  The static and dynamic properties of V^{4+} spins (S = 1/2) in the frustrated
square lattice compound Pb2(VO)(PO4)2 were investigated by means of magnetic
susceptibility chi and 31P nuclear magnetic resonance (NMR) shift (K) and 31P
nuclear spin-lattice relaxation rate 1/T1 measurements on a single crystal.
This compound exhibits long-range antiferromagnetic order below TN \simeq 3.65
K. NMR spectra above TN 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
towards 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 to be J1/kB = (-5.4 \pm 0.5) K
(ferromagnetic) and J2/kB = (9.3 \pm 0.6) K (antiferromagnetic), respectively.
1/(T1 T chi) is almost T-independent at high temperatures due to random
fluctuation of spin moments. Below 20 K, the compound shows an enhancement of
1/(T1 T chi) which arises from a growth of antiferromagnetic spin correlations
above TN. Below TN 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 J2/J1 \simeq -1.72
ratio. The critical exponent beta = 0.25 \pm 0.02 estimated from the
temperature dependence of sublattice magnetization as measured by 31P NMR at
11.13 MHz is close to the value (0.231) predicted for the two-dimensional XY
model.
