The Jahn-Teller effect

The crystal field was not always described in highly symmetric octahedral environment. There were so many factors which may lead to additional distortion of the environment, such as alternative valence, defects of crystal structure and external uniaxial pressure. The symmetry-breaking associated with displacement of the atoms would remove the electronic degeneracy. In Fig. 1.6, the distortion of octahedra resulted in splitting of the t2g and eg levels. The energy saving came from the lowering of the single-occupied eg level. The energy for rising of the dxy level was balanced by the lowering of the dxz and dyz. Such a phenomenon of the crystal structure’s distortion was known as the Jahn-Teller effect. There were three different kinds of Jahn-Teller effect. Static Jahn-Teller effect: spontaneously occurred distortion was fixed on a particular axis of an octahedron and was permanently present in a crystal. Dynamic Jahn-Teller effect: originated from the special coupling to vibrational modes and low frequency electronic motion. The distortion occurred along different axes depending on temperature and may involve rapid hopping of the distortion from site to site (for materials involving ions with mixed valence). Cooperative Jahn-Teller distortion: spontaneous transition throughout the crystal at certain temperature. Because the  Jahn-Teller effect occurred due to lattice orbital coupling only, it was independent of spin and spin ordering temperatures, and the cooperative distortion may exhibit a thermal hysteresis [19]. For example, complexes of Cr2+ (d 4 ), high-spin Mn3+ (d 4 ), and Cu2+ (d 9 ) could produce the significant Jahn-Teller effects.

Reference: Thesis (http://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/59990/1/Yuan_Yahua.pdf)