We performed powder neutron diffraction experiments on a $\frac{1}{2}$ quantum magnetization plateau compound ${\mathrm{Ni}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{7}$ for magnetic fields in the range 0--10 T. The incommensurate magnetic structures with the propagation vector $({k}_{x}\ensuremath{\sim}0.45,0,0)$ were determined at 0 T and at 6.0 K (between ${T}_{\mathrm{N}1}=6.7$ K and ${T}_{\mathrm{N}2}=5.7$ K) and 2.3 K. Consequently, the Ni1 and Ni2 moments were disordered and ordered at 6.0 K, respectively, indicating a partially disordered state. The magnetic structure of Ni2 moments was a spin density wave structure with moments ordered parallel to the $b$ axis and perpendicular to the propagation vector. Both Ni1 and Ni2 moments exhibited ellipsoidal cycloidal incommensurate magnetic structures at 2.3 K. These moments lay in the $ab$ plane. The maximum magnitudes of Ni1 and Ni2 moments [1.62(16) and 2.50(6) ${\textmu{}}_{\mathrm{B}}$] at 2.3 K were sufficiently smaller and slightly larger than the value ($\ensuremath{\sim}2.2\phantom{\rule{0.28em}{0ex}}{\textmu{}}_{\mathrm{B}}$) expected from the classical picture. Further, we evaluated the field-induced magnetic moments as follows: ${m}_{1}=0.3$ and ${m}_{2}=1.9\phantom{\rule{0.28em}{0ex}}{\textmu{}}_{\mathrm{B}}$ at Ni1 and Ni2 sites, respectively, at 10 T and 1.9 K, where the $\frac{1}{2}$ quantum magnetization plateau was observed. The results indicating both the ordered moment at 0 T and the field-induced moment at 10 T being small and large at Ni1 and Ni2 sites, respectively, were consistent with results expected in the $\text{dimer}+\text{monomer}$ model that was proposed by J. J. Cao et al. [Phys. Rev. B 106, 184409 (2022)].
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