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Recently, two-dimensional (2D) multiferroics have attracted numerousattention 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, 2Dferromagnetic-ferroelectric (FM-FE) multiferroics remain to be discovered sinceFM insulators are very rare. Here, we proposed for the first time the conceptof 2D hyperferroelectric metals, with which the insulating prerequisite for theFM-FE multiferroic is no longer required in 2D systems. We validate the conceptof 2D hyperferroelectric metals and 2D metallic FM-FE multiferroics byperforming first-principle calculations on 2D CrN and CrB2 systems. The 2Dbuckled monolayer CrN is found to be a hyperferroelectic metal with the FMground state, i.e., a 2D FM-FE multiferroic. With the global optimizationapproach, we find the 2D CrB2 system has an antiferromagnetic (AFM)/planarground state and a FM/FE metastable state, suggesting that it can be used torealize electric field control of magnetism. Our analysis demonstrates that thespin-phonon coupling and metal-metal interaction are two new mechanisms forstabilizing the out-of-plane electric polarization in 2D systems. Our work notonly extends the concept of FE to metallic systems, but also paves a new way tosearch the long-sought high temperature FM-FE multiferroics.

Two-Dimensional Hyperferroelectric Metals: a Different Route to Ferromagnetic-Ferroelectric Multiferroics