Thermodynamics of a frustrated quantum magnet on a square lattice

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.