First-principles investigation of the cooperative Jahn-Teller effect for octahedrally coordinated transition-metal ions

Fundamental aspects of the cooperative Jahn-Teller effect are investigated using density functional theory in the generalized gradient approximation. LiNiO2, LiMnO2, and LiCuO2 are chosen as candidate materials as they possess small, intermediate, and large cooperative Jahn-Teller distortions, respectively. The cooperative distortion is decomposed into the symmetrized-strain modes and k=0 optical phonons, revealing that only the Eg and A1g strain modes and Eg and A1g k=0 optical-phonon modes participate in the cooperative distortion. The first-principles results are then used to find values for the cooperative Jahn-Teller stabilization energy and the electron-strain and electron-phonon coupling. It is found that the dominant source of anisotropy arises from the third-order elastic contributions, rather than second-order vibronic contributions. Additionally, the importance of higher-order elastic coupling between the Eg and A1g modes is identified, which effectively causes expansion of A1g-type modes and allows for a larger Eg distortion. Finally, the strain anisotropy induced by the antiferromagnetically ordered states is shown to cause a significant difference in the cooperative Jahn-Teller stabilization energy for the different orientations of the cooperative distortion