$^{31}$P-NMR Study of the Effect of Pressure on the Magnetic Properties of the 2d Frustrated Square-Lattice Compound BaCdVO(PO$_{4})_{2}$ at Low Temperatures*

BaCdVO(PO$_{4})_{2}$ is a spin $S =$ 1/2 frustrated square-lattice compound with a nearest-neighbor exchange coupling $J_{1} = -$3.62 K and a next-nearest-neighbor exchange coupling $J_{2} =$ 3.18 K yielding \textbar $J_{2}$/$J_{1}$\textbar $=$ 0.88. A transition to an antiferromagnetic (AFM) ground state occurs below a temperature $T_{\mathrm{N}} =$ 1.0 K under ambient pressure $p$. Based on the $J_{2}$/$J_{1}$ ratio, the system is located close to the disordered ground state (``nematic state'') regime of the phase diagram. We carried out $^{31}$P-NMR measurements under high $p$, ranging from 0.74 GPa to 1.88 GPa, and at low temperatures $T$ down to 100 mK, to investigate the effects of $p$ on the magnetic properties of the system. With increasing $p$, the $T_{\mathrm{N}}$ does not change much, but the magnetization saturation field $H_{\mathrm{S}}$ is significantly suppressed from $H_{\mathrm{S}} =$ 4.2 T at ambient $p$ to $H_{\mathrm{S}} =$ 0.55 T at $p =$ 1.88 GPa. Our $^{31}$P-NMR spectra and spin-lattice relaxation rate (1/$T_{1})$ data establish the first $H$--$p$--$T$ phase diagram for this system.