The static and dynamic properties of ${\text{V}}^{4+}$ spins $\left(S=1/2\right)$ in the frustrated square-lattice compound ${\text{Pb}}_2\left(\text{VO}\right){\left({\text{PO}}_4\right)}_2$ were investigated by means of magnetic susceptibility $\chi$ and ${}^{31}\text{P}$ nuclear magnetic resonance (NMR) shift $\left(K\right)$ and ${}^{31}\text{P}$ nuclear spin-lattice relaxation rate $1/T_1$ measurements on a single crystal. This compound exhibits long-range antiferromagnetic order below $T_{\text{N}}\simeq 3.65\text{K}$. NMR spectra above $T_{\text{N}}$ show two distinct lines corresponding to two inequivalent P sites present in the crystal structure. The observed asymmetry in hyperfine coupling constant for the in-plane (P1) P site directly points toward a distortion in the square lattice at the microscopic level, consistent with the monoclinic crystal structure. The nearest- and next-nearest-neighbor exchange couplings were estimated by fitting $K$ versus temperature $T$ by a high-temperature series expansion for the spin susceptibility of the frustrated square lattice to be $J_1/k_{\text{B}}=\left(-5.4\pm 0.5\right)\text{K}$ (ferromagnetic) and $J_2/k_{\text{B}}=\left(9.3\pm 0.6\right)\text{K}$ (antiferromagnetic), respectively. $1/\left(T_{1}T\chi \right)$ is almost $T$ independent at high temperatures due to random fluctuation of spin moments. Below 20 K, the compound shows an enhancement of $1/\left(T_{1}T\chi \right)$ which arises from a growth of antiferromagnetic spin correlations above $T_{\text{N}}$. Below $T_{\text{N}}$ and for the field applied along the $c$ axis, the NMR spectrum for the P1 site splits into two satellites and the spacing between them increases monotonically with decreasing $T$ which is a direct evidence of a columnar antiferromagnetic ordering with spins lying in the $ab$ plane. This type of magnetic ordering is consistent with expectation from the $J_2/J_1\simeq -1.72$ ratio. The critical exponent $\beta =0.25\pm 0.02$ estimated from the temperature dependence of the sublattice magnetization as measured by ${}^{31}\text{P}$ NMR at 11.13 MHz is close to the value (0.231) predicted for the two-dimensional XY model.

• Received 18 September 2009

DOI:https://doi.org/10.1103/PhysRevB.80.214430