The magneto-optical Kerr effect (MOKE)
is a powerful probe of magnetism
and has recently gained new attention in antiferromagnetic (AFM) materials.
Through extensive first-principles calculations and group theory analysis,
we have identified Fe2CX2 (X = F, Cl) and Janus
Fe2CFCl monolayers as ideal A-type collinear AFM materials
with high magnetic anisotropy and Néel temperatures. By applying
a vertical external electrical field (Ef) of 0.2 V/Å, the MOKE is activated for Fe2CF2 and Fe2CCl2 monolayers without changing
their magnetic ground state, and the maximum Kerr rotation angles
are 0.13 and 0.08°, respectively. Due to the out-of-plane spontaneous
polarization, the intrinsic and nonvolatile MOKE is found in the Janus
Fe2CFCl monolayer and the maximal Kerr rotation angle without
external electronic field is 0.25°. Moreover, the intrinsic built-in
electronic field also gives origin to more robust A-type AFM ordering
and reversible Kerr angle against external Ef. Our study suggests that Ef is
an effective tool for controlling MOKE in two-dimensional (2D) AFM
materials. This research opens the possibility of related studies
and applications in AFM spintronics.