The connection of strength of magnetic interactions and type ordering the
magnetic moments with crystal chemical characteristics in low-dimensional
magnets is investigated. The new method to calculate the sign and relative
strength of magnetic interactions in low-dimensional systems on the basis of
the structural data is proposed. This method allows to estimate magnetic
interactions not only inside low-dimensional fragments but also between them,
and also to predict the possibility of the occurrence of magnetic phase
transitions and anomalies of the magnetic interactions. Moreover, it can be
used for search of low-dimensional magnets among the compounds whose crystal
structures are known. The possibilities of the method are illustrated in an
example of research of magnetic interactions in familiar low-dimensional
magnets SrCu2(BO3)2, CaCuGe2O6, CaV4O9, Cu2Te2O5Cl2, Cu2Te2O5Br2, BaCu2Si2O7,
BaCu2Ge2O7, BaCuSi2O6, LiCu2O2, and NaCu2O2.Comment: 18 pages, 8 figures, 2 tables, published versio