Magnetic order in frustrated Kagome-Triangular lattice antiferromagnet NaBa$_{\mathrm{2}}$Mn$_{\mathrm{3}}$F$_{\mathrm{11}}$

We performed powder neutron diffraction experiments on NaBa$_{\mathrm{2}}$Mn$_{\mathrm{3}}$F$_{\mathrm{11}}$ [1], a model compound of \textit{Kagome-Triangular} lattice where three of six next-nearest neighbor interactions are non-negligible. More than 10 magnetic Bragg peaks are clearly observed below $T \quad =$ 2 K, meaning that the ground state is a magnetically ordered state. From indexing the magnetic Bragg peaks, magnetic propagation vector of \textbf{\textit{q}}$_{\mathrm{0}} \quad =$ (0, 0, 0) and two incommensurate vectors which are close to (1/3, 1/3, 0) are identified. Combination of representation analysis and Rietveld refinement reveals that the propagation vector of \textbf{\textit{q}}$_{\mathrm{0}}$ exhibits the 120º structure in the \textit{ab}-plane. Our calculation of the ground state suggests that the non-negligible magnetic dipolar interaction is responsible for the determined 120º structure in NaBa$_{\mathrm{2}}$Mn$_{\mathrm{3}}$F$_{\mathrm{11}}$. Reference [1] H. Ishikawa \textit{et al}., J. Phys. Soc. Jpn. \textbf{83}, 043703 (2014).