Prediction of single-atom-thick transition metal nitride CrN4 with a square-planar network and high-temperature ferromagnetism

Abstract

Single-atom-thick two-dimensional (2D) materials such as graphene usually have a hexagonal lattice while the square-planar lattice is uncommon in the family of 2D materials. Here, we demonstrate that single-atom-thick transition metal nitride ${\mathrm{CrN}}_{4}$ monolayer is a stable free-standing layer with a square-planar network. The stability of square-planar geometry is ascribed to the combination of N=N double bond, Cr-N coordination bond, and $\ensuremath{\pi}\ensuremath{-}d$ conjugation, in which the double $\ensuremath{\pi}\ensuremath{-}d$ conjugation is rarely reported in previous studies. This mechanism is entirely different from that of the reported 2D materials, leading to lower formation energy and more robust stability than the synthesized $g\ensuremath{-}{\mathrm{C}}_{3}{\mathrm{N}}_{4}$ monolayer. On the other hand, the ${\mathrm{CrN}}_{4}$ layer has a ferromagnetic (FM) ground state, in which the FM coupling between two Cr atoms is mediated by electrons of the half-filled large $\ensuremath{\pi}$ orbitals from $\ensuremath{\pi}\ensuremath{-}d$ conjugation. The high-temperature ferromagnetism in ${\mathrm{CrN}}_{4}$ monolayer is confirmed by solving the Heisenberg model with the Monte Carlo method.