  Crystal structure and magnetic properties of the layered vanadium phosphate
PbZnVO(PO4)2 are studied using x-ray powder diffraction, magnetization and
specific heat measurements, as well as band structure calculations. The
compound resembles AA'VO(PO4)2 vanadium phosphates and fits to the extended
frustrated square lattice model with the couplings J(1), J(1)' between
nearest-neighbors and J(2), J(2)' between next-nearest-neighbors. The
temperature dependence of the magnetization yields estimates of averaged
nearest-neighbor and next-nearest-neighbor couplings, J(1) ~ -5.2 K and J(2) ~
10.0 K, respectively. The effective frustration ratio alpha=J(2)/J(1) amounts
to -1.9 and suggests columnar antiferromagnetic ordering in PbZnVO(PO4)2.
Specific heat data support the estimates of J(1) and J(2) and indicate a likely
magnetic ordering transition at 3.9 K. However, the averaged couplings
underestimate the saturation field, thus pointing to the spatial anisotropy of
the nearest-neighbor interactions. Band structure calculations confirm the
identification of ferromagnetic J(1), J(1)' and antiferromagnetic J(2), J(2)'
in PbZnVO(PO4)2 and yield J(1)'-J(1) ~ 1.1 K in excellent agreement with the
experimental value of 1.1 K, deduced from the difference between the expected
and experimentally measured saturation fields. Based on the comparison of
layered vanadium phosphates with different metal cations, we show that a
moderate spatial anisotropy of the frustrated square lattice has minor
influence on the thermodynamic properties of the model. We discuss relevant
geometrical parameters, controlling the exchange interactions in these
compounds, and propose a new route towards strongly frustrated square lattice
materials.
