Sliding ferroelectric control of unconventional magnetism in stacked bilayers

The control of unconventional magnetism, which displays ferromagnetism-like properties with compensated magnetization, has drawn intense attention for advancing antiferromagnetic spintronics. Here, through symmetry analysis, we propose a general stacking rule, characterized by a connection operator linking two stacked bilayers, for controlling unconventional magnetism via sliding ferroelectricity. Such rule enables the simultaneous switching of both electric polarization and nonrelativistic spin splitting or anomalous Hall effect in altermagnets, a class of collinear unconventional magnets. By comprehensively surveying the 80 layer groups, we identify all the stacking orders that allow for such two types of simultaneous switching. Furthermore, we extend the stacking rule to collinear compensated ferrimagnets, where the opposite-spin sublattices are not connected by any symmetry operator, yet the net magnetization remains zero. Combined with first-principles calculations, we demonstrate the sliding ferroelectric control of spin polarization and anomalous Hall effect in the altermagnetic AgF2 and Fe2MoSe4 bilayers. Our work provides a symmetry strategy for achieving ferroelectric control of unconventional magnetism in bilayer systems and opens avenues for exploring new types of magnetoelectric coupling.