High Pressure $^{31}$P-NMR Study of the 2D Frustrated Square-Lattice Compound BaCdVO(PO$_{4})_{2}$ at Low Temperatures*

BaCdVO(PO$_{4})_{2}$ is a $S $= 1/2 frustrated square-lattice (FSL) compound with a nearest neighbor exchange coupling $J_{1}\sim $ - 3.36 K and a next-nearest neighbor exchange coupling $J_{2}\sim $ 3.53 K bearing $J_{2}$/$J_{1}\sim $ 1.05. Based on the $J_{2}$/$J_{1}$ ratio, the system is known to be located close to the disordered ground state (known as `nematic state') regime of the phase diagram. We have carried out $^{31}$P-NMR measurements under high pressure ($\sim $ 1 GPa) and at low temperatures using dilution refrigerator to investigate the pressure effects on the magnetic properties of the system. Under ambient pressure at $H $= 2.67 T, we observed a sharp peak in $^{31}$P spin lattice relaxation rate (1/$T_{1})$ at $T_{N}\sim $ 1.05 K, which corresponds to the antiferromagnetic ordering temperature. On the other hand, under a pressure of 1 GPa, the peak in 1/$T_{1}$ is suppressed and 1/$T_{1}$ shows a sudden decrease below $\sim $ 0.75 K. This indicates that $T_{N}$ decreases with the application of pressure. We will report the temperature dependence of the NMR spectra and of the 1/$T_{1}$ under different magnetic fields and pressures.