Two-Dimensional Semiconducting Metal Organic Frameworks with Auxetic Effect, Room Temperature Ferrimagnetism, Chiral Ferroelectricity, Bipolar Spin Polarization and Topological Nodal Lines/Points

Two-dimensional (2D) semiconductors integrated with two or more functions are the cornerstone for constructing multifunctional nanodevices, but remain largely limited. Here, by tuning the spin state of organic linkers and the symmetry/topology of crystal lattice, we predict a class of unprecedented multifunctional semiconductors in 2D Cr(II) five-membered heterocyclic metal organic frameworks that simultaneously possess auxetic effect, room temperature ferrimagnetism, chiral ferroe-lectricity, electrically reversible spin polarization and topological nodal lines/points. Taking 2D Cr(TDZ)$_2$ (TDZ=1.2.5-thiadiazole) as an exemplification, the auxetic effect is produced by the anti-tetra-chiral lattice structure. The high temperature ferrimagnetism originates from the strong d-p direct magnetic exchange interaction between Cr cations and TDZ doublet radical anions. Meanwhile, the clockwise-counterclockwise alignment of TDZ' dipoles results in unique 2D chiral ferroelectricity with atomic-scale vortex-antivortex states. 2D Cr(TDZ)$_2$ is an intrinsic bipolar magnetic semiconductor where half-metallic conduction with switchable spin-polarization direction can be induced by applying a gate voltage. Besides, the symmetry of the little group C$_4$ of lattice structure endows 2D Cr(TDZ)$_2$ with topological nodal lines and a quadratic nodal point in the Brillouin zone near the Fermi level.