Influence of reduced mass differences on the Raman spectra of ternary mixed compounds:Zn1−xFexSandZn1−xMnxS

A Raman scattering study of the mixed crystals ${\mathrm{Zn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}\mathrm{S}$ and ${\mathrm{Zn}}_{1\ensuremath{-}y}{\mathrm{Mn}}_{y}\mathrm{S}$ has been carried out for different Fe $(0l~xl~0.05)$ and Mn $(0l~yl~0.5)$ concentrations. It is found that both the strengths and the frequencies of the TO and LO modes of ZnS are approximately independent of the Mn (or Fe) concentration. However, as Mn (or Fe) is substituted for Zn, four additional first-order modes with frequencies $\ensuremath{\omega}(\mathrm{TO})l\ensuremath{\omega}l\ensuremath{\omega}(\mathrm{LO})$ are observed in the Raman spectra. Three of the new modes have frequencies equal to those of sharp peaks in the density of states of ZnS and thus they are attributed to resonance or band modes. Another extra mode, with frequency at 323 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, is observed in samples with $xg~0.10,$ and it is assigned to a breathing mode of the nearest-neighbor sulfur atoms around Mn atoms. The observation of such extra features does not correspond to the usual behavior observed in other ternary mixed crystals where either one-, two-, or mixed-mode behavior is observed. Conversely, it is found that the measured frequencies of all the new peaks are nearly constant, independent of the Fe or Mn concentration. This ``frozen-mode'' behavior is believed to occur because of the small reduced mass difference between the binary end members when the Zn atoms are replaced by either Fe or Mn. More specifically it is suggested that the frozen-mode behavior will occur whenever the reduced mass difference between the end pairs (\ensuremath{\Delta}\ensuremath{\mu}) is less than or equal to approximately 2.0 amu. It appears that consideration of the reduced mass difference may also be used to delineate between one- and two-mode behavior. That is, the available data suggest that one-mode behavior occurs in samples with $2\ensuremath{\lesssim}\ensuremath{\Delta}\ensuremath{\mu}\ensuremath{\lesssim}7$ and two-mode behavior in samples with $\ensuremath{\Delta}\ensuremath{\mu}\ensuremath{\gtrsim}7.$