The concept of topology has been widely applied to condensed matter, going beyond the band crossover in reciprocal spaces. A recent breakthrough suggested unconventional topological physics in a quadruple perovskite ${\mathrm{TbMn}}_3{\mathrm{Cr}}_4{\mathrm{O}}_{12}$, whose magnetism-induced polarization manifests a unique Roman surface topology [G. Liu et al., Nat. Commun. 13, 2373 (2022)]. However, the available experimental evidence based on tiny polarizations of polycrystalline samples could be strengthened. Here, this topological multiferroicity is demonstrated by using density functional theory calculations, which ideally confirms the Roman surface trajectory of magnetism-induced polarization. In addition, an alternative material in this category is proposed to systematically enhance the performance, by promoting its magnetism-induced polarization to an easily detectable level.

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• Antiferromagnetism
• Electric polarization
• First-principles calculations
• Magnetoelectric effect
• Spin-orbit coupling
• Topological phases of matter
• Multiferroics