Multiferroic Metallic Monolayer Cu(CrSe2)2

The two-dimensional (2D) Cu(CrSe₂)₂ monolayer stands out for its combined ferromagnetic (FM), ferroelectric (FE), and metallic properties, marking itself as a prominent 2D multiferroic metal. This work studies those properties and the relevant physics, using density functional calculations, Monte Carlo simulations, and $ab$ $initio$ molecular dynamics. Our results show that Cu(CrSe₂)₂ monolayer is in the Cr³⁺ t2g³ state with S = 3/2 and Cu¹⁺ 3d¹⁰ with S = 0. A ligand hole in the Se 4p orbitals gives rise to metallic behavior and enhances the FM coupling between the local Cr³⁺ S = 3/2 spins. The observed in-plane magnetic anisotropy primarily arises from exchange anisotropy, which is associated with the Cr-Se-Cr itinerant ferromagnetism. In contrast, both single-ion anisotropy and shape magnetic anisotropy contribute negligibly. The Dzyaloshinskii-Moriya interaction is also quite weak, only about 3% of the intralayer exchange parameters. Our Monte Carlo simulations show a FM Curie temperature (TC) of 190 K. Moreover, the monolayer exhibits a vertical FE polarization of 1.79 pC/m and a FE polarization switching barrier of 182 meV/f.u., and the FE state remains stable above 800 K as shown by $ab$ $initio$ molecular dynamics simulations. Furthermore, a magnetoelectric coupling is partially manifested by a magnetization rotation from in-plane to out-of-plane associated with a FE-to-paraelectric transition. The magnetization rotation can also be induced by either hole or electron doping, and the hole doping increases the TC up to 238 K. In addition, tensile strain reduces the FE polarization but enhances TC to 290 K, while a compressive strain gives an opposite effect. Therefore, the multiferroic metallic Cu(CrSe₂)₂ monolayer may be explored for advanced multifunctional electronic devices.