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 KEY WORDS: low-dimensional magnetic system; magnetic interaction; crystal chemistry; new method. 3NN. The nearest-neigh or couplings 1NN ( = s J 1 -0.003 Å -1 (AF), d(Cu-Cu) = 3.072 Å), 2NN ( = 0.001 Å -1 (FM), d(Cu-Cu) = 5.213 Å) and 3NN ( = 0.002 Å -1 (FM), d(Cu-Cu) = 5.576 Å) are really very weak ( s J 2 s J 3 s s J J 4 1 = 0.06, s s J J 4 2 = -0.02 and s s J J 4 3 J 4 s J 4 s s J J 4 1 =0.22(0.19), and it to be represented as tetramers because the intratetrahedral couplings s s J J 2 4 >> ( s s J J 4 2 = -0.13 (-0.17)). In both Cl(Br) systems these tetramers are coupled in layers, which are perpendicular to c axes, by strong AF interactions , and ( s J 12 s J 15 s J 14 s s J J 4 12 = 0.62(0.49), s s J J 4 15 = 0.58(0.46), and s s J J 4 14 = 0.37(0.36)), and also by strong and ( s J 11 s J ' 11 s s J J 4 11 = -0.85(-1.06), s s J J 4 ' 11 =-0.91(-0.83)) and weak and ( s J 3 s J 16 s s J J 4 3 = -0.26(-0.15) and s s J J 4 16 = -0.37(-0.08)) FM interactions. Notice that the absolute value decreases ( s J 11 s s J J 4 11 = -0.26 (-0.55)) if the large contribution to the interactions from the intermediate ions Cl(1) for Cl compound and O(1) for Br compound, located in critical position near to border of the space of interaction (critical point (a), see Section 3) are not to take into account. In addition, between the tetramers in a layer exist the couplings and , which are different for Cl and Br systems. In Cl system, the couplings are weak AF ( s J 8 s J 13 s s J J 4 8 = 0.06, s s J J 4 13 = 0.06), and in Br system, the opposite, i.e. strong FM ( s s J J 4 8 = -0.47, s s J J 4 13 = -0.30). This is because the intermediate ions O(3) are located in critical position (critical point (a), see Section 3). The layers from tetramers are bound together by strong and weak FM interactions , , and ( s J 9 s J 7 s J 5 s J 10 s s J J 4 9 = -0.87(-0.81), s s J J 4 7 = -0.87(-0.89), s s J J 4 5 = -0.52(-0.66) and s s J J 4 10 = -0.11(-0.13)) and weak AF interactions ( s J 1 s s J J 4 1 = 0.22(0.19), which are similar in both the systems. Notice that the value | s s J J 4 7 | decreases till −0.26 (−0.25) if the calculation of coupling does not take into account the contribution from an intermediate ion Cu, locat...
