We report on observations of random lasers with coherent feedback in highly transparent polymer films embedded with silver nanoparticles. The hybrid materials were fabricated via in situ synthesis method, through which silver nanoparticles were precipitated by thermal treatment. Sharp peaks with linewidth $\sim 0.5\mathrm{nm}$ were observed to emerge on the broad emission background when the pump energy reached a threshold, together with unidirectional laser irradiation. Random lasers with coherent feedback induced by silver nanoparticles have been rarely reported, hence, we expect that this work will add an aspect to random lasers by using metal nanostructures to obtain coherent feedback.

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.