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

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.

💡 Research Summary

This paper presents a comprehensive first‑principles investigation of the entire CrₓSeₓ₊₁ family, ranging from bulk crystals to the ultimate two‑dimensional (2D) limit. Using density‑functional theory (DFT) with the GGA‑PBE functional, the authors performed structural relaxations with both the all‑electron WIEN2k code and the plane‑wave VASP code. For bulk systems containing van der Waals gaps, the DFT‑D3 dispersion correction with Becke‑Johnson damping was employed, while monolayers were treated without additional vdW terms because the interlayer spacing disappears. A dense Monkhorst‑Pack k‑mesh ensured convergence of total energies, forces, and electronic properties.

The study systematically explores three principal crystallographic motifs that appear in Cr‑selenide compounds: (i) the high‑symmetry 1T phase (octahedral coordination of Se around Cr), (ii) the 2H phase (trigonal prismatic coordination), and (iii) a three‑dimensional NiAs‑type structure that lacks a van der Waals gap and can host ordered Cr‑vacancy layers. Within each motif, a wide range of stoichiometries (CrSe₂, Cr₂Se₃, Cr₃Se₄, etc.) is constructed, allowing the authors to examine how the number of Cr layers, the presence of vacancies, and the overall Cr/Se ratio affect lattice parameters, layer thickness, and electronic band topology.

Dynamic stability is assessed through phonon calculations performed with the real‑space supercell method. The authors find that bulk 1T‑CrSe₂ exhibits imaginary phonon modes, indicating a structural instability that would likely drive a charge‑density‑wave (CDW) distortion. In contrast, bulk 2H‑CrSe₂ and the NiAs‑type structures are dynamically stable, showing no imaginary frequencies. For monolayers, the 2H phase remains stable, while the 1T monolayer inherits the bulk instability unless a symmetry‑lowering distortion is introduced. The paper also reports a linear decrease of interlayer height with increasing number of Cr layers in the NiAs‑type series, whereas the in‑plane lattice constant grows non‑linearly with Cr content, reflecting the changing Cr–Se bond lengths and Se coordination geometry.

Electronic structure analysis reveals that the high‑symmetry 1T bulk is metallic but dynamically unstable, whereas the 2H bulk is a semiconductor with a modest band gap. Upon thinning to a single layer, the in‑plane ferromagnetic (FM) exchange becomes dominant, while interlayer antiferromagnetic (AFM) coupling disappears. This dimensional crossover is quantified by calculating total energies for several magnetic configurations (FM, various AFM patterns) and by evaluating the magnetocrystalline anisotropy energy (MAE) via a second‑variational inclusion of spin‑orbit coupling. The MAE is defined as MAE = E_in − E_out, where E_in and E_out are the total energies with magnetization oriented in‑plane and out‑of‑plane, respectively. Positive MAE values are obtained for the monolayers, indicating an out‑of‑plane easy axis. Such perpendicular anisotropy circumvents the Mermin‑Wagner theorem and suggests that long‑range FM order could persist at finite temperatures in the 2D limit.

To bridge theory and experiment, the authors construct model systems that mimic experimentally observed nanoflakes, such as Cr₁₅Se₁₈ (effectively a Cr₂.₅Se₃ stoichiometry) and ultra‑thin Cr₂Se₃ layers. Phonon spectra for these engineered structures show no imaginary modes, confirming their dynamical stability. Calculated lattice constants (e.g., a ≈ 6.3 Å for a three‑layer Cr₂Se₃ slab) match experimental values within a few percent, and the predicted magnetic ground states (in‑plane FM with out‑of‑plane anisotropy) are consistent with reported Néel temperatures and magnetic measurements.

Overall, the paper delivers a detailed map of how structural motifs, stoichiometry, and dimensionality intertwine to determine the electronic bands, magnetic exchange pathways, and anisotropy in Cr‑selenide compounds. By providing a clear set of design rules—such as favoring the 2H phase for stability, engineering vacancy‑ordered NiAs‑type layers to achieve desired Cr/Se ratios, and exploiting the intrinsic out‑of‑plane MAE for 2D ferromagnetism—the work offers a valuable theoretical foundation for future experimental synthesis of Cr‑based 2D magnets and their integration into van der Waals heterostructures.