The magnetoelectric (ME) effect, the induction of electric polarization ($P$) by an applied magnetic field or magnetization ($M$) by an electric field, provides a pathway for low-power-consumption data memory devices. In this work, we present a systematic experimental investigation of the magnetism, heat capacity, and anisotropic ME effect in $\mathrm{BaN}{\mathrm{i}}_2{\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$ single crystals. Our results reveal long-range antiferromagnetic (AFM) ordering below the Néel temperature $T_N=24\mathrm{K}$, where the $\mathrm{N}{\mathrm{i}}^{2+}$ spins are AFM aligned along the $x$ // [1-10] axis. Detailed ME measurements reveal that $\mathrm{BaN}{\mathrm{i}}_2{\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$ exhibits dominant out-of-plane electric polarization and significant in-plane electric polarization along the $y$ // [110] direction. The largest magnetically induced electric polarization of 128 $\mu \mathrm{C}/{\mathrm{m}}^2$ along the $z$ // [001] axis is observed at $T =2$ K under the magnetic field of ${\mu }_{0}H=9$ T applied along the $x$ direction, with a ME coefficient of α $\sim 16.8$ ps/m. The angular-dependent measurement demonstrates that the induced in-plane electric polarization $P_y$ changes its direction by −2θ around the $z$ axis upon rotating the magnetic field $H$ by an angle θ. Based on the crystal and magnetic symmetry of the honeycomb layer, the microscopic origin of in-plane electric polarization $P_x$ and $P_y$ under $H$ // $z$ and $P_y$ under $H$ // $x$ and $H$ // $y$ can be attributed to the inverse Dzyaloshinskii-Moriya mechanism and the spin-dependent $p\text{−}d$ hybridization mechanism, respectively. Thus, in this work, we provide insights for understanding the microscopic origin of the ME coupling in linear ME materials.

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• Electric polarization
• Magnetoelectric effect
• Antiferromagnets
• Multiferroics
• Crystal growth
• Magnetization measurements