magnetic form factor by inelastic neutron scattering. While the data bears no resemblance to the atomic form factor for chromium, they are perfectly consistent with the form factor for hexagonal spin loop directors. The hexagon directors are to a first approximation decoupled from each other and hence their reorientations embody the long-sought local zero energy modes for the pyrochlore lattice.
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