Geometric frustrated kagome systems can show complex and exotic magnetic properties. We theoretically predict ways in which these can be manipulated in two-dimensional (2D) multiferroic materials from first-principles density functional theory calculations. We propose that ${\mathrm{Ti}}_3{X}_8$ ($X=\mathrm{Br}$ or I) compounds are shown to form 2D intrinsic semiconductors with breathing kagome lattices containing coexisting ferroelectric (FE) and ferromagnetic ordering. Inside the lattice, Ti atoms distort from high-symmetry locations to produce trimers with shorter interatomic distances that form the basis of local cluster magnets. Lattice breathing interchanges trimer patterns, switching the direction of out-of-plane FE polarization while simultaneously rearranging the interactions between the cluster magnets. FE switching of the monolayer ${\mathrm{Ti}}_3{X}_8$, which is concomitant with the direction reversal of the vector of the Dzyaloshinskii-Moriya interaction, is feasible to be manipulated by the application of out-of-plane electric fields. Through the interlayer interaction, the coupling of FE and magnetism is achieved in bilayer ${\mathrm{Ti}}_3{\mathrm{I}}_8$. The magnetic configurations are transformed between interlayer ferromagnetism and antiferromagnetism by switching the FE polarization directions of bilayer ${\mathrm{Ti}}_3{\mathrm{I}}_8$. Our findings expand the arena for realizing 2D multiferroics and magnetoelectric effect.

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• Ferroelectricity
• Ferromagnetism
• First-principles calculations
• 2-dimensional systems
• Kagome lattice
• Multiferroics