Light scattering study of low-energy vibrational excitations in the metallic glass Ni${}_{67}$Zr${}_{33}$ using electronic Raman scattering

The Raman response of the metallic glass ${\mathrm{Ni}}_{67}{\mathrm{Zr}}_{33}$ is measured as a function of polarization and temperature and analyzed theoretically. Unexpectedly, the intensity in the range up to 300${\mathrm{cm}}^{-1}$ increases upon cooling, which is counterintuitive when the response originates from vibrations alone as in insulators. The increase finds a natural explanation if the conduction electrons are assumed to scatter on localized vibrations with a scattering probability proportional to the Debye-Waller factor. None of our assumptions is material specific, and the results are expected to be relevant for disordered systems in general.

Figure 1

Raman response $R{\chi }^{\prime \prime }(\omega ,T)$ of ${\mathrm{Ni}}_{67}{\mathrm{Zr}}_{33}$ for perpendicular (VH) and parallel (VV) light polarizations. (a) and (b) show on an extended energy range that the spectra consist of a polarization-independent linear continuum and superposed peaks in the range below 300${\mathrm{cm}}^{-1}$. (c),(d) After subtraction of the linear part, the low-energy peaks have nearly identical shapes for all temperatures [cf. (e)], but the overall intensity in VH is only approximately $30\%$ of that in VV. (e) The ratio $\rho ={\chi }_{\mathrm{VH}}^{\prime \prime }/{\chi }_{\mathrm{VV}}^{\prime \prime }$ is temperature independent and increases slightly with energy.

Figure 2

“Boson” peak in ${\mathrm{Ni}}_{67}{\mathrm{Zr}}_{33}$ [same temperatures as in Figs. 1c–1(e)]. The inset shows the spectrum at 315 K, which was measured down to 6${\mathrm{cm}}^{-1}$, on a logarithmic scale. The slight increase toward $\omega \to 0$ is a remainder of the laser line. At the other temperatures, the spectra were measured only for $\omega \ge 15$${\mathrm{cm}}^{-1}$. In the plot ${\chi }^{\prime \prime }/\omega$, a Drude-like spectrum appears as a constant (lower dashed line in the inset). The measured low-energy spectrum saturates above the Drude response (upper dashed line), indicating scattering which could originate from vibrations with a Debye-like spectrum (see text).

Figure 3

Response from localized oscillators ${\chi }_{\mathrm{loc}}^{\prime \prime }/\omega$. The low-energy cutoff due to the Debye-Waller factor is moving downward with decreasing temperature. At room temperature, the cutoff can be clearly resolved in the experiments (inset of Fig. 2).