  Altermagnets (AM) are a recently discovered third class of collinear magnets,
distinctly different from conventional ferromagnets (FM) and antiferromagnets
(AF). AM have been actively researched in the last few years, but two aspects
so far remain unaddressed: (1) Are there realistic 2D single-layer
altermagnets? And (2) is it possible to functionalize a conventional AF into AM
by external stimuli? In this paper we address both issues by demonstrating how
a well-known 2D AF, MnP(S,Se)$_3$ can be functionalized into strong AM by
applying out-of-plane electric field. Of particular interest is that the
induced altermagnetism is of a higher even-parity wave symmetry than expected
in 3D AM with similar crystal symmetries. We confirm our finding by
first-principles calculations of the electronic structure and magnetooptical
response. We also propose that recent observations of the time-reversal
symmetry breaking in the famous Fe-based superconducting chalchogenides, either
in monolayer form or in the surface layer, may be related not to an FM, as
previously assumed, but to the induced 2D AM order. Finally, we show that
monolayer FeSe can simultaneously exhibit unconventional altermagnetic
time-reversal symmetry breaking and quantized spin Hall conductivity indicating
possibility to research an intriquing interplay of 2D altermagnetism with
topological and superconducting states within a common crystal-potential
environment.
