  Mermin-Wagner-Coleman theorem predicts no long-range magnetic order at finite
temperature in the two-dimensional (2D) isotropic systems, but a
quasi-long-range order with a divergent correlation length at the
Kosterlitz-Thouless (KT) transition for planar magnets. As a representative of
two-dimensional planar antiferromagnets, single-layer CoPS3 carries the promise
of monolayer antiferromagnetic platforms for the ultimately thin spintronics.
Here, with the aid of magnetostriction which is sensitive to the local magnetic
order, we observe the signatured phonon mode splitting of below TKT in
monolayer CoPS3, revealing the presence of quasi-long-range ordering in XY-type
antiferromagnet. Moreover, the ratio (J'/J) between the interlayer and
intralayer interactions, which characterizes the 2D behaviors, is evaluated to
be around 0.03 for the first time. Our results provide an efficient method to
detect the quasi-long-range antiferromagnetic ordering in the two-dimensional
magnets down to monolayer limit.
