Magnetoelectric coupling and cross control in two-dimensional ferromagnets

The coexistence and coupling of multiple ferroics may not only cause some novel physical phenomena but also provide new means for the detection and control of electronic degrees of freedom. In recent years, two-dimensional (2D) ferroelectricity and ferromagnetism have been experimentally confirmed in van der Waals materials but their coexistence and coupling have rarely been demonstrated in single-phase materials. Here, a general mechanism for the coexistence and coupling of three ferroics has been demonstrated in van der Waals monolayer ferromagnets lacking inversion symmetry, in which spin-orbit coupling leads to spin-direction-dependent ferroelectricity and ferrovalley. This causes the emergence of some interesting phenomena, such as the anomalous valley Hall effect without an applied electric field. The ferroelectric polarization induced in a 2D ferromagnet with strong spin-orbit coupling can be close to the largest known spin-induced polarization. Importantly, the magnetoelectric coupling effect enables the cross control of ferroic order parameters by external fields, such as controlling magnetization by an electric field and polarization by a magnetic field.