  We have synthesized single crystals of Na$_3$Co$_2$SbO$_6$ and characterized
the structure and magnetic order by measuring anisotropic magnetic properties,
heat capacity, x-ray and neutron single crystal diffraction. Magnetic
properties and specific heat of polycrystalline Na$_3$Co$_2$SbO$_6$ were also
measured for comparison. Na$_3$Co$_2$SbO$_6$ crystallizes in a monoclinic
structure (space group $C2/m$) with [Co$_2$SbO$_6$]$^{3-}$ layers separated by
Na$^+$ ions. The temperature dependence of magnetic susceptibility shows
significant anisotropic behavior in the whole temperature range 2\,K-350\,K
investigated in this work. An effective moment of about 5.5\,$\mu_B$/Co$^{2+}$
from a Curie-Weiss fitting of the magnetic susceptibility is larger than the
spin only value and signals significant orbital contribution.
Na$_3$Co$_2$SbO$_6$ single crystal undergoes a transition into a long-range
antiferromagnetically ordered state below $T_N$=5\,K. Neutron single crystal
diffraction confirmed the zigzag magnetic structure with a propagation vector
k\,=\,(0.5, 0.5, 0). The ordered moment is found to be 0.9\,$\mu_B$ at 4\,K and
align along the crystallographic \textit{b}-axis. Density functional theory
calculations suggest that the experimentally observed zigzag order is
energetically competing with the Neel order. It is also found that the
covalency between Co $d$ and O $p$ is quite strong and competes with the local
spin-orbit coupling, suggesting a $J_{eff}$=1/2 ground state may not be
realized in this compound.
