Competing Magnetic Superexchange Interactions in Layered Vanadyl Phosphate Hydrates

Abstract We present a comprehensive investigation of the layered vanadyl phosphate hydrates Ni(VO)2(PO4)2·4H2O (NiVP) and Co(VO)2(PO4)2·4H2O (CoVP), combining anisotropic magnetic susceptibility, heat capacity measurements, Density Functional Theory (DFT) calculations, and X-ray charge density analysis. Magnetization measurements reveal a ferromagnetic response along the crystallographic c-axis and an antiferromagnetic response within the ab-plane. Both compounds exhibit the presence of magnetocrystalline anisotropy, consistent with an easy-plane anisotropic magnetic state in NiVP, while in CoVP, strong spin–orbit coupling leads to a more complex behaviour that prevents a straightforward determination of the moment orientation. Prior to the onset of three-dimensional magnetic ordering at TN ≈ 4 K, both systems develop significant short-range spin correlations, as evidenced by deviations from the Curie–Weiss behaviour and a reduced λ-type anomaly in heat capacity, indicating a gradual crossover from low-dimensional correlations to three-dimensional ordering. DFT calculations consistently identify a ground state of columnar antiferromagnetic intralayer ordering and ferromagnetic interlayer coupling mediated by trimeric units. The exchange hierarchy indicates anisotropic intralayer interactions dominated by next-nearest-neighbour exchange, while interlayer coupling plays a leading role in establishing a three-dimensional order. Comparison between 3d orbital populations obtained from multipole model-refined experimental charge densities and DFT Mulliken analysis shows good agreement, validating the electronic structure description. The results highlight the importance of orbital polarization in establishing different superexchange pathways through phosphate groups, with interlayer coupling primarily governed by σ-type interactions and intralayer exchange involving π-mediated interactions, mediated by the molecular orbital of the bridging phosphate group between the metal centers.