Design and Theory of Switchable Linear Magnetoelectricity by Ferroelectricity in Type-I Multiferroics

We present a comprehensive theoretical investigation of magnetoelectric (ME) coupling mechanisms in 19 altermagnetic and 4 ferrimagnetic type-I multiferroics using electronic band structure calculations with spin-orbit coupling, a first-principles ME response framework, and spin-space-group theory analysis. We formulate a universal scheme for realizing nonvolatile ME coupling in type-I multiferroics, where two distinct pathways emerge, each dictated by spin-space symmetry. The first pathway is associated with switching of the spin splitting or the now familiar spin-momentum locking in reciprocal space, characteristic of some altermagnetic multiferroics that exhibit coexisting antiferromagnetism and ferroelectricity. The second pathway involves real-space magnetization switching via electric polarization reversal, characterized by switchable components of the linear ME tensor, despite the traditionally weak coupling in type-I systems due to the independent origins of magnetism and ferroelectricity. We demonstrate that these two intrinsic ME coupling mechanisms are mutually exclusive and propose thermodynamically stable compounds for experimentation. Our findings establish general design principles for controlling robust nonvolatile ME effects in multiferroic materials.