High-resolution neutron diffraction determination of noncollinear antiferromagnetic order in the honeycomb magnetoelectric <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Fe</mml:mi> <mml:mn>4</mml:mn> </mml:ms

Magnetoelectric systems offer potential for device applications exploiting coupled states between electric and magnetic properties. Among magnetoelectric materials, ${\mathrm{Fe}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$ has attracted special attention because of its pronounced dielectric signal at high magnetic transition temperatures. However, the magnetic ground state, which is essential information for understanding its unusual magnetoelectricity, remains unclarified. Here, we report a noncollinear magnetic ground state of ${\mathrm{Fe}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$. To examine the magnetoelectric effect associated with sequential magnetic and structural transitions upon cooling, we conducted combined x-ray diffraction, magnetic susceptibility, magnetization, dielectric constant, and magnetodielectric experiments. Powder neutron diffraction experiments revealed a series of magnetic Bragg peaks and clear splitting of peaks via structural transition. Magnetic Rietveld refinements, combined with group theory analysis, determined a noncollinear antiferromagnetic structure including a significant $c$-axis moment component at 1.5 K. This study provides insights into the understanding of its magnetoelectric properties.