Electron spin resonance, dynamic Jahn-Teller effect, and electric transport mechanism in Na-doped type II silicon clathrates

Silicon clathrates are Si-cage-based structures capable of hosting other atoms, such as sodium, in their Si polyhedron cages. Electron spin resonance (ESR) can provide information on the electronic structure of localized or delocalized electrons in cage-like type II silicon clathrates of the form NaxSi136 (0 < x <= 24). The ESR lines observed at low temperatures are classified into four distinct groups ascribed to (1) an isolated single-Na-containing cage, (2) a pair of single-Na-containing cages or dusters composed of more than two single-Na-containing cages, (3) an electron localized around a silicon deficit with dangling bonds, and (4) a conduction electron. The spin-Hamiltonian parameters for the Na atom of group 1 can be explained by the combination of an off-center model and the dynamic Jahn-Teller effect for the single-Na-containing Si polyhedron. The Na content, x, dependence of the ESR signal of group 1 can be explained by the statistical formation probability of the isolated single-Na-containing cage in type II silicon clathrates. Deviation of the ESR signals of groups 1-3 from Curie's law as temperature increases from 110 to 500 K indicates the transition of bound electrons to delocalized states in type II silicon clathrates. The higher transition temperatures of approximately 170 K for the ESR signals of groups 1 and 2 and approximately 300 K for the ESR signals of group 3 correspond to large activation energies of approximately 0.12 eV and approximately 0.35 eV, respectively, from the electron-localized states to the conduction band.