Ferrodistortive ordering

Figure 34 ESR spectra for axial environment involving (a) ferrodistortive order and (b) antiferrodistortive order396...

Hydrates. A2MnmF5 H20 compounds (A = K, Rb, Cs) are suitable examples of Heisenberg chain antiferromagnets. The 1-D behavior is enhanced by the ferrodistortive ordering of dj2 orbitals, antiparallel along the c direction. In the ab plane weak d°2 y2 interactions occur between the chains. 

It is easy to see from formula (16) that the interaction constant can be of any sign depending upon concrete situation. If the interaction with strain is very big the constant at k = 0 is positive and the ferrodistortive ordering is favorable. 

For simplicity, consider the so-called ferrodistortive ordering pattern. We assume that all elementary cells are distorted in exactly the same way. Therefore, explicitly, the averages, Q and a, do not depend on the elementary cell number, i. Assuming the flucmations, q i) and s(i), much smaller than the respective averages, Q and CT, we can neglect terms of second-order in q(i) and s(i) and keep just the linear ones. The JT Hamiltonian (7) decouples into the following sum of translationally identical one-cell terms. 

Fig. 8. Ferrodistortive order of elongated octahedra in elpasolite-type compounds A2BB X [B (open circles) non-Jahn-Teller cations]...

A ferrodistortive order with the long octahedral z-axes parallel to the crystallographic c-direction [a = 0] corresponds to a strain of symmetry ... 

In general the antiferrodistortive pattern is more stable than the ferrodistortive order in a 3-dimensional frame-work of comer-connected octahedra (jperov tes, lead nitrocomplexes). As discussed just before the antiferrodistortive order leads to appreciable deformations of those octahedral sites which are occupied by non-Jahn-Teller ions in elpasolite-type stmctuies. Thus the ferrodistortive order may be stabilized also (oxidic elpasolites, alkaline earth nitrocomplexes). The lower transition temperatures of the lead compared to the alkaline earth compounds indicate weaker cooperative-elastic interactions and are possibly caused by the less distinct distortion of the CuNg polyhedra (Table 3). Finally it should be mentioned that the g tensor in the (001) planes of the 7-modifications has an orientation [K 15° ... 

Fig. 22. Orbital ordering in (001) planes of structures with comer-connected TLg polyhedra [T d cations] (a) compressed octahedra in ferrodistortive order (b) elongated octahedra in antiferrodistortive order...

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