Intrinsic triferroicity in a two-dimensional lattice

Intrinsic triferroicity is essential and highly sought for novel device applications, such as high-density multistate data storage. So far, the intrinsic triferroicity has only been discussed in three-dimensional systems. Herein on the basis of first principles, we report the intrinsic triferroicity in a two-dimensional lattice. Being exfoliatable from the layered bulk, single-layer $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$ is shown to be an intrinsically triferroic semiconductor, presenting antiferromagnetism, ferroelasticity, and ferroelectricity simultaneously. Moreover, the directional control of its ferroelectric polarization is achievable by 90 ° reversible ferroelastic switching. In addition, single-layer $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$ is identified to harbor in-plane piezoelectric effect. The unveiled phenomena and mechanism of triferroics in this two-dimensional system not only broaden the scientific and technological impact of triferroics but also enable a wide range of nanodevice applications.

Figure 1

Crystal structure of SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$ from top and side views, with the black square marking the primitive cell. Inset shows the distorted $\mathrm{Fe}{\mathrm{O}}_6$ octahedra.

Figure 2

Magnetism of SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$. (a) Fat band structure of $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$ based on HSE06 functional. The Fermi level is shifted to VBM. Inset in (a) is the first Brillouin zone (BZ) with the high-symmetry points marked. (b) Edge-sharing configuration for adjacent octahedrons. (c) Corner-sharing configuration for adjacent octahedrons. (d) Schematic diagram of the exchange interaction between Fe1 and Fe2/Fe3 in SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$. (e) Schematic diagram of exchange interaction between Fe1 and Fe4 in SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$.

Figure 3

Ferroelasticity of SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$. (a) Schematic diagram of ferroelastic switching for SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$. (b) Minimum energy pathway of ferroelastic switching as a function of step number within NEB for SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$.

Figure 4

Ferroelectricity of SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$. (a) Total polarization as a function of normalized displacement for SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$. The difference between those vertically shifted curves is known as the polarization quantum. (b) Energy profile of ferroelectric switching as a function of step number within NEB for SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$. (c) Polarization as a function of temperature for SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$ obtained from MD simulations. (d) Schematic diagram of the manipulation of the ferroelasticity orders by ferroelastic in SL $\mathrm{Fe}{\mathrm{O}}_2\mathrm{H}$. Fat arrows in (d) denote the directions of spontaneous polarization.