Research on the thermal-shifts and electron-phonon coupling parameters for two spectral lines in Nd3+-doped Gd3Sc2Ga3O12 and La3Lu2Ga3O12 garnets

The thermal red-shift of spectral line E1 (R2 → Y3) and the thermal blue-shift of spectral line E2 (R1 → Z5) for Nd3+ in Gd3Sc2Ga3O12 (GSGG) and La3Lu2Ga3O12 (LLGG) garnet crystals are studied by using a full expression including both the dynamic factor due to electron-phonon interaction and the static factor due to lattice thermal expansion. The results indicate that the full expression enables explaining not only the thermal red-shift, but also the thermal blue-shift. For both the spectral lines E1 and E2, the dynamic factor leads to the red-shift because the true electron-phonon coupling parameters α′ are always negative, whereas the static factor results in the blue-shift due to the positive static parameter A. The observed thermal blue-shift of line E2 for GSGG: Nd3+ and LLGG: Nd3+ is owing to the static factor being larger than the dynamic one rather than to the positive apparent electron-phonon parameter α obtained by a simple expression containing only the dynamic factor. The true electron-phonon parameters α′ acquired by the full expression in sign (for line E2) and in magnitude (for both the lines E1 and E2) differ from the apparent parameters α obtained from the simple expression. So, the reasonable studies of thermal-shift and electron-phonon coupling parameters should employ the full expression.