Abstract: | Magnetic susceptibility, specific heat, and neutron powder diffraction measurements have been performed on polycrystalline Li$_{2}$Co(WO$_{4}$)$_{2}$ samples. Under zero magnetic field, two successive magnetic transitions at $T_{\rm N1}\sim 9.4$ K and $T_{\rm N2}\sim 7.4$ K are observed. The magnetic ordering temperatures gradually decrease as the magnetic field increases. Neutron diffraction reveals that Li$_{2}$Co(WO$_{4}$)$_{2}$ enters an incommensurate magnetic state with a temperature dependent $\bm k$ between $T_{\rm N1}$ and $T_{\rm N2}$. The magnetic propagation vector locks-in to a commensurate value $\bm k = (1/2, 1/4, 1/4)$ below $T_{\rm N2}$. The antiferromagnetic structure is refined at 1.7 K with Co$^{2+}$ magnetic moment 2.8(1) $\mu_{\rm B}$, consistent with our first-principles calculations. |