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.

Figure 1

(a) In a 2D material without inversion symmetry breaking, the magnetic atoms have opposite layer spin polarization (A-type antiferromagnetic ordering) which leads to (b) spin-degenerate bands. (c) In a 2D Janus material with A-type AFM ordering, the out-of-plane built-in electric field $E_b$ destroys the spin degeneracy of the bands (d). (e), (f) The top and side views of Janus monolayer ${\mathrm{Mn}}_2\mathrm{ClF}$. In (e), the rhombus primitive cell (rectangle supercell) is marked by the red (black) frame.

Figure 2

For monolayer ${\mathrm{Mn}}_2\mathrm{ClF}$, (a) the FM, and three AFM configurations: (b) AFM1, (c) AFM2, and (d) AFM3.

Figure 3

Energy band structures of ${\mathrm{Mn}}_2\mathrm{ClF}$ (a) without SOC and (b) with SOC. In (a), the spin-up and spin-down channels are depicted in blue and red, respectively. (c), (d) The partially enlarged view of (a) and (b) around the valence band edges.

Figure 4

Layer-characters energy band structures of ${\mathrm{Mn}}_2\mathrm{ClF}$ without SOC (a and b) and with SOC (c). In (a) and (b), the spin-up and spin-down bands are depicted in blue and red, respectively. In (c), the spin-up and spin-down channels are not distinguished.

Figure 5

Energy differences (per unit cell) between FM/AFM2/AFM3 and AFM1 ($E_{AFM1}=0\mathrm{eV}$) as a function of $U$ for ${\mathrm{Mn}}_2\mathrm{ClF}$.

Figure 6

Band structures of ${\mathrm{Mn}}_2\mathrm{ClF}$ at representative $U$ without SOC. The spin-up and spin-down channels are depicted in blue and red.

Figure 7

(a) For a 2D altermagnet, the magnetic atoms have opposite layer spin polarization (A-type antiferromagnetic ordering) without the out-of-plane built-in electric field, destroying the degeneration of electron spin without spin-valley polarization (b). (c) For a 2D Janus altermagnet, the magnetic atoms have opposite layer spin polarization (A-type antiferromagnetic ordering) with the out-of-plane built-in electric field $E_b$, destroying the degeneration of electron spin with spin-valley polarization (d).