Topological magnetic phase transition in Eu-based A -type antiferromagnets

Recently, a colossal magnetoresistance (CMR) was observed in $\mathrm{Eu}{\mathrm{Cd}}₂{\mathrm{P}}₂$, a compound that does not fit the conventional mixed-valence paradigm. Instead, experimental evidence points to a resistance driven by strong magnetic fluctuations within the two-dimensional ferromagnetic planes of the layered antiferromagnetic 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 $\mathrm{Eu}{\mathrm{Cd}}₂{\mathrm{P}}₂$, 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.