In ultracold atoms, achieving a period-3 structure poses a significant challenge. In this work, we propose a three-sublattice spin-flop transition mechanism, differing from the two-sublattice counterpart used to explain the emergence of ferrimagnetic orders in higher dimensions. Guided by this mechanism, we design a setup of alkaline-earth-metal atoms to create a spin-orbit-coupled optical lattice, where we identify a triplefold degenerate $YX\overline{Y}$ state with a period-3 coplanar spin ordering within the deep Mott-insulating phase region of the ground-state phase diagram. The $YX\overline{Y}$ state is protected by a finite gap, and its characteristic angle can be finely tuned by specific setup parameters. Moreover, we use the Rabi spectroscopy technique to detect the $YX\overline{Y}$ state. Our work not only shows the feasibility of achieving a period-3 structure via the new mechanism but also suggests its potential applications for exploring other periodic structures in optical lattices.

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• Cold atoms & matter waves
• Cold gases in optical lattices
• Spin-orbit coupling