  Realizing topological magnetism and its electric control are intensive topics
in the spintronics due to their promising applications in information storage
and logic technologies. Here we unveil that both can be achieved in the
two-dimensional (2D) magnetoelectric multiferroics. Using first-principles
calculations, we show that strong Dzyaloshinskii-Moriya interaction (DMI),
which is the key ingredient for the formation of exotic chiral magnetism, could
be induced in 2D multiferroics with vertical electric polarization via Rashba
effect. We verify that such significant DMI can promote sub-10 nm skyrmion in
2D multiferroics with perpendicular magnetic anisotropy such as CrN monolayer.
In addition, the presence of both magnetization and electric polarization in 2D
multiferroics provides us unique opportunity for the effective electric control
of both strength and chirality of DMI and thereby the topological magnetism. As
an example, we introduce the four multiferroic skyrmions with different
chirality and polarity that can be manipulated by external field.
