Atomic vibrational density of states of crystallineβ−FeSi2and amorphousFeSi2thin films

Abstract

Nuclear resonant inelastic x-ray scattering of $14.4125\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ synchrotron radiation was used to measure directly the partial vibrational density of states (VDOS), $g(E)$, of crystalline $\ensuremath{\beta}\text{\ensuremath{-}}^{57}\mathrm{Fe}{\mathrm{Si}}_{2}$ and amorphous$(a\text{\ensuremath{-}})^{57}\mathrm{Fe}{\mathrm{Si}}_{2}$ thin films prepared by codeposition in ultrahigh vacuum. The structure of the samples was characterized by x-ray diffraction and M\ossbauer spectroscopy. The VDOS of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Fe}{\mathrm{Si}}_{2}$ extends up to ${E}_{\mathit{max}}\ensuremath{\sim}65\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ and exhibits a strong peak at $E\ensuremath{\sim}36\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ and weaker bands centered at about 25, 43, and $53\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. These characteristic features coincide with positions of prominent IR and Raman spectral lines reported in the literature. The measured VDOS shows good agremeent with the theoretical VDOS of crystalline $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Fe}{\mathrm{Si}}_{2}$ computed by using the density functional theory combined with the direct method. Contrary to the crystalline phase, the VDOS of $a\text{\ensuremath{-}}\mathrm{Fe}{\mathrm{Si}}_{2}$ shows a broad peak at $\ensuremath{\sim}30\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ with little structure, and a deviation from Debye behavior at small excitation energies $(l15\phantom{\rule{0.3em}{0ex}}\mathrm{meV})$. This is revealed as a peak in the reduced VDOS, $g(E)∕{E}^{2}$, at ${E}_{\mathit{bp}}\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, which is interpreted as ``boson peak.'' Above the boson peak $(30\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\ensuremath{\lesssim}E\ensuremath{\lesssim}60\phantom{\rule{0.3em}{0ex}}\mathrm{meV})$ $g(E)∕{E}^{2}$ was observed to be approximately $\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}E∕{E}_{0})$, with ${E}_{0}=7.4\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ being close to ${E}_{\mathit{bp}}$.