Probing magnetic symmetry in antiferromagnetic <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:msub><mml:msub><mml:mi>Nb</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>9</mml:mn></mml:msub></mml:mrow></mml:math> single crystals by linear magnetoelectric tensor

In the present study, we investigated magnetodielectric, magnetoelectric (ME), and angular-dependent polarization in single-crystal ${\mathrm{Fe}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$. The magnetodielectric effects ${\ensuremath{\varepsilon}}_{x}$ ($x//[100]$), ${\ensuremath{\varepsilon}}_{y}$ ($y//[120]$), ${\ensuremath{\varepsilon}}_{z}$ ($z//[001]$) are found to be significant only around ${T}_{\mathrm{N}}\ensuremath{\approx}95\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ when magnetic fields applied along three orthogonal x-, y- $z$ directions. finite ${P}_{x}, {P}_{y}$, ${P}_{z}$ of 70, 100, $30\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{C}/{\mathrm{m}}^{2}$, respectively, can induced antiferromagnetic phase a field up 9 T is measurements verify dominating linear ME below ${T}_{\mathrm{N}}$. From above experimental results, tensor ${a}_{ij}$ with all nine nonzero components inferred, demonstrating much lower point group $\ensuremath{-}{\mathbf{1}}^{\ensuremath{'}}$ for canted configuration.