Magnetic structure and anisotropic spin dynamics in Ba$_{\mathrm{\mathbf{2}}}${CoO}$_{\mathrm{\mathbf{4}}}$*

Ba$_{\mathrm{2}}$CoO$_{\mathrm{4}}$ crystallizes in a monoclinic structure with Co in the tetrahedral environment, in contrast to the octahedral coordination of Co in BaCoO$_{\mathrm{3}}$. Single-crystal neutron diffraction determined an antiferromagnetic ground state with propagation vector (1/2 0 1/2), and Co spins mainly confined in the\textit{ ab} plane below $T_{\mathrm{N}} \quad =$ 25 K. The moment is found to be 3.42(4) u$_{\mathrm{B}}$, pointing to the $a $axis with a canting to $b$ axis, indicating a high-spin Co$^{\mathrm{4+}}$ state in Ba$_{\mathrm{2}}$CoO$_{\mathrm{4}}$. Inelastic neutron scattering studies show an energy gap $\approx $ 2 meV, and approaches zero as temperature increases to $T_{\mathrm{N}}$, which probably results from the single-ion anisotropy of high-spin Co$^{\mathrm{4+}}$. The spin wave spectra show distinct dispersion along the $H$ and $K $directions without dispersion along the$ L$ direction in the reciprocal lattice unit, indicating a strong anisotropic spin dynamic behavior. Our findings imply that Ba$_{\mathrm{2}}$CoO$_{\mathrm{4}}$ exhibits a low-dimensional magnetism although the crystalline structure is three dimensional.