20. Spectroscopic Detection of Hopping Induced Mixed Valence of Ti and Sc in GdSc_1-xTi_xO₃ for x Greater than Percolation Threshold of 0.16

Only two of the first row transition metal binary oxides are either ferro- or ferri-magnetic. These are CrO₂ and Fe₃O₄. The electron spin alignment promoting electron spin alignment is associated with a double exchange mechanism requiring mixed valence as well as metallic conductivity. This chapter describes a novel way to realize these two necessary, but not sufficient conditions for double exchange magnetism. These are mixed valence and a hopping conductivity that can promote intra-plane electron spin alignment in a complex oxide host perovskite, \({\mathrm{GeSc}}_{1-\mathrm{x}}{\mathrm{Ti}}_{\mathrm{x}}{\mathrm{O}}_{3}\). This in-plane spin-correlation does necessarily produce for producing spin alignment between alternating (Sc,Ti)O₂ atomic planes, especially in distorted perovskite structures. Intra-plane alignment is obtained when the A-atom of a trivalent atom AB(D)O₃ peroskite, in this example Gd, is an ordinary metal or a rare earth atom, the B-atom, in this example Sc, is a d⁰ transition metal, and the dopant atom, D, in this example, Ti^{3 +} in d¹ state, is a dⁿ transition with n ≥ 1, as in \({\mathrm{GdSc}}_{1-\mathrm{x}}{\mathrm{Ti}}_{\mathrm{x}}{\mathrm{O}}_{3}\). This article combines X-ray absorption spectroscopy, multiplet theory, and degeneracy removal by a Jahn-Teller effect mechanisms to demonstrate intra-layer mixed valence for Sc and Ti above a percolation threshold x ∼ 0.16 at which hopping transport is associated with a metal to insulator transition. This has been observed in epitaxial films, and not in nano-grain nanocrystalline, where the number of Sc atoms in a grain with 2–5nm dimensions is orders of magnitude too small for observation of an a hopping conductivity that requires a percolation mechanism.