Energy Spectra,g Factors and Their Pressure-Induced and/or Thermal Shifts of SrTiO3:Cr3+ and SrTiO3:Mn4+III: R-Line Thermal Shifts of SrTiO3:Mn4+

By taking into account all the irreducible representations andtheir components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of basic wavefunctions within d³ electronic configuration, the values of the parameters in the expressions of thermal shift (TS) from EPI for the ground level, R level and R line of SrTiO₃:Mn⁴⁺ have been evaluated; the R-line TS and various contributions to it have been calculated in the low-temperature region. It is found that all the threeterms of R-line TS from EPI relevant to the lattice vibration are red shifts. The Raman term is the largest, the neighbor-level term is the second, and the optical-branch term is very smallover the range of T≤80 K. The contribution to R-line TS from thermalexpansion has been approximately neglected in this work. Thevery strong EPI relevant to its lattice vibration forSrTiO₃:Mn⁴⁺ causes its R-line TS to be an unusually large red-shift. Only by taking into account the strong softening of the low-frequency acoustic modes of the lattice vibration at low temperatures, can we successfully explain the variationof R-line TS of SrTiO₃$:Mn⁴⁺with temperature.