Jahn-Teller effect in the emission and absorption spectra of $\mathrm{Zn}\mathrm{S}:{\mathrm{Cr}}^{2+}$ and $\mathrm{Zn}\mathrm{Se}:{\mathrm{Cr}}^{2+}$

The Jahn-Teller effect is invoked to explain the fine structure (isolated zero-phonon lines) observed in both the infrared emission and absorption spectra of substitutional ${\mathrm{Cr}}^{2+}$ impurities in ZnSe and ZnS. The ground ${}^{5}D_2$ term of ${\mathrm{Cr}}^{2+}$ is split by crystal field into a ${}^{5}T_2$ ground multiplet and an excited ${}^{5}E$ multiplet. We look at transitions among levels belonging to these two multiplets, which happen to be in the near infrared region. Spin-orbit and spin-spin interactions are taken into account. The Jahn-Teller coupling is introduced as a linear coupling considering both $ϵ$ and ${\tau }_2$ phonons. The Lanczos-recursion procedure with a proper choice of the initial state is used to calculate the vibronic functions and energies. It is found that $ϵ$ modes only lead to intensities that do not agree well with those of the zero-phonon doublet observed both in emission and absorption in the cases of ZnS and ZnSe, while ${\tau }_2$ modes give a good explanation of transition energies and transitions strengths in the same cases. A discussion of the relatively high strength of the vibronic coupling for Cr in comparison with other impurities in the same compounds is also included.

Figure 1

Emitted lines as predicted by coupling to $ϵ$ modes only. Half-widths for the Lorentzian line shapes are $1{\mathrm{cm}}^{-1}$ for lines around $5218{\mathrm{cm}}^{-1}$ (with large component of zero-phonon vibronic levels) and $2{\mathrm{cm}}^{-1}$ for the other lines with large components of one-phonon lines. This spectrum reproduces well the energy positions but not the intensities (compare to Fig. 1 of Ref. 9).

Figure 2

Emitted lines predicted by coupling the ${}^{5}T_2$ multiplet to ${\tau }_2$ modes only. Half-widths are $1{\mathrm{cm}}^{-1}$ for lines around $5218{\mathrm{cm}}^{-1}$, $2{\mathrm{cm}}^{-1}$ for lines around $5212{\mathrm{cm}}^{-1}$ and $3{\mathrm{cm}}^{-1}$ for the other lines. Energy of the coupling mode is $90{\mathrm{cm}}^{-1}$ at the bottom, $100{\mathrm{cm}}^{-1}$ at the center and $120{\mathrm{cm}}^{-1}$ at the top.

Figure 3

Energy of vibronic levels as functions of $E_{JT}^{\left(\tau \right)}$ for a coupling phonon of energy $\hslash {\omega }_T=100{\mathrm{cm}}^{-1}$.

Figure 4

Absorption spectrum for $\mathrm{Zn}\mathrm{S}:{\mathrm{Cr}}^{2+}$ directly calculated using the same wave functions used to calculate emission spectrum in the central part of Fig. 2.

Figure 5

Scheme of vibronic levels for $\mathrm{Zn}\mathrm{S}:{\mathrm{Cr}}^{2+}$ leading to emissions (downward arrows) and absorptions (upward arrows). Clearly observed transitions are depicted by thick arrows, while thin arrows show the possible origin for some weak zero-phonon emission lines observed for the case of ZnS, but not to be observed for ZnSe due to background noise.

Figure 6

Emission spectrum for $\mathrm{Zn}\mathrm{Se}:{\mathrm{Cr}}^{2+}$ predicted by coupling ${}^{5}T_2$ multiplets to ${\tau }_2$ modes; $\hslash {\omega }_T=70{\mathrm{cm}}^{-1}$, $E_{JT}^{\left(\tau \right)}=180{\mathrm{cm}}^{-1}$, and $E_{JT}^{\prime }=270{\mathrm{cm}}^{-1}$.

Figure 7

Absortion spectrum for $\mathrm{Zn}\mathrm{Se}:{\mathrm{Cr}}^{2+}$ directly calculated using the same wave functions used to calculate emission spectrum.