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 $\left(\mathrm{Zn}{\mathrm{Fe}}_2{\mathrm{O}}_4\right)$ 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 $800°\mathrm{C}$ 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 ${\left[\mathrm{Zn}_{1-x}{}^{2+}\mathrm{Fe}_x{}^{3+}\right]}_A{\left[\mathrm{Zn}_x{}^{2+}\mathrm{Fe}_{2-x}{}^{3+}\right]}_B{\mathrm{O}}_4$, 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.

Figure 1

(Color online) Structural models for XANES simulations: (a) ideal normal spinel structure, and (b) disordered spinel structure containing one tetrahedral ${\mathrm{Fe}}^{3+}$ ion at $(1∕81∕81∕8)$ and one octahedral ${\mathrm{Zn}}^{2+}$ ion at $(1∕21∕21∕2)$.

Figure 2

Temperature dependences of ZFC (solid symbols) and FC (open symbols) magnetizations measured at an external magnetic field of $50\mathrm{Oe}$ for (a) $\mathrm{Zn}{\mathrm{Fe}}_2{\mathrm{O}}_4$ bulk specimen, (b) as-deposited thin film, and thin films annealed at (c) $350°\mathrm{C}$, (d) $400°\mathrm{C}$, (e) $500°\mathrm{C}$, and (f) $800°\mathrm{C}$.

Figure 3

(Color online) Comparison of experimental and theoretical Zn-$K$ edge XANES spectra. From bottom to top, thick solid lines correspond to the experimental spectra for the as-deposited thin film, the thin film annealed at $800°\mathrm{C}$, and the bulk specimen. Thin dashed-dotted, dashed, and solid lines represent theoretical spectra for $\mathrm{Zn}_A{}^{2+}$ in the ideal normal spinel $\mathrm{Zn}{\mathrm{Fe}}_2{\mathrm{O}}_4$, $\mathrm{Zn}_A{}^{2+}$ in the disordered $\mathrm{Zn}{\mathrm{Fe}}_2{\mathrm{O}}_4$, and $\mathrm{Zn}_B{}^{2+}$ in the disordered $\mathrm{Zn}{\mathrm{Fe}}_2{\mathrm{O}}_4$, respectively. These theoretical spectra are shifted by an energy $\Delta E=37\mathrm{eV}$ $(\Delta E∕E=0.38\%)$ in order to align the peak energies of the experimental spectra with those of the theoretical spectra.

Figure 4

(Color online) Comparison of experimental and theoretical Fe-$K$ edge XANES spectra. From bottom to top, thick solid lines correspond to the experimental spectra for the as-deposited thin film, the thin film annealed at $800°\mathrm{C}$, and the bulk specimen. Thin dashed and solid lines represent the theoretical spectra for $\mathrm{Fe}_B{}^{3+}$ in ideal normal spinel $\mathrm{Zn}{\mathrm{Fe}}_2{\mathrm{O}}_4$ and $\mathrm{Fe}_A{}^{3+}$ in the disordered $\mathrm{Zn}{\mathrm{Fe}}_2{\mathrm{O}}_4$, respectively. These theoretical spectra are shifted by an energy $\Delta E=24\mathrm{eV}$ $(\Delta E∕E=0.34\%)$ in order to align peak energies of the experimental spectra with those of the theoretical spectra.

Figure 5

Variation of experimental Zn $K$-edge XANES spectra with annealing temperature. Theoretical spectra obtained by different weighted sums of contributions from ${\mathrm{Zn}}^{2+}$ ions at $A$ and $B$ sites in the spinel structure are also shown for comparison.

Figure 6

Variation of experimental Fe $K$-edge XANES spectra with annealing temperature. Theoretical spectra obtained by different weighted sums of contributions from ${\mathrm{Fe}}^{3+}$ ions at the $A$ and $B$ sites in the spinel structure are also shown for comparison.

Figure 7

(Color online) Fourier transforms of Zn-$K$ EXAFS data collected from the bulk specimen, the as-deposited thin film, and the thin film annealed at $800°\mathrm{C}$ (solid lines). Corrections for phase shift have not been included in the Fourier transformation. The dashed line is a theoretical one showing the best fit to the experimental data in the range of $1–4\mathrm{\AA }$ for the Fourier transform of as-deposited thin film.