Magnetoelectric effect in multiferroic metals via a direct spin-charge interaction

Much is known about the magnetoelectric effect of multiferroic insulators, yet little is understood about multiferroic metals. In this work, we propose a stacking engineering strategy based on monolayer magnets to construct multiferroic metals, with validation through first-principles calculations on six experimentally synthesized materials. Such multiferroic metals exhibit predominantly linear magnetoelectric response, originating from direct spin-charge interactions as a result of external field-modulated Fermi energy. This fundamentally differs from spin-charge-lattice or spin-orbit coupling mechanisms in multiferroic insulators, offering application advantages in the field of high-speed response. We derive a universal formula for understanding the magnetoelectric coupling in these multiferroic metals. Our work provides insights for exploring magnetoelectric coupling mechanisms and designing functional materials with strong magnetoelectric coupling.