  We design a multiferroic metal that combines seemingly incompatible
ferromagnetism, ferroelectricity, and metallicity by hole doping a
two-dimensional (2D) ferroelectric with high density of states near the Fermi
level. The strong magnetoelectric effect is demonstrated in hole-doped and
arsenic-doped monolayer {\alpha}-In2Se3 using first-principles calculations.
Taking advantage of the oppositely charged surfaces created by an out-of-plane
polarization, the 2D magnetization and metallicity can be electrically switched
on and off in an asymmetrically doped monolayer. The substitutional arsenic
defect pair exhibits an intriguing electric field-tunable charge
disproportionation process accompanied with an on-off switch of local magnetic
moments. The charge ordering process can be controlled by tuning the relative
strength of on-site Coulomb repulsion and defect dipole-polarization coupling
via strain engineering. Our design principle relying on no transition metal
broadens the materials design space for 2D multiferroic metals.
