Employing first-principles based calculations, we reexamined the high-pressure phases of the vacancy-ordered iron-selenides, i.e., $A_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ phase. A magnetic transition from the block-spin antiferromagnetic phase to the Néel-altermagnetism (AM) phase is observed under high pressure when the iron-vacancy order is preserved. Thus, ternary iron-selenides under pressure may be a rare example for coexisting altermagnetism and superconductivity. In particular, an equal-spin triplet pairing would be naturally favored, if the reentrant superconducting phase of ${\mathrm{K}}_y{\mathrm{Fe}}_{2-x}{\mathrm{Se}}_2$ under high pressure emerges from the Néel-AM normal state. In addition, the Néel-AM phase is an intrinsic altermagnetism that does not require ligand atoms nor supercell construction to break the spatial inversion or translational symmetry between the two spin sublattices, with a spin splitting of the band structure as large as 300 meV.

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• Altermagnetism
• Electronic structure
• Magnetic phase transitions
• Superconductivity
• Chalcogenides
• DFT+DMFT
• Density functional calculations