  We report polarized and unpolarized neutron scattering measurements of the
magnetic order in single crystals of Na0.5CoO2. Our data indicate that below
T_N=88 K the spins form a novel antiferromagnetic pattern within the CoO2
planes, consisting of alternating rows of ordered and non-ordered Co ions. The
domains of magnetic order are closely coupled to the domains of Na ion order,
consistent with such a two-fold symmetric spin arrangement. Magnetoresistance
and anisotropic susceptibility measurements further support this model for the
electronic ground state.
