Interplay of the Jahn--Teller Effect and Spin-Orbit Coupling: The Case of Trigonal Vibronic Modes

TL;DR

This paper investigates how spin-orbit coupling influences the Jahn-Teller effect in systems with trigonal vibronic modes, revealing occupation-dependent enhancement or suppression of the effect and exploring broader electron-lattice interactions.

Contribution

It provides a detailed analysis of the interplay between Jahn-Teller distortions and spin-orbit coupling in $t_{2g}$ electron systems, including effects of trigonal and tetragonal vibrations.

Findings

Spin-orbit coupling can both suppress and enhance the Jahn-Teller effect.

Occupation of $t_{2g}$ levels determines the nature of the interaction.

The study extends to general electron-lattice interactions involving multiple vibrational modes.

Abstract

We study an interplay between the orbital degeneracy and spin-orbit coupling giving rise to spin-orbital entangled states. As a specific example, we analyze the interaction of electrons occupying triply degenerate single-ion $t_{2g}$ levels with trigonal vibronic modes (the $t\otimes T$ problem). A more general problem of the electron-lattice interaction involving both tetragonal and trigonal vibrations is also considered. It is shown that the result of such interaction crucially depends on the occupation of $t_{2g}$ levels leading to either the suppression or enhancement of the Jahn-Teller effect by the spin-orbit coupling.