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...

The origin of magnetic frustration was stated and the ions whose shift is accompanied by emerging magnetic ordering and ferroelectricity in TbMn 2 O 5 and BiMn 2 O 5 were determined on the basis of calculation of magnetic coupling parameters by using the structural data. The displacements accompanying the magnetic ordering are not polar, they just induce changes of bond valence (charge disordering) of Mn1 and Mn2, thus creating instability of the crystal structure. To approximate again the bond valence to the initial value (charge ordering) under magnetic ordering conditions is possible only due to polar displacement of Mn2 (or O1) and O4 ions along the b axis that is the cause of ferroelectric transition.

In this paper we examine the role of crystal chemistry factors in creating conditions for formation of magnetoelectric ordering in BiFeO 3 . It is generally accepted that the main reason of the ferroelectric distortion in BiFeO 3 is concerned with a stereochemical activity of the Bi lone pair. However, the lone pair is stereochemically active in the paraelectric orthorhombic ß-phase as well. We demonstrate that a crucial role in emerging of phase transitions of the metal-insulator, paraelectric-ferroelectric and magnetic disorder-order types belongs to the change of the degree of the lone pair stereochemical activity -its consecutive increase with the temperature decrease. Using the structural data, we calculated the sign and strength of magnetic couplings in BiFeO 3 in the range from 945º down to 25º С and found the couplings, which undergo the antiferromagneticferromagnetic transition with the temperature decrease and give rise to the antiferromagnetic ordering and its delay in regard to temperature, as compared to the ferroelectric ordering. We discuss the reasons of emerging of the spatially modulated spin structure and its suppression by doping with La 3+ .

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The hydrosilylation of four isomers of tetra(dimethylsiloxy)tetraphenylcyclotetrasiloxane with (4´ cyanobiphenyl 4 yl)undec 10 enoate in the presence of a platinum catalyst afforded four liquid crystalline stereoisomers of phenylcyclotetrasiloxane with mesogenic cyanobiphenyl groups. The reaction was performed for the first time. The influence of the spatial structure of the stereoisomers of tetraphenylcyclotetrasiloxanes with mesogenic groups on the formation of the liquid crystalline state by thermooptical, X ray diffraction, and calorimetric methods. The temperatures and enthalpies of phase transitions were determined, and their reversibility was shown. Differences in both the textures of melts formed on cooling and the phase state and in interplanar distances were found by optical microscopy and X ray diffraction methods. Based on these data, the spatial structure of the isomers was concluded to affect the phase composi tion and type of packing in the liquid crystalline state.Data on the influence of the structure of stereoisomers of cyclosiloxanes on the properties and type of packing in the liquid crystalline (LC) state are lacking in literature. This is related, first of all, to the fact that methyl(hydri do)cyclosiloxanes used for the synthesis of LC compounds usually represent mixtures of isomers (regardless of the cycle size). The influence of the flexibility of the central core and spacer on the type of the forming LC phase has been revealed 1,2 to the present time by computer simula tion. Weak interactions between mesogens, a sufficiently long spacer, and a flexible core favor the formation of nematic phases, whereas discotic molecules with a rigid core, a short spacer, and strongly interacting mesogenic groups form smectic or columnar phases. For example, studying methylcyclosiloxanes, the authors assumed the existence of several types of packing: cylindrical, 3-5 sheaf like, and disk like. 6 Since several stereoisomers of methyl cyclosiloxanes can exist, the types of packing in the LC state for the cis isomer and r 2,t 4,t 6,t 8 isomer should differ due to different intramolecular interactions of mesogenic groups. Unfortunately, none of the published works discusses the influence of the spatial structure of stereoisomers or the composition of a mixture of isomers of methylcyclosiloxanes on the type of packing in the LC state. 3- 10 We earlier 11 attempted to study this influence for cyclohexasiloxane. It was found that methylcyclosiloxanes enriched in the trans isomer form different LC textures on cooling of the isotropic melt. 11 cis Isomers of cyclo tetra and cyclohexasiloxanes with the same mesogenic groups also form different types of packing in the LC state. 12 The purpose of this work is to synthesize structural isomers of cyclosiloxanes with a certain position of mesogenic cyanobiphenyl groups and to identify phase transitions and the type of packing in the LC state. Results and DiscussionSynthesis of LC stereoisomers of tetraphenylcyclo tetrasiloxanes with cyanobiphenyl mesogenic groups. A...