Cr-based compounds are among the first single-layer magnets ever found. 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 ${\mathrm{Cr}}_x{\mathrm{Se}}_{x+1}$ 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 quasi-two-dimensional Cr selenides.

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• Charge density waves
• Electronic structure
• Magnetic anisotropy
• Magnetism
• Phonons
• 2-dimensional systems
• Transition metal dichalcogenides
• van der Waals systems
• Density functional theory