Extension of the spin-1/2 frustrated square lattice model: The case of layered vanadium phosphates

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' = Pb-2, 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: J(1) and J(1)' between nearest-neighbors and J(2) and J(2)' between next-nearest-neighbors. The estimates of individual exchange couplings suggest different regimes, from J(1)'/J(1) and J(2)'/J(2) close to 1 in BaCdVO(PO4)(2), a nearly regular frustrated square lattice, to J(1)'/J(1) similar or equal to 0.7 and J(2)'/J(2) similar or equal to 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 (J(1) + J(1)')/2 between nearest-neighbors and (J(2) + J(2)')/2 between next-nearest-neighbors.