Odd-Parity Selection in Parity-Forbidden Electronic Transitions Revealed by Mn4+ Fluorescence Spectroscopy

Abstract: Mn4+-doped fluoride phosphors represent a significant class of narrow band red-emitting materials, whose luminescent properties are profoundly influenced by electron-phonon coupling. However, the parity-forbidden nature of these electronic transition systems is incompatible with the conventional Condon approximation, which is widely adopted in the classic theories such as the Huang-Rhys theory, a framework established on the assumption of parity-allowed electric dipole transitions. This results in a critical knowledge gap regarding the principles governing the phonon sidebands of parity-forbidden electronic transitions. This study experimentally reveals a pronounced parity-dependent intensity distribution in the phonon sidebands of these systems: significantly suppressed even-order sidebands and normally observed odd-order sidebands. To elucidate the phenomenon, we extend the Huang-Rhys theory to parity-forbidden systems by incorporating the Herzberg-Teller approximation into the treatment of the transition matrix elements. The improved theory successfully uncovers the physical mechanism behind the strong suppression of the even-order sidebands in the parity-forbidden systems, in which the Huang-Rhys factor is derived as S=((2I_3)/(9I_1 ))^1/2. This work not only reveals new findings regarding the phonon sidebands of the parity-forbidden electronic transition systems, but also establishes an improved theoretical framework for understanding the electron-phonon coupling mechanisms of color centers in solids.