An ab initio description of the family of Cr selenides: structure, magnetism and electronic structure from bulk to the single-layer limit

TL;DR

This work provides a comprehensive ab initio exploration of the Cr–Se family CrxSe{x+1} from bulk to the monolayer limit, combining DFT with phonon analysis to map structural phases, electronic structure, magnetism, and CDW instabilities. It reveals a rich interplay between dimensionality, vacancies, and phase (1T, 2H, NiAs-type) that governs metallicity vs. insulating behavior and ferromagnetic vs. antiferromagnetic order. Notably, CDW reconstructions in monolayer CrSe$_2$ stabilize low-energy, dynamically stable states with potential flat bands and enhanced correlations, while MAE tuning via strain and layer number emerges as a crucial control knob for 2D magnetism. The results establish design principles for Cr-based 2D magnets and van der Waals heterostructures with tailored electronic and magnetic properties.

Abstract

Compounds based on Cr have been found to be among the first single-layer magnets. In addition, transition metal dichalcogenides are promising candidates to show long-range ferromagnetic order down to the two-dimensional limit. We use ab initio calculations to provide a description of the various Cr$_x$Se$_{x+1}$ stoichiometries that may occur by analyzing from the bulk materials to the monolayer limit. We study the different structural distortions, including charge density waves that each system can present by analyzing their phonon spectra and dynamic stability. We provide a description of their basic electronic structure and study their magnetic properties, including the magnetocrystalline anisotropy energy. The evolution of all these properties with the dimensionality of the systems is discussed. This intends to be a comprehensive view of the broad family of Cr selenides.

Figures (5)

• Figure 1: Cr$_x$Se$_{x+1}$ 2-H structure from (a) a top view and (b) a side and slanted view, where the trigonal environment can be seen. Cr$_x$Se$_{x+1}$ 1-T structure from (c) a top view and (d) a side and slanted view, where the octahedral environment can be seen. NiAs-type structure from a side view with no Cr vacancies (e) and with some Cr vacancies (f).
• Figure 2: Cr$_x$Se$_{x+1}$ van der Waals units. (a) In-plane lattice parameter as a fucntion of Cr ($x$) and Se ($x+1$) in the system (stoichiometry). (b) Layer height (number of layers) as a function of Cr ($x$) and Se ($x+1$) in the system (stoichiometry).
• Figure 3: Electronic structure and magnetism of the Cr$_x$Se$_{x+1}$ family represented through the number of Cr layers as a function of the amount of Se (X). (a) Structural details of the analyzed structures from bulk to monolayer. Red marker borders indicate there is a van der Waals gap in the system, crosses indicate an H-phase, squares indicate there are vacancies present in the structure and the black line indicates a NiAs-type structure as we increase stoichiometry (layers). (b) Metallic and insulating character where data marked in purple (yellow) indicates a metal (insulator). (c) The magnetic moment is represented in a color map, where blue (red) represents the minimum (maximum) computed value. Also, pairs of red and blue arrows indicate antiferromagnetic magnetic order in the system.
• Figure 4: CrSe$_2$ CDW structures. (a) NS hexagonal high symmetry structure, its phonon band structure (b) and electronic band structure (c) where the majority spin channel is represented in green and the minority in blue. (d) CDW associated to the $\sqrt{3}\times\sqrt{3}$ supercell, its phonon band structure (e) and electronic band structure (f) where the majority spin channel is represented in green and the minority in blue. (g) CDW associated to the $2\times2$ supercell, its phonon band structure (h) and electronic band structure (i) where the majority spin channel is represented in green and the minority in blue. (j) Exchange couplings for the spin model. Double headed arrows indicate neighbour exchange interactions: Red arrows for first nearest neighbours ($J_1$), blue arrows for second nearest neighbours ($J_2$) and black arrows for third nearest neighbours ($J_3$). (k) Magnetic configurations used for the calculations of exchange couplings.
• Figure 5: MAE as a function of in-plane strain. (a) MAE for the 1T-CrSe$_2$ system, in particular, for the NS and the $\sqrt{3}$$\times$$\sqrt{3}$ and 2$\times$2 CDW reconstructions. MAE as a function of in-plane strain for the two different vdw Cr$_2$Se$_3$ units (b) and for Cr$_3$Se$_4$ and Cr$_4$Se$_5$ (c).