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 in ${\varepsilon }_x$ ($x//\left[100\right]$), ${\varepsilon }_y$ ($y//\left[120\right]$), and ${\varepsilon }_z$ ($z//\left[001\right]$) are found to be significant only around $T_{\mathrm{N}}\approx 95\mathrm{K}$ when magnetic fields are applied along three orthogonal x-, y- ($y//\left[120\right]$), and $z$ directions. The finite polarization $P_x, P_y$, and $P_z$ of 70, 100, and $30\mu \mathrm{C}/{\mathrm{m}}^2$, respectively, can be induced in the antiferromagnetic phase when a finite magnetic field up to 9 T is applied along the three orthogonal directions. The angular-dependent polarization measurements verify the dominating linear ME effects below $T_{\mathrm{N}}$. From the above experimental results, a linear ME tensor $a_{ij}$ with all nine nonzero components can be inferred, demonstrating a much lower magnetic point group of $-{\mathbf{1}}^{\prime }$ for the canted antiferromagnetic configuration.

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• Antiferromagnetism
• Ferroelectricity
• Magneto-dielectric effect
• Magnetoelectric effect