We report static and dynamic properties of the antiferromagnetic compound ${\mathrm{Zn}}_2\left(\mathrm{VO}\right)\left({\mathrm{PO}}_4\right){}_2$, and the consequences of nonmagnetic ${\mathrm{Ti}}^{4+}$ doping at the ${\mathrm{V}}^{4+}$ site. ${}^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rate $\left(1/T_1\right)$ consistently show the formation of the long-range antiferromagnetic order below $T_N=3.8\text{–}3.9$ K. The critical exponent $\beta =0.33\pm 0.02$ estimated from the temperature dependence of the sublattice magnetization measured by ${}^{31}\mathrm{P}$ NMR at 9.4 MHz is consistent with universality classes of three-dimensional spin models. The isotropic and axial hyperfine couplings between the ${}^{31}\mathrm{P}$ nuclei and ${\mathrm{V}}^{4+}$ spins are $A_{\mathrm{hf}}^{\mathrm{iso}}=(9221\pm 100) \mathrm{Oe}/{\mu }_{\mathrm{B}}$ and $A_{\mathrm{hf}}^{\mathrm{ax}}=(1010\pm 50) \mathrm{Oe}/{\mu }_{\mathrm{B}}$, respectively. Magnetic susceptibility data above 6.5 K and heat capacity data above 4.5 K are well described by quantum Monte Carlo simulations for the Heisenberg model on the square lattice with $J\simeq 7.7$ K. This value of $J$ is consistent with the values obtained from the NMR shift, $1/T_1$, and electron spin resonance intensity analysis. Doping ${\mathrm{Zn}}_2\mathrm{VO}{(\mathrm{PO}}_4{)}_2$ with nonmagnetic ${\mathrm{Ti}}^{4+}$ leads to a marginal increase in the $J$ value and the overall dilution of the spin lattice. In contrast to the recent ab initio results, we find neither evidence for the monoclinic structural distortion nor signatures of the magnetic one-dimensionality for doped samples with up to 15% of ${\mathrm{Ti}}^{4+}$. The Néel temperature $T_{\mathrm{N}}$ decreases linearly with increasing the amount of the nonmagnetic dopant.

• Received 10 September 2014
• Revised 9 December 2014

DOI:https://doi.org/10.1103/PhysRevB.91.024413