Coupling of magnetic order and charge transport in the candidate Dirac semimetal $\mathrm{EuCd_{2}As_{2}}$

EuCd$_2$As$_2$ is a magnetic semimetal with unusual transport properties. It features similar networks of edge-sharing CdAs$_4$ tetrahedra to those found in the bulk Dirac semimetal Cd$_3$As$_2$, but in a layered, rather than three-dimensional, geometry and with interleaved planes of magnetic Eu$^{2+}$ ions. Here we use resonant elastic x-ray scattering to determine the evolution of magnetic order in EuCd$_2$As$_2$ below $T_\textrm{N}=9.5\,\textrm{K}$, as a function of temperature and applied magnetic field. We find an A-type antiferromagnetic structure with in-plane magnetic moments, and we observe dramatic magnetoresistive effects associated with field-induced changes in the magnetic structure and domain populations. Our ab initio electronic structure calculations indicate that the Dirac dispersion found in Cd$_3$As$_2$ is also present in EuCd$_2$As$_2$, but is gapped for $T < T_\textrm{N}$ due to the breaking of $C_3$ symmetry by the magnetic structure.