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We report the structural and magnetic properties of a new spin-$\frac12$antiferromagnet NaZnVOPO$_4$(HPO$_4$) studied via x-ray diffraction, magneticsusceptibility, high-field magnetization, specific heat, and $^{31}$P nuclearmagnetic resonance (NMR) measurements, as well as density-functionalband-structure calculations. While thermodynamic properties of this compoundare well described by the $J_1-J_2$ square-lattice model, \textit{ab initio}calculations suggest a significant deformation of the spin lattice. From fitsto the magnetic susceptibility we determine the averaged nearest-neighbor andsecond-neighbor exchange couplings of $\bar J_1\simeq -1.3$ K and $\barJ_2\simeq 5.6$ K, respectively. Experimental saturation field of 15.3\,T isconsistent with these estimates if 20\% spatial anisotropy in $J_1$ is takeninto account. Specific heat data signal the onset of a magnetic long-rangeorder at $T_{\rm N} \simeq 2.1$ K, which is further supported by a sharp peakin the NMR spin-lattice relaxation rate. The NMR spectra mark the superpositionof two P lines due to two noneqivalent P sites where the broad line with thestrong hyperfine coupling and short $T_1$ is identified as the P(1) sitelocated within the magnetic planes, while the narrow line with the weakhyperfine coupling and long $T_1$ is designated as the P(2) site locatedbetween the planes.

Deformed spin-$\frac12$ square lattice in antiferromagnetic NaZnVOPO$_4$(HPO$_4$)