Cage electron-hydroxyl complex state as electron donor in mayenite

It is inferred from the chemical shift of muon spin rotation $\left(\mu \mathrm{SR}\right)$ spectra that muons implanted in pristine (fully oxidized) mayenite, ${\left[{\mathrm{Ca}}_{12}{\mathrm{Al}}_{14}{\mathrm{O}}_{32}\right]}^{2+}\left[{\square }_5{\mathrm{O}}^{2-}\right]$ (C12A7, with $\square$ referring to the vacant cage), are bound to ${\mathrm{O}}^{2-}$ at the cage center to form ${\mathrm{OMu}}^{-}$ (where Mu represents muonium, a muonic analog of the H atom). However, an isolated negatively charged state $({\mathrm{Mu}}^{-}$, an analog of ${\mathrm{H}}^{-})$ becomes dominant when the compound approaches the state of electride ${\left[{\mathrm{Ca}}_{12}{\mathrm{Al}}_{14}{\mathrm{O}}_{32}\right]}^{2+}\left[{\square }_{4}2{\mathrm{e}}^{-}\right]$ as a result of the reduction process. Moreover, the ${\mathrm{OMu}}^{-}$ state in the pristine specimen exhibits depolarization of paramagnetic origin at low temperatures (below $\sim 30$ K), indicating that ${\mathrm{OMu}}^{-}$ accompanies a loosely bound electron in the cage that can be thermally activated. This suggests that interstitial muons (and hence H) forming a “cage electron-hydroxyl” complex can serve as electron donors in C12A7.

Figure 1

Examples of wTF-$\mu \mathrm{SR}$ time spectra observed at 300 and 5 K in mayenite with (a) pristine (5 mT), (b) ${10}^{19}$ ${\mathrm{cm}}^{-3}$ (2 mT), and (c) ${10}^{21}$ ${\mathrm{cm}}^{-3}$ (2 mT) doping levels. ZF-$\mu \mathrm{SR}$ spectra observed at 5 K are also shown by filled diamonds to confirm the line shape of the envelope function. The solid curves are the best fits obtained using Eq. (1). Pictures of respective samples are shown in the right column.

Figure 2

Temperature dependence of (a) muon depolarization rate deduced from wTF-$\mu \mathrm{SR}$ measurements and (b) frequency shift $\left(K_{\mu }\right)$ deduced from HTF-$\mu \mathrm{SR}$ measurements in mayenite with different levels of electron doping. The dashed lines in (b) are the best fit assuming a temperature-independent $K_{\mu }$. Inset: fractional yield of $\mu \mathrm{SR}$ signal at $t=0$ with respect to the value corresponding to 100% ${\mathrm{Mu}}^{+/-}$ formation (see text).

Figure 3

(a) Hartree potential map at $z=0.378$ plane in pristine mayenite, where a free O atom is placed at the center of a cage $(0,0.25,0.375)$. The brown, gray, and blue dots represent the Ca, Al, and O atoms, respectively, within $0.25\le z\le 0.5$. Potential minima for muon (shown by the blue hatched area) are circularly spread around O. (b) Angle dependence of muon spin relaxation rate $\left({\delta }_{\mathrm{n}}\right)$ under a transverse field of 20 mT. Dashed curves are simulated ${\delta }_{\mathrm{n}}$ for muons located at the position of $1–4$, with their average represented by a solid curve. Inset: Schematic view of the relation between the magnetic field and sample rotation angle $\theta$ from (001) surface.

Figure 4

Schematic energy diagrams of mayenite [26, 27, 28]. The blue (pink) and yellow hatched regions show the occupied levels of oxygen (electron) in the cage center. The red dashed lines show the electronic levels associated with muon. FCB (FVB) and CCB (CVB) denote the frame conduction (valence) band and cage conduction (valence) band, respectively.