Charge orbital ordering is observed in most of the manganites. Its melting on application of a field is responsible for the observed large MCE and CMR properties. Most of the time the super-lattice of charge-orbital order phase adopts a unit cell, with lattice parameter an integer multiply of the basic lattice (commensurate configurations). But in certain cases the super-lattice has incommensurate configurations ( i.e. lattice parameter a non-integer multiply of the basic lattice), which on lowering temperature, transform to commensurate configurations. What are the possible reasons for the commensurate to incommensurate phase transition?
Unfortunately without looking into the literature in great detail, I'm not sure of the answer to this question. The general answer
My experience with commensurate to incommensurate phase transitions usually stems in magnetic structures. For example, Ba3NbFe3Si2O14 has adopts a magnetic structure that is incommensurate with the nuclear structure. This is thought to accompany a P321 to P3 transition, although the evidence for that is still ambiguous. We have shown that Pb3TeMn3P2O14 has a nuclear supercell that is incommensurate with the subcell, although I have yet to determine the cause of such a feature. I believe in that case, it may be due to the presence of spin-orbit coupling in Mn and the nonspherical charge distribution in Pb atoms. However, these systems do not have a commensurate phase transition upon lowering the temperature. I'm sorry I couldn't be of more help!
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