Two-dimensional hyperferroelectric metals: A different route to ferromagnetic-ferroelectric multiferroics

Recently, two-dimensional (2D) multiferroics have attracted a lot of attention due to their fascinating properties and promising applications. Although the ferroelectric (FE)-ferroelastic and ferromagnetic (FM)-ferroelastic multiferroics have been observed/predicted in 2D systems, 2D ferromagnetic-ferroelectric (FM-FE) multiferroics remain to be discovered since FM insulators are very rare. Here we proposed the concept of 2D hyperferroelectric metals, with which the insulating prerequisite for the FM-FE multiferroic is no longer required in 2D systems. We validate the concept of 2D hyperferroelectric metals and 2D metallic FM-FE multiferroics by performing first-principle calculations on 2D CrN and $\mathrm{Cr}{\mathrm{B}}_{2}$ systems. The 2D buckled monolayer CrN is found to be a hyperferroelectic metal with the FM ground state, i.e., a 2D FM-FE multiferroic. With the global optimization approach, we find the 2D $\mathrm{Cr}{\mathrm{B}}_{2}$ system has an antiferromagnetic (AFM)/planar ground state and a FM/FE metastable state, suggesting that it can be used to realize electric field control of magnetism. Our analysis demonstrates that the spin-phonon coupling and metal-metal interaction are two mechanisms for stabilizing the out-of-plane electric polarization in 2D systems. Our work not only extends the concept of FE to metallic systems, but also paves a way to search the long-sought high temperature FM-FE multiferroics.