  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.
