  Recently, two-dimensional (2D) multiferroics have attracted numerous
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 for the first time 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 CrB2 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 CrB2 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 new 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 new way to
search the long-sought high temperature FM-FE multiferroics.
