Two-dimensional (2D) triferroic materials, which simultaneously host ferroelectric, ferromagnetic, and ferrovalley orders, are regarded as ideal platforms for developing next-generation nonvolatile multistate memory devices. However, achieving coupling among these order parameters, stability above room temperature, and their coexistence with higher-order topology in an intrinsic monolayer remains challenging. Based on first-principles calculations, we predict that monolayer ${\mathrm{TcIrGe}}_2{\mathrm{Se}}_6$ (TIGS) is an intrinsic 2D triferroic semiconductor stable above room temperature. Specifically, this system possesses switchable out-of-plane ferroelectric polarization and polarization-controllable valley polarization, together with a ferromagnetic ground state stabilized by the supersuperexchange mechanism, with a Curie temperature reaching 405 K. More importantly, pronounced coupling among ferroelectric order, magnetic order, and valley physics is found in TIGS. As a result, polarization reversal modulates the magnetic interactions, reverses both the sign of the valley splitting and the DMI chirality, and modulates Berry-curvature-related transport responses. In addition, TIGS exhibits higher-order topological characteristics and supports a long-range-ordered skyrmion lattice. These results identify TIGS as a promising platform for exploring the cooperative interplay among 2D multiferroic coupling, higher-order topology, spin textures, and valley physics.

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• Magnetism
• Room-temperature magnet calculations
• Skyrmions
• Spin texture
• Valley degrees of freedom
• Ferroelectrics
• Multiferroics
• Topological materials