The study of nearest- and next-nearest-neighbour magnetic interactions   in seven tetragonal compounds V(IV) containing linear chains and square   lattices
  A new crystal chemical method was used to calculate the sign and strength not only of the nearest-neighbor (NN)interactions, but also of the next-nearest-neighbor (NNN) ones in tetragonal compounds Zn2(VO)(PO4)2 (I),(VO)(H2PO4)2 (II), (VO)SiP2O8 (III), (VO)SO4 (IV), (VO)MoO4 (V), Li2(VO)SiO4 (VI) and Li2(VO)GeO4 (VII) with similar sublattices of V4+ ions on the basis of the room-temperature structural data. The reason for difference between respective magnetic interactions characteristics of these compounds was established. It is shown that the characteristic feature of these compounds is a strong dependence of the strength of magnetic interactions and the magnetic moments ordering type on slight displacements of XO4 (X = P, Mo, Si or Ge) groups even without change of the crystal symmetry. In addition to extensively studied square lattice, other specific geometrical configurations of V4+ were discovered. These configurations can result in frustration of magnetic interactions, namely linear chains along the c-axis with competing nearest- and next-to-nearest-neighbor interactions; rectangular (in I) and triangular (in II-VII) lattices with non-equivalent nearest-to-neighbor interactions, which can be also considered as n-leg ladders; one extra square lattice in the ab-plane with longer range interactions. It was concluded that virtually all magnetic interactions in these compounds were frustrated. 
L.M. Volkova and S.A. Polyshchuk