Crystal Distortion in Magnetic Compounds

The crystal distortion which arises from the Jahn-Teller effect is discussed in several examples. In the case of compounds containing ${\mathrm{Cu}}^{\text{2+}}$ or ${\mathrm{Mn}}^{\text{3+}}$ at octahedral sites, the lowest orbital level of these ions is doubly degenerate in the undistorted structure, and there is no spin-orbit coupling in this level. It is shown that, introducing a fictitious spin to specify the degenerate orbital states, we can discuss the problem by analogy with the magnetic problems. The “ferromagnetic” and “antiferromagnetic” distortions are discussed in detail. The transition from the distorted to the undistorted structure is of the first kind for the former and of the second kind for the latter. Higher approximations are discussed briefly. In compounds like FeO, CoO, and ${\mathrm{CuCr}}_2{\mathrm{O}}_4$ , the lowest orbital level is triply degenerate, and the spin-orbit coupling is present in this level. In this case the distortion is dependent on the magnitude of the spin-orbit coupling relative to the strength of the Jahn-Teller effect term. The distortion at absolute zero temperature and its temperature dependence are discussed.