We report here a comprehensive study of the AFM structures of the Eu and Mn magnetic sublattices as well as the interplay between Eu and Mn magnetism in this compound by using both polarized and non-polarized single-crystal neutron diffraction. Magnetic susceptibility, specific heat capacity measurements and the temperature dependence of magnetic diffractions suggest that the AFM ordering temperature of the Eu and Mn moments is at 22 and 337 K, respectively. The magnetic moments of both Eu and Mn ions are oriented along the crystallographic $c$ axis, and the respective magnetic propagation vector is $textbf{k}_{Eu} = (0,0,1)$ and $textbf{k}_{Mn}=(0,0,0)$. With proper neutron absorption correction, the ordered moments are refined at 3 K as 7.7(1) $mu_B$ and 4.1(1) $mu_B$ for the Eu and Mn ions, respectively. In addition, a spin-flop (SF) phase transition of the Eu moments in an applied magnetic field along the $c$ axis was confirmed to take place at a critical field of B$_c$ $sim$ 5.3 T. The evolution of the Eu magnetic moment direction as a function of the applied magnetic field in the SF phase was also determined. Clear kinks in both field and temperature dependence of the magnetic reflections ($pm1$, 0, 1) of Mn were observed at the onset of the SF phase transition and the AFM order of the Eu moments, respectively. This unambiguously indicates the existence of a strong coupling between Eu and Mn magnetism. The interplay between two magnetic sublattices could bring new possibilities to tune Dirac fermions via changing magnetic structures by applied fields in this class of magnetic topological semimetals.
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