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We report static and dynamic properties of the antiferromagnetic compoundZn$_{2}$(VO)(PO$_{4}$)$_{2}$, and the consequences of non-magnetic Ti$^{4+}$doping at the V$^{4+}$ site. $^{31}$P nuclear magnetic resonance (NMR) spectraand spin-lattice relaxation rate ($1/T_1$) consistently show the formation ofthe long-range antiferromagnetic order below $T_N= 3.8-3.9$\,K. The criticalexponent $\beta=0.33 \pm 0.02$ estimated from the temperature dependence of thesublattice magnetization measured by $^{31}$P NMR at 9.4\,MHz is consistentwith universality classes of three-dimensional spin models. The isotropic andaxial hyperfine couplings between the $^{31}$P nuclei and V$^{4+}$ spins are$A_{\rm hf}^{\rm iso} = (9221 \pm 100)$ Oe/$\mu_{\rm B}$ and $A_{\rm hf}^{\rmax} = (1010 \pm 50)$ Oe/$\mu_{\rm B}$, respectively. Magnetic susceptibilitydata above 6.5\,K and heat capacity data above 4.5\,K are well described byquantum Monte-Carlo simulations for the Heisenberg model on the square latticewith $J\simeq 7.7$\,K. This value of $J$ is consistent with the values obtainedfrom the NMR shift, $1/T_1$ and electron spin resonance (ESR) intensityanalysis. Doping Zn$_2$VO(PO$_4)_2$ with non-magnetic Ti$^{4+}$ leads to amarginal increase in the $J$ value and the overall dilution of the spinlattice. In contrast to the recent \textit{ab initio} results, we find neitherevidence for the monoclinic structural distortion nor signatures of themagnetic one-dimensionality for doped samples with up to 15\% of Ti$^{4+}$. TheN\'eel temperature $T_{\rm N}$ decreases linearly with increasing the amount ofthe non-magnetic dopant.

Antiferromagnetism of Zn$_2$VO(PO$_4)_2$ and the dilution with Ti$^{4+}$