  Recently, the real topology has been attracting widespread interest in two
dimensions (2D). Here, based on first-principles calculations and theoretical
analysis, we reveal the monolayer Cr$_2$Se$_2$O (ML-CrSeO) as the first
material example of a 2D antiferromagnetic (AFM) real Chern insulator (RCI)
with topologically protected corner states. Unlike previous RCIs, we find that
the real topology of the ML-CrSeO is rooted in one certain mirror subsystem of
the two spin channels, and can not be directly obtained from all the valence
bands in each spin channel as commonly believed. In particular, due to
antiferromagnetism, the corner modes in ML-CrSeO exhibit strong
corner-contrasted spin polarization, leading to spin-corner coupling (SCC).
This SCC enables a direct connection between spin space and real space.
Consequently, large and switchable net magnetization can be induced in the
ML-CrSeO nanodisk by electrostatic means, such as potential step and in-plane
electric field, and the corresponding magnetoelectric responses behave like a
sign function, distinguished from that of the conventional multiferroic
materials. Our work considerably broadens the candidate range of RCI materials,
and opens up a new direction for topo-spintronics and 2D AFM materials
research.
