Raman spectra of neutron-irradiated and Al-doped ${\mathrm{MgB}}_2$

We carried out Raman measurements on neutron-irradiated and Al-doped ${\mathrm{MgB}}_2$ samples. The Raman spectrum changes substantially in both cases and in a similar way, with the appearance of high-frequency spectral structures, whose spectral weight increases with increasing Al concentration and neutron irradiation fluence. In particular, in Al-doped samples the high-frequency peaks slightly harden with increasing Al concentration, due to the lattice compression, whereas in the neutron-irradiated samples, where no atomic substitution occurs, no frequency shift is detected. The appearance of high-frequency spectral structures in the irradiated samples, similar to those observed in Al-doped ones, is quite unexpected. By direct comparison of the Raman spectra with literature experimental phonon densities of states, we show that the modifications of the Raman spectrum in both irradiated and Al-doped samples are due to disorder-induced violations of the Raman selection rules. Theoretical calculations of the phonon density of states support this hypothesis, and demonstrate that the high-frequency structures arise mostly from contributions at $\mathbf{q}\ne \mathbf{0}$ of the $E_{2g}$ phonon mode.

Figure 1

Background-subtracted Raman spectra of Al-doped (a) and neutron-irradiated (b) ${\mathrm{MgB}}_2$ samples. Spectra are shifted upward by a constant value.

Figure 2

Raman spectrum of the most irradiated sample (full line) compared with the PDOS from the neutron experiment of Ref. 17 (squares) and with the calculated $E_{2g}$-projected PDOS (dashed line). All the reported quantities are normalized to the same peak intensity.

Figure 3

Left panel: phonon dispersion of ${\mathrm{MgB}}_2$ within the FC model. The thickness of the lines in the phonon dispersion reflects the magnitude of the $E_{2g}$ component for each mode. Right panel: the corresponding total PDOS (dashed line), and the $E_{2g}$-projected PDOS (shaded area).

Figure 4

Raman intensity from Eqs. (1) for different values of the cutoff $q_c$: (from the bottom to the top) $q_c=0.30,0,45,0.60,0.75{\mathrm{\AA }}^{-1}$. Curves are shifted upward for clarity.