Detailed ${}^{31}$P nuclear magnetic resonance (NMR) measurements are presented on well-characterized single crystals of antiferromagnetic van der Waals Ni$_2$P$_2$S$_6$. An anomalous breakdown is observed in the proportionality of the NMR shift $K$ with the bulk susceptibility $chi$. This so-called $K$$-$$chi$ anomaly occurs in close proximity to the broad peak in $chi(T)$, thereby implying a connection to quasi-2D magnetic correlations known to be responsible for this maximum. Quantum chemistry calculations show that crystal field energy level depopulation effects cannot be responsible for the $K$$-$$chi$ anomaly. Appreciable in-plane transferred hyperfine coupling is observed, which is consistent with the proposed Ni$-$S$-$Ni super- and Ni$-$S$-$S$-$Ni super-super-exchange coupling mechanisms. Magnetization and spin$-$lattice relaxation rate ($T_1^{-1}$) measurements indicate little to no magnetic field dependence of the Neel temperature. Finally, $T_1^{-1}(T)$ evidences relaxation driven by three-magnon scattering in the antiferromagnetic state.
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