  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.
