Canted Antiferromagnetic phases in the layered candidate Weyl material EuMnSb$_2$

EuMnSb$_2$ is a candidate topological material which can be tuned towards a Weyl semimetal, but there are differing reports for its antiferromagnetic (AFM) phases. The coupling of bands dominated by pure Sb layers hosting topological fermions to Mn and Eu magnetic states provides a potential path to tune the topological properties. We present a detailed analysis of the magnetic structure on three AFM phases based on single-crystal neutron diffraction, magnetization, and heat capacity data as well as polycrystalline $^{151}$Eu M\"ossbauer data. The Mn magnetic sublattice orders into a C-type AFM structure below $323(1)$~K with the ordered Mn magnetic moment $\mu_{\text{Mn}}$ lying perpendicular to the layers. AFM ordering of the Eu sublattice occurs below $23(1)$~K with the ordered Eu magnetic moment $\mu_{\text{Eu}}$ canted away from the layer normal and $\mu_{\text{Mn}}$ retaining its higher-temperature order. $\mu_{\text{Eu}}$ is ferromagnetically aligned within each Eu layer but exhibits a complicated AFM layer stacking. Both of these higher-temperature phases are described by magnetic space group (MSG) $Pn^{\prime}m^{\prime}a^{\prime}$ with the chemical and magnetic unit cells having the same dimensions. Cooling below $=9(1)$~K reveals a third AFM phase where $\mu_{\text{Mn}}$ remains unchanged but $\mu_{\text{Eu}}$ develops an additional in-plane canting. This phase has MSG $P11\frac{2_1}{a^{\prime}}$. We additionally find evidence of short-range magnetic correlations associated with the Eu between $12~\text{K} \lesssim T \lesssim 30~\text{K}$. Using the determined magnetic structures, we postulate the signs of nearest-neighbor intralayer and interlayer exchange constants and the magnetic anisotropy within a general Heisenberg-model. We then discuss implications of the various AFM states in EuMnSb$_2$ and its topological properties.