Collinear compensated magnets with nonrelativistic spin splitting have attracted considerable interests, such as altermagnets and compensated ferrimagnets, offering new opportunities for spintronics beyond ferromagnets. In this work, we propose that the ${\mathrm{TaN}}_2{\mathrm{H}}_2$ bilayer is a room-temperature sliding multiferroic material with a compensated ferrimagnetic phase. The coexistence of ferroelectricity and compensated ferrimagnetism induces nonrelativistic spin splitting, magneto-optical Kerr effect, and valley polarization, all of which depend on ferroelectric polarization. Notably, we reveal that the valley polarization in the ${\mathrm{TaN}}_2{\mathrm{H}}_2$ bilayer originates from the combined effect of nonrelativistic spin splitting and spin-orbit coupling. The magnitude of the valley polarization in the ${\mathrm{TaN}}_2{\mathrm{H}}_2$ bilayer is directly related to the nonrelativistic spin splitting, rather than the spin-orbit coupling constant. External electrical fields can efficiently modulate the nonrelativistic spin splitting and valley polarization, introducing a phase transition from a valley semiconductor to a half-valley metal. Our findings provide a new perspective for spintronics and valleytronics based on multiferroic materials with compensated ferrimagnetism.

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• Electronic structure
• Ferroelectricity
• Magnetic anisotropy
• Magnetic order
• Magneto-optical Kerr effect
• Spintronics
• Valley degrees of freedom
• Valleytronics
• 2-dimensional systems
• Ferrimagnets
• Multiferroics
• First-principles calculations