Abstract
Experimental evidence of two-phonon vibronic progressions due to second-order linear electron-phonon interactions is obtained in Ni${\mathrm{Cl}}_{2}$ and Ni${\mathrm{Br}}_{2}$ crystals, by comparing the phonon structure observed in $^{3}A_{2}(F)\ensuremath{\rightarrow}^{1}E(D)$ transition with Raman data. The vanishing of the spin-dependent first-order electron-phonon interaction is shown to be a necessary condition for observing prominent second-order phonon structures in isoconfigurational crystal-field transitions. According to this rule we predict and discuss the appearance of second-order progressions in other $d$-metal layered compounds.
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