  Recently, a colossal magnetoresistance (CMR) was observed in EuCd$_2$P$_2$ --
a compound that does not fit the conventional mixed-valence paradigm. Instead,
experimental evidence points at a resistance driven by strong magnetic
fluctuations within the two-dimensional ($2d$) ferromagnetic (FM) planes of the
layered antiferromagnetic (AFM) structure. While the experimental results have
not yet been fully understood, a recent theory relates the CMR to a topological
vortex-antivortex unbinding, i.e., Berezinskii-Kosterlitz-Thouless (BKT), phase
transition. Motivated by these observations, in this work we explore the
magnetic phases hosted by a microscopic classical magnetic model for
EuCd$_2$P$_2$, which easily generalizes to other Eu A-type antiferromagnetic
compounds. Using Monte Carlo techniques to probe the specific heat and the
helicity modulus, we show that our model can exhibit a vortex-antivortex
unbinding phase transition. We find that this phase transition displays the
same sensitivity to in-plane magnetization, interlayer coupling, and easy-plane
anisotropy that is observed experimentally in the CMR signal, providing
qualitative numerical evidence that the effect is related to a magnetic BKT
transition.

Mesoscale and Nanoscale Physics;Statistical Mechanics