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Binary transition metal nitride with a graphene-like structure and strong magnetic properties is rare. Based on the first-principles calculations, we design two kinds of $M$N$_4$ ($M$ =transition metal) monolayers, which are transition metal nitrides with a planar structure, made up of $M$N$_4$ units aligned in the rhombic and square patterns. The two structural lattices have robust stability and good compatibility with different metal atoms, and the underlying mechanism is the combination of $sp^2$ hybridization, coordinate bond, and $\pi$ conjugation. With the metal atom changing from V, Cr, Mn, Fe to Co, the total charge of $M$N$_4$ system increases by one electron in turn, which results in continuous adjustability of the electronic and magnetic properties. The planar ligand field is another feature of the two $M$N$_4$ lattices, which brings about the special splitting of five suborbitals of 3$d$ metal atom and gives rise to strong magnetism. Moreover, room-temperature ferromagnetism in square-CoN$_4$ monolayer with the Curie temperatures of 321 K is determined by solving the Heisenberg model combined with Monte Carlo method.

MnSn monolayer synthesized recently is a novel two-dimensional ferromagnetic material with a hexagonal lattice, in which three Mn atom come together to form a trimer, making it remarkably different from other magnetic two-dimensional materials. Most impressively, there happens a sharp increase of Curie temperature from 54 K to 225 K when the number of layers increase from 1 to 3. However, no quantitative explanation is reported in previous studies. Herein, by means of first-principle calculations method and Monte carlo method, we demonstrate that strong interlayer ferromagnetic coupling is the essential role in enhancing its critical temperature, which act as a magnetic field to stabilize the ferromagnetism in the MnSn multilayers.

Single-atom-thick two-dimensional materials such as graphene usually have a hexagonal lattice while the square-planar lattice is uncommon in the family of two-dimensional materials. Here, we demonstrate that single-atom-thick transition metal nitride 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 $\pi$-d conjugation, in which the double $\pi$-d conjugation is rarely reported in previous studies. This mechanism is entirely different from that of the reported two-dimensional materials, leading to lower formation energy and more robust stability compared to the synthesized g-C$_3$N$_4$ monolayer. On the other hand, CrN$_4$ layer has a ferromagnetic ground state, in which the ferromagnetic coupling between two Cr atoms is mediated by electrons of the half-filled large $\pi$ orbitals from $\pi$-d conjugation. The high-temperature ferromagnetism in CrN$_4$ monolayer is confirmed by solving the Heisenberg model with Monte Carlo method., Comment: https://link.aps.org/doi/10.1103/PhysRevB.106.125421

Magnetic two-dimensional materials have potential application in next-generation electronic devices and have stimulated extensive interest in condensed matter physics and material fields. However, how to realize high-temperature ferromagnetism in two-dimensional materials remains a great challenge in physics. Herein, we propose an effective approach that the dimerization of magnetic ions in two-dimensional materials can enhance the exchange coupling and stabilize the ferromagnetism. Manganese carbonitride Mn$_2$N$_6$C$_6$ with a planar monolayer structure is taken as an example to clarify the method, in which two Mn atoms are gathered together to form a ferromagnetic dimer of Mn atoms and further these dimers are coupled together to form the overall ferromagnetism of the two-dimensional material. In Mn$_2$N$_6$C$_6$ monolayer, the near-room-temperature ferromagnetism with the Curie temperature of 272.3 K is determined by solving Heisenberg model using Monte Carlo simulations method., Comment: Journal of Physical Chemistry C Cite This: https://doi.org/10.1021/acs.jpcc.2c02593