Analytical approach to the magneto-fluorescence of triplet excitons

TL;DR

This work tackles the challenge of modeling magneto-fluorescence for randomly oriented triplet excitons by developing an analytical framework to average orientation-dependent spin matrix elements. It combines an expansion around the average characteristic polynomial with Lagrange inversion to obtain accurate, tractable expressions for averaged eigenvalues and their associated radiative overlaps, complemented by semi-analytic Padé-based lineshapes for practical fitting. Validation against Monte Carlo simulations shows strong agreement, enabling faster interpretation of MPL spectra and direct connection to the spin Hamiltonian parameters $D_z$ and $E$. The approach offers a transparent, computationally efficient route to link spin-dependent radiative rates and triplet populations to measurable magneto-fluorescence traces, with potential extensions to finite-temperature regimes.

Abstract

The fluorescence of triplet excitons and color-centers is strongly dependent on magnetic field that mixes the zero field spin eigenstates that determine the radiative recombination rates back into the singlet ground state through spin-orbit coupling. For films of molecules, and polycrystalline color-centers samples an average over molecular orientations has to be performed to model the magneto-fluorescence lineshapes. This limits our analytical understanding of the lineshapes and complicates the analysis of the fluorescence dependence on magnetic field. Here, we present a framework that allows to average over triplet molecular orientations analytically. Our approach provides very accurate numerical routines computing precisely the averages matrix elements that appear in magneto-fluorescence and semi-analytical approximations that can be used to model experimental traces.

Figures (3)

• Figure 1: Isotropic average of $\Psi_{z,0}$ and $\Psi_{z,2}$, the normalized versions of $\Sigma_{z,0}$ and $\Sigma_{z,2}$ defined in Eqs. (\ref{['PsiZ0']},\ref{['PsiZ2']}), for $E = 0.2 D_z$. The averages are computed using a numerical Monte-Carlo method, the series expansion around averaged characteristic polynomial and the semi-analytic Padé approximation (see Tab. \ref{['tabalpha123']}). The difference between MC and the series expansion is within the numerical Monte Carlo noise. The Padé approximation is accurate in the limits $B \rightarrow 0$ and $B \rightarrow \infty$ with sufficient 10% accuracy at $B \sim D_z$, the accuracy is lower in this regime because this approximation takes into account only on the second order term of the power series.
• Figure 2: The isotropic average of $\Sigma_{xy,0}$ and $\Sigma_{xy,2}$ based on the three methods for $E = 0.1 D_z$.
• Figure 3: Monte Carlo simulation of $\Sigma_z$ the finite temperature averages of the matrix elements for ${\hat{S}_z}^2$ introduced in Eq. (\ref{['eqTemp']}) compared with the uncorrelated approximation Eq. (\ref{['eqTempU']}). A very good agreement is observed at both low and high temperatures.