First-principles XANES simulations of spinel zinc ferrite with a disordered cation distribution

Theoretical calculations of Zn $K$ and Fe $K$ x-ray absorption near-edge structures (XANES) using a first-principles method have been performed to evaluate the degree of cation disordering in spinel zinc ferrite $(\mathrm{Zn}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4})$ thin film prepared by a sputtering method, $\mathrm{Zn}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ thin films annealed at elevated temperatures, and $\mathrm{Zn}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ bulk specimen prepared by a solid-state reaction. Using the full-potential linearized augmented plane-wave + local orbitals method, a theoretical spectrum is generated for the tetrahedral and octahedral environments for each of the two cations. The experimental XANES spectrum of the thin film annealed at $800\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ as well as that of bulk specimen is successfully reproduced by using either the theoretical spectrum for ${\mathrm{Zn}}^{2+}$ on the tetrahedral site ($A$ site) or that for ${\mathrm{Fe}}^{3+}$ on the octahedral site ($B$ site), which is indicative of the normal spinel structure. For the as-deposited film, on the other hand, excellent agreement between theoretical and experimental spectra is obtained by considering the presence of either ion in both the $A$ and $B$ sites. The degree of cation disordering, $x$, defined as ${[\mathrm{Zn}_{1\ensuremath{-}x}{}^{2+}\mathrm{Fe}_{x}{}^{3+}]}_{A}{[\mathrm{Zn}_{x}{}^{2+}\mathrm{Fe}_{2\ensuremath{-}x}{}^{3+}]}_{B}{\mathrm{O}}_{4}$, is estimated to be approximately 0.6 in the as-deposited film, which is consistent with the analysis of the extended x-ray absorption fine structure on the Zn $K$ edge. Curious magnetic properties as we previously observed for the as-deposited thin film---i.e., ferrimagnetic behaviors accompanied by large magnetization at room temperature and cluster spin-glass-like behavior---are discussed in connection with disordering of ${\mathrm{Zn}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions in the spinel-type structure.