Motivated by theoretical predictions suggesting that ilmenite-type $\mathrm{MnGe}{\mathrm{O}}_3$ (i-MGO) may host a topological quantum state known as an antiferromagnetic Dirac semimetal, we have conducted a comprehensive investigation of its structural, magnetic, electronic, both linear and nonlinear optical properties, using both polycrystalline and single-crystalline samples obtained via high-pressure synthesis techniques. Single-crystal magnetization measurements have not only confirmed the antiferromagnetic transition at $T_{\mathrm{N}}=96\mathrm{K}$, previously observed in the polycrystalline samples, but also revealed a clear spin-flop transition at 60 kOe in an applied field along the $c$ axis. This bulk observation provides macroscopic evidence supporting the previously proposed antiferromagnetic structure, characterized by $\mathrm{M}{\mathrm{n}}^{2+}$ magnetic moments aligned along the $c$ axis with a propagation vector $\mathbf{k}=(0,0,0)$, which breaks both space-inversion ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetries. Furthermore, our powder neutron diffraction measurements independently confirm this magnetic structure. Electrical and optical measurements have shown that i-MGO is highly insulating and transmissive in the visible range, thereby excluding the theoretically predicted Dirac semimetal state. Our density functional theory calculations reveal that this discrepancy originates from the use of incorrect structural parameters in previous theoretical studies. As a clear manifestation of the broken $\mathcal{P}$ and $\mathcal{T}$ symmetries in the antiferromagnetic phase, we have observed a linear magnetoelectric effect and a pronounced optical second harmonic generation signal. These findings not only resolve the inconsistency with prior predictions but also establish i-MGO as a platform for studying symmetry-breaking-driven electromagnetic responses in ilmenite-type materials.

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• Electronic structure
• Magnetoelectric effect
• Topological materials
• Antiferromagnets
• Honeycomb lattice
• Magnetic insulators
• Density functional calculations
• Optical second-harmonic generation