Collinear Magnetic Structure in the Diamond Network Magnet EuTi$_2$Al$_{20}$

The magnetic structure of EuTi$_2$Al$_{20}$, in which magnetic Eu$^{2+}$ ions form a diamond network, was investigated using neutron and resonant X-ray diffraction on powder and single-crystal samples. The propagation vector was determined to be $\textbf{\textit{q}}_{\rm m}=(1,0,0)$~r.l.u. from these diffraction measurements. All possible magnetic structures in the space group $Fd\bar{3}m$ with this propagation vector were examined using the irreducible representation method and magnetic space group analysis. This magnetic structure was identified as a collinear antiferromagnetic structure with the magnetic space group $P_Inna$ (\#52.320) or $P_Inn2$ (\#34.164) under zero magnetic field. In these magnetic structure, frustration arises from competing magnetic interactions on the diamond network. These findings provide a concrete experimental reference for assessing the role of competing interactions in diamond-network magnets and motivate further studies of interaction-driven quantum states.