  We report the magnetic and calorimetric measurements in single crystal
samples of the square lattice $J_{1}-J_{2}$ quantum antiferromagnet
BaCdVO(PO$_4$)$_2$. An investigation of the scaling of magnetization reveals a
"dimensionality reduction" indicative of a strong degree of geometric
frustration. Below a characteristic temperature of $T^{\ast}\simeq150$~mK we
observe the emergence of an additional strongly fluctuating quantum phase close
to full magnetic saturation. It is separated from the magnetically ordered
state by first- and second-order phase transitions, depending on the
orientation of the applied magnetic field. We suggest that this phase may
indeed be related to the theoretically predicted spin-nematic state.
