Neutron scattering study of novel magnetic order in Na$_{0.5}$CoO$_{2}$.

The layered sodium cobaltates, Na$_{x}$CoO$_{2}$, have attracted much recent attention, due to their unusual thermodynamic properties, as well as the recent discovery of superconductivity in the hydrated composition.~ These strongly correlated systems exhibit a rich electronic phase diagram as a function of sodium doping, $x$. A particularly intriguing insulating phase is realized at $x$=1/2, featuring a long range sodium order, a metal-insulator phase transition at 51 K, and a magnetic ordering transition at 88 K.~ We present polarized and unpolarized neutron scattering measurements of the magnetic order in single crystals of Na$_{0.5}$CoO$_{2}$. 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.