Type-II multiferroics offer a promising route to strong magnetoelectric coupling due to the magnetic-order-driven ferroelectricity. Most experimentally realized type-II multiferroics exhibit noncollinear magnetic order, whose complex interaction with external fields can impede the practical control of magnetoelectric effects. In contrast, type-II multiferroics with collinear magnetic order remain underexplored, with prior work largely limited to conventional antiferromagnets. In this work, using Landau theory and symmetry analysis, we investigate spin-order-induced ferroelectricity in collinear ferrimagnetic systems and derive the criteria in the minimal-case scenario. According to these criteria, we perform a rapid and efficient search and ultimately identify three promising ferrimagnetic multiferroic candidates from the Inorganic Crystal Structure Database (ICSD). Among them, the largest net magnetic moment per unit cell (u.c.) reaches 3.0 ${\mu }_B$, and the maximum polarization reaches 0.08 $\mu \mathrm{C}/{\mathrm{cm}}^2$, comparable to the typical multiferroics material ${\mathrm{TbMnO}}_3$. In addition, for the altermagnetic system, we searched for known magnetic structures in the MAGNDATA database and identified ${\mathrm{MnSe}}_2$ as a promising candidate material, exhibiting a polarization as high as 0.07 $\mu \mathrm{C}/{\mathrm{cm}}^2$. Notably, our results show that ferroelectric polarization behavior provides a clear criterion for distinguishing the two experimentally reported magnetic structures of ${\mathrm{MnSe}}_2$.

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• Altermagnetism
• Electronic structure
• Multiferroics
• First-principles calculations