A classical realization of directional coupling in two dimension of the effective orbital-orbital interaction in the Mott insulating phase of the transition metal oxides (TMO) was presented. The model exhibited partial orbital ordering in the form of directional ordering of fluctuation at low temperatures stabilized by an entropy gap. The directional ordering was necessarily accompanied by a lattice distortion and the bond length in horizontal and vertical directions became unequal when the couplings of the orbital isosopin to lattice modes were included. Analysis shows that the compass model has a low temperature phase which exhibited long-ranged correlations in the directions of fluctuations in both isospin and lattice spaces.
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- Physics and Astronomy(all)