Raman scattering on α-Sn: Dependence on isotopic composition

The frequencies, widths, and shapes of the one-phonon Raman spectra of isotopically enriched and highly isotopically disordered $\alpha$-Sn samples have been measured. The isotopically enriched samples show a frequency inversely proportional to the square root of the mass, in agreement with the harmonic approximation, and a linewidth inversely proportional to the mass, in agreement with perturbative calculations of anharmonic effects (Fermi’s golden rule). The disordered samples show a higher Raman frequency and broader linewidth than expected from their average masses. We attribute the additional shift and broadening to disorder effects and show that it agrees well with calculations based on the coherent potential approximation (CPA). The Raman lines of the disordered samples displayed a shoulder on the low-energy side that is reproduced by a spectral function based on the CPA calculations.