We study $\mathbb{C}{P}^2$ skyrmion crystals in the ferromagnetic $\mathrm{SU}\left(3\right)$ Heisenberg model with a generalization of the Dzyaloshinskii-Moriya interaction and the Zeeman term. The model possesses two different types of skyrmion crystals with unit skyrmions that can be interpreted as bound states of two half-skyrmions or four quarter-skyrmions. Our study on $\mathbb{C}{P}^2$ skyrmion crystals opens up the possibility for useful future applications since $\mathbb{C}{P}^2$ skyrmions have more degrees of freedom than the usual $\mathbb{C}{P}^1$ (magnetic) skyrmions.

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• Dzyaloshinskii-Moriya interaction
• Skyrmions
• Spin texture
• Solitons