Spin–cavity interactions in relativistic Jahn–Teller systems under strong light–matter coupling

Abstract

We extend our recent work on the cavity-modified spin Zeeman effect of an effective spin-1/2-system [E. W. Fischer and M. Roemelt, J. Chem. Phys. 163, 174307 (2025)] to a relativistic Jahn–Teller scenario under strong light–matter coupling. Here, the effective spin-1/2-system is realized via a single electron or a single hole in a doubly degenerate molecular orbital system of trigonal symmetric transition metal complexes. Single-particle and single-hole systems are subject to both vibronic and spin–orbit coupling (SOC) augmented by interactions with a quantized cavity field via the cavity–Zeeman interaction. Methodologically, we combine the relativistic E × e-Jahn–Teller model with a recently introduced effective Hamiltonian formalism based on quasi-degenerate perturbation theory, which treats the cavity–spin interaction in leading order beyond the dipole approximation. We derive analytic expressions for Kramers pair energies in weak and strong SOC regimes, as well as related cavity-modified effective electronic g-factors. We find cavity-induced modifications of the electronic g-factor to become relevant in the weak SOC regime for both single-particle and single-hole systems while being effectively quenched under strong SOC. Alternating signs of the cavity–Zeeman correction render single-particle and single-hole scenarios distinct in their response to the cavity field from a g-factor perspective.