  The antiferromagnetic (AFM) materials are robust to external magnetic
perturbation due to missing any net magnetic moment. In general, the spin
splitting in the band structures disappears in these antiferromagnets. However,
the altermagnetism can achieve spin-split bands in collinear
symmetry-compensated antiferromagnet with special magnetic space group. Here,
we propose a new mechanism that can achieve spin splitting in two-dimensional
(2D) Janus A-type AFM materials. Since the built-in electric field caused by
Janus structure creates a layer-dependent electrostatic potential, the
electronic bands in different layers will stagger, producing the spin
splitting, which can be called electric-potential-difference antiferromagnetism
(EPD-AFM). We demonstrate that Janus monolayer $\mathrm{Mn_2ClF}$ is a possible
candidate to achieve the EPD-AFM by the first-principles calculations. It is
proposed that the spin splitting can be tuned in EPD-AFM by piezoelectric
effect. Our works provide a new design principle for generating spin
polarization in 2D AFM materials.
