  We study the influence of the spin lattice distortion on the properties of
frustrated magnetic systems and consider the applicability of the spin-1/2
frustrated square lattice model to materials lacking tetragonal symmetry. We
focus on the case of layered vanadium phosphates AA'VO(PO4)2 (AA' = Pb2, SrZn,
BaZn, and BaCd). To provide a proper microscopic description of these
compounds, we use extensive band structure calculations for real materials and
model structures and supplement this analysis with simulations of thermodynamic
properties, thus facilitating a direct comparison with the experimental data.
Due to the reduced symmetry, the realistic spin model of layered vanadium
phosphates AA'VO(PO4)2 includes four inequivalent exchange couplings: J1 and
J1' between nearest-neighbors and J2 and J2' between next-nearest-neighbors.
The estimates of individual exchange couplings suggest different regimes, from
J1'/J1 and J2'/J2 close to 1 in BaCdVO(PO4)2, a nearly regular frustrated
square lattice, to J1'/J1 ~ 0.7 and J2'/J2 ~ 0.4 in SrZnVO(PO4)2, a frustrated
square lattice with sizable distortion. The underlying structural differences
are analyzed, and the key factors causing the distortion of the spin lattice in
layered vanadium compounds are discussed. We propose possible routes for
finding new frustrated square lattice materials among complex vanadium oxides.
Full diagonalization simulations of thermodynamic properties indicate the
similarity of the extended model to the regular one with averaged couplings. In
case of moderate frustration and moderate distortion, valid for all the
AA'VO(PO4)2 compounds reported so far, the distorted spin lattice can be
considered as a regular square lattice with the couplings (J1+J1')/2 between
nearest-neighbors and (J2+J2')/2 between next-nearest-neighbors.
