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Intrinsic ferromagnetism and restrictive thermodynamic stability in MA$_2$N$_4$ and Janus VSiGeN$_4$ monolayers

The seminal experimental discovery of the remarkably stable MoSi$_2$N$_4$ monolayer has led to a handful of predicted magnetic two-dimensional (2D) materials in the MA$_2$Z$_4$ family (M = transition metals, A = Si, Ge, and Z = N, P, As). These magnetic monolayers were predicted to be dynamically stable, but none of them has been synthesized to date. In this Research Letter, from first-principles thermodynamic stability analysis, we demonstrate that only the nitrides are thermodynamically stable and this occurs under N-rich conditions. Based on this finding, we propose two ferromagnetic, semiconducting Janus monolayers in the family: VSiGeN$_4$ and VSiSnN$_4$. They are both dynamically and thermally stable, but only the former is thermodynamically stable. Intriguingly, Janus VSiGeN$_4$ and VSiSnN$_4$ monolayers show weak in-plane anisotropy compared with the VSi$_2$N$_4$ monolayer. These two emerging Janus magnetic semiconductors offer opportunities for studying 2D magnetism and spin control for spintronics applications.