Frustrated systems are ubiquitous1-3, and they are interesting because their behaviour is difficult to predict; frustration can lead to macroscopic degeneracies and qualitatively new states of matter. Magnetic systems offer good examples in the form of spin lattices, where all interactions between spins cannot be simultaneously satisfied4. Here we report how unusual composite spin degrees of freedom can emerge from frustrated magnetic interactions in the cubic spinel ZnCr2O4. Upon cooling, groups of six spins self-organize into weakly interacting antiferromagnetic loops, whose directors-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; the data show that neutrons scatter from hexagonal spin clusters rather than individual spins. 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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