  Large spin systems can exhibit unconventional types of magnetic ordering
different from the ferromagnetic or N\'eel-like antiferromagnetic order
commonly found in spin 1/2 systems. Spin-nematic phases, for instance, do not
break time-reversal invariance and their magnetic order parameter is
characterized by a second rank tensor with the symmetry of an ellipsoid. Here
we show direct experimental evidence for spin-nematic ordering in a spin-1
Bose-Einstein condensate of sodium atoms with antiferromagnetic interactions.
In a mean field description this order is enforced by locking the relative
phase between spin components. We reveal this mechanism by studying the spin
noise after a spin rotation, which is shown to contain information hidden when
looking only at averages. The method should be applicable to high spin systems
in order to reveal complex magnetic phases.
