Spontaneous spin splitting in electric potential difference antiferromagnetism

Antiferromagnetic (AFM) materials are robust to external magnetic perturbation due to the absence of net magnetic moment, which also eliminates spin splitting in the band structures. Altermagnetism provides a route to resurrect the spin-split bands in a collinear symmetry-compensated antiferromagnet with special magnetic space group. Here we propose an alternative mechanism to achieve spin splitting in a two-dimensional (2D) Janus A-type AFM material. Since the built-in electric field intrinsic to the Janus structure creates a layer-dependent electrostatic potential, the electronic bands in different layers stagger to produce the spin-splitting effect, resulting in the electric potential difference antiferromagnetism (EPD-AFM). We demonstrate that Janus monolayer ${\mathrm{Mn}}_{2}\mathrm{ClF}$ is a candidate material for achieving EPD-AFM by first-principles calculations. We further show that the spin splitting in EPD-AFM can be tuned by the piezoelectric effect. This work reveals a different class of 2D AFM materials with spin polarization.