Mixed-valence magnetism in TiO$_{2}$/TiO$_{\mathrm{x}}$ superlattices

Epitaxial TiO$_{2}$ and TiO$_{\mathrm{x}}$ superlattices, $\sim$ 1-nm thick per layer by sputtering at 570$^{\circ}$C using pure argon on sapphire substrates. From HR-TEM, the periodically alternating layers are well-defined. XPS analyses based on the binding energy of Ti 2p$_{3/2}$ peaks suggest the co-existence of Ti$^{+3}$ and Ti$^{+4}$, thus verifying the mixed-valence nature. The M(H) curves measured at room temperature using SQUID showed hysteretic loops typical of ferromagnetism. Electrical transport measurements were done at zero field demonstrate transition of charge ordering at low temperatures, reminiscent of what was found in Ti-rich Ti$_{\mathrm{1+x}}$O$_{2}$ single-layer thin films, made by Ti ion implantation into TiO$_{2}$ crystals, in which randomly distributed TiO$_{2}$, Ti$_{2}$O$_{3}$ and TiO were found to coexist. Preliminary First-principle (\textit{ab initio}) calculations to understand the roles of oxygen vacancies in various TiO$_{2}$ super-cells could indeed lead to spontaneous magnetizations. We thus argue that mixed-valence titanium ions are responsible for the magnetism