Theoretical studies of sliding ferroelectricity, magnetoelectric couplings, and piezo-multiferroicity in two-dimensional magnetic materials

It has been predicted that for a series of two-dimensional (2D) materials, their van der Waals bilayers may possess sliding ferroelectricity with vertical polarizations switchable via interlayer sliding. Such intriguing ferroelectricity has been recently experimentally confirmed in a series of nonmagnetic bilayer systems like BN, MoS2, etc., while magnetic bilayers remain unexplored in those reports. In this paper we show first-principles evidence that three most prevalent 2D ferromagnetic materials, CrI3, Cr2Ge2Te6 and Fe3GeTe2, can all be entailed with sliding ferroelectricity (FE) with vertical polarizations over 0.1 pC/m in their bilayers and are thus multiferroic. In particular, Fe3GeTe2 bilayer may exhibit magnetoelectric coupling effect with a net magneti-zation moment of 0.01 mu B per unit cell switchable upon ferroelectric switching. Moreover, it is shown to be both piezoelectric and piezomagnetic as both its vertical electric polarization and the net magnetic moment can be approximately doubled when the interlayer distance is compressed by 10%, giving rise to unprecedented "piezo-multiferroic" effect where the magnetoelectric coupling effect is intensified with reduced interlayer distance.