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

New Method to Calculate the Sign and Relative Strength of Magnetic Interactions in Low-Dimensional Systems on the Basis of Structural Data