Heitler-London Approach To Electrical Conductivity and Application to <i>d</i>-Electron Conductions

Abstract

Conduction by the movement of an extra electron which is tightly bound to an ion in an ionic lattice is discussed. We assume that the wave function of the electron is localized closely around an ion and the motion of the electron is so slow that lattice polarization is induced around the electron. Further, we assume that the potential in the lattice deviates slightly from a perfectly periodic arrangement owing to the existence of many impurity-ions. In these circumstances the current is connected with a hopping motion of the electron from ion to ion rather than with a translational motion of the electron in a nearly perfect lattice. In § 2 we discuss the self-trapped state of a positive hole in a polar lattice with a fluctuating potential. In § 3 we develop a theory of the transition of the hole from ion to ion by using the non-adiabatic approximation, and further in § 4 we discuss the same problem by the adiabatic approximation. In the last section we compare the theory with experiments. The electrical conduction through d -electrons in the crystals such as Li x Ni 1- x O, LaMnO 3 +SrMnO 3 , magnetite and CoFe 2 O 4 is regarded as good examples to which the Heitler-London conduction mechanism is applicable. We also discuss the impurity conduction in germanium from a similar point of view.