Atomic vibrational density of states of crystalline β-Fe Si 2 and amorphous Fe Si 2 thin films

摘要: 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 states (VDOS), $g(E)$, 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 samples characterized diffraction M\"ossbauer spectroscopy. VDOS $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Fe}{\mathrm{Si}}_{2}$ extends up ${E}_{\mathit{max}}\ensuremath{\sim}65\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ exhibits a strong peak at $E\ensuremath{\sim}36\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ weaker bands centered about 25, 43, $53\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. These characteristic features coincide with positions prominent IR Raman spectral lines reported literature. measured shows good agremeent theoretical computed using functional theory combined direct method. Contrary phase, $a\text{\ensuremath{-}}\mathrm{Fe}{\mathrm{Si}}_{2}$ broad $\ensuremath{\sim}30\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ little structure, deviation from Debye behavior small excitation energies $(l15\phantom{\rule{0.3em}{0ex}}\mathrm{meV})$. This is revealed as reduced VDOS, $g(E)∕{E}^{2}$, ${E}_{\mathit{bp}}\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, which interpreted ``boson peak.'' Above boson $(30\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\ensuremath{\lesssim}E\ensuremath{\lesssim}60\phantom{\rule{0.3em}{0ex}}\mathrm{meV})$ $g(E)∕{E}^{2}$ observed be approximately $\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}E∕{E}_{0})$, ${E}_{0}=7.4\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ being close ${E}_{\mathit{bp}}$.