Abstract
We have analyzed different correlation functions in a realistic spin-orbital model for half-doped manganites. Using a finite-temperature diagonalization technique the CE phase was found in the charge-ordered phase in the case of small antiferromagnetic interactions between ${t}_{2g}$ electrons. It is shown that the ingredient responsible for stabilization of the CE-type spin and orbital-ordered state is the cooperative Jahn-Teller (JT) interaction between next-nearest ${\mathrm{Mn}}^{+3}$ neighbors mediated by the breathing mode distortion of ${\mathrm{Mn}}^{+4}$ octahedra and displacements of ${\mathrm{Mn}}^{+4}$ ions. The topological phase factor in the Mn--Mn hopping leading to gap formation in one-dimensional models for the CE phase as well as the nearest neighbor JT coupling are not able to produce the zigzag chains typical for the CE phase in our model.
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