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We report the anomalous breakdown in the scaling of the microscopic magneticsusceptibility, as measured via the ${}^{31}$P nuclear magnetic resonance (NMR)shift $K$, with the bulk magnetic susceptibility $\chi$ in the paramagneticstate of Mn$_2$P$_2$S$_6$. This anomaly occurs near $T_\mathrm{max} \sim 117$ Kthe maximum in $\chi(T)$ and is therefore associated with the onset ofquasi-two-dimensional (quasi-2D) magnetic correlations. The spin-latticerelaxation rate divided by temperature $(T_1T)^{-1}$ in Mn$_2$P$_2$S$_6$exhibits broad peak-like behavior as a function of temperature, qualitativelyfollowing $\chi$, but displaying no evidence of critical slowing down above theN\'{e}el temperature $T_N$. In the magnetic state of Mn$_2$P$_2$S$_6$, NMRspectra provide good evidence for 60 degree rotation of stacking-fault-inducedmagnetic domains, as well as observation of the spin-flop transition thatonsets at 4 T. The temperature-dependent critical behavior of the internalhyperfine field at the P site in Mn$_2$P$_2$S$_6$ is consistent with previousmeasurements and the two-dimensional anisotropic Heisenberg model. In a sampleof Ni$_2$P$_2$S$_6$, we observe only two magnetically split resonances in themagnetic state, demonstrating that the multiple-peaked NMR spectra previouslyassociated with 60 degree rotation of stacking faults is sample dependent.Finally, we report the observation of a spin-flop-induced splitting of the NMRspectra in Ni$_2$P$_2$S$_6$, with an onset spin-flop field of $H_\mathrm{sf} =14$ T.

${}^{31}$P NMR investigation of quasi-two-dimensional magnetic correlations in $T_2$P$_2$S$_6$ ($T$ = Mn & Ni)