Polaron Formation and Motion in Magnetic Solids

This paper addresses aspects of the theory of the formation and motion of polarons that appear relevant to understanding some metal-to-semiconductor transitions in oxides. First, the physical bases of both the long- and short-range electron-lattice interactions usually considered in polaron theory are described and contrasted with one another. Then the notion of self-trapping and the formal theory of polaron formation are presented. Using a scaling analysis of the nonlinear wave equation that lies at the heart of polaron formation, essential features of polaron formation are readily obtained for both types of electron-lattice interaction operating individually and in tandem. The theory is extended to apply to a carrier bound within a Coulomb potential. Two distinct types of bound polaron state can exist. A “small” polaron’s electronic carrier is confined to a single site. Alternatively, a “large” polaron’s electronic carrier is distributed over multiple sites. When separated by an energy barrier, these distinct states can coexist. A “collapse” occurs when a continuous change of physical parameters produces an abrupt change of the groundstate from being large-polaronic to being small-polaronic. To introduce magnetic effects, the scaling analysis is first applied to the formation of a large magnetic polaron, a charge carrier that moves freely within a large ferromagnetic cluster embedded within an antiferromagnet. The polaron is large enough that the predominant interactions are the exchange interactions of local magnetic moments among themselves and with the charge carrier. The scaling analysis is then extended to describe the donor-state collapse that is thought to drive the metal-to-insulator transition that occurs in n-type EuO as this ferromagnet is heated toward its paramagnetic state. In this case, the metallic impurity conduction that dominates transport at low-temperatures is suppressed when the ferromagnet’s large-radius donor states collapse to small-polaronic states upon approaching the paramagnetic regime. At appropriate doping levels, this transition is associated with a huge negative magneto-resistance. This paper finally addresses small-polaronic hopping transport in p-type LaMnO3. Attention is focused on the effects of compensating holes with electrons generated by oxygen vacancies. The Curie temperature is reported to be insensitive to this compensation. The low-temperature ferromagnetism is even unaffected when the hole density is reduced enough to eliminate metallic conductivity. These results imply that the ferromagnetism is not carrier-induced. Furthermore, the strong sensitivity of the high-temperature Seebeck coefficient to compensation suggests that the carriers hop amongst only a small subset of Mn sites. These cation sites may be associated with the divalent cation dopants. The observation of an n-type Hall effect is consistent with the notion that the hopping is a type of impurity conduction. Indeed, Hall effect sign anomalies are predicted and observed for the hopping of holes in disordered solids. In this view the transition from a ferromagnetic-metal to a paramagnetic-semiconductor in doped LaMnO3 is similar to that of EuO, in that both transitions are associated with the collapse of carriers from extended states into small-polaronic impurity states as the temperature approaches the Curie temperature.