On the multi-$\mathbf{q}$ characteristics of magnetic ground states of honeycomb cobalt oxides

The Kitaev honeycomb model has received significant attention for its exactly solvable quantum spin liquid ground states and fractionalized excitations. For realizing the model, layered cobalt oxides have been considered a promising platform. Yet, in contrast to the conventional wisdom about single-$\mathbf{q}$ zigzag magnetic order inferred from previous studies of the Na$_2$IrO$_3$ and $\alpha$-RuCl$_3$ candidate materials, recent experiments on two of the representative honeycomb cobalt oxides, hexagonal Na$_2$Co$_2$TeO$_6$ and monoclinic Na$_3$Co$_2$SbO$_6$, have uncovered evidence for more complex multi-$\mathbf{q}$ variants of the zigzag order. This review surveys on experimental strategies to distinguish between single- and multi-$\mathbf{q}$ orders, along with the crystallographic symmetries of the cobalt oxides in comparison to the previously studied systems. General formation mechanism of multi-$\mathbf{q}$ order is also briefly discussed. The goal is to provide some rationales for examining the relevance of multi-$\mathbf{q}$ order in the honeycomb cobalt oxides, along with its implications on the microscopic model of these intriguing quantum magnets.