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We present first-principles results on the structural, electronic, and magnetic properties of a new family of two-dimensional antiferromagnetic (AFM) manganese chalcogenides, namely monolayer MnX and Janus XMnY (X, Y= S, Se, Te), among which monolayer MnSe was recently synthesized in experiments [\href{https://pubs.acs.org/doi/abs/10.1021/acsnano.1c05532}{ACS Nano 15 (8),13794 (2021)}]. By carrying out calculations of the phonon dispersion and \textit{ab-initio} molecular dynamics simulations, we first confirmed that these systems, characterized by an unconventional strongly coupled bilayer atomic structure (consisting of Mn atoms buckled to chalcogens forming top and bottom ferromagnetic (FM) planes with antiparallel spin orientation) are dynamically and thermally stable. The analysis of the the magnetic properties shows that these materials have robust AFM order, retaining a much lower energy than the FM state even for under strain. Our electronic structure calculations reveal that pristine MnX and their Janus counterparts are indirect-gap semiconductors, covering a wide energy range and displaying tunable band gaps by the application of biaxial tensile and compressive strain. Interestingly, owing to the absence of inversion and time-reversal symmetry, and the presence of an asymmetrical potential in the out-of-plane direction, Janus XMnY become spin-split gapped systems, presenting a rich physics yet to be explored. Our findings provide novel insights in this physics, and highlight the potential for these two-dimensional manganese chalcogenides in AFM spintronics.