Spin–Phonon Coupling and Dynamic Zero-Field Splitting Contributions to Spin Conversion Processes in Iron(II) Complexes

Abstract

Magnetization dynamics of transition metal complexes manifest in properties and phenomena of fundamental and applied interest (e.g., slow magnetic relaxation in single molecule magnets (SMMs), quantum coherence in quantum bits (qubits), and intersystem crossing (ISC) rates in photophysics). While spin–phonon coupling is recognized as an important determinant of these dynamics, additional fundamental studies are required to unravel the nature of the coupling and thus leverage it in molecular engineering approaches. To this end, we describe here a combined ligand field theory and multireference <i>ab initio</i> model to define spin–phonon coupling terms in S = 2 transition metal complexes and demonstrate how couplings originate from both the static and dynamic properties of ground and excited states. By extending concepts to spin conversion processes, ligand field dynamics manifest in the evolution of the excited state origins of zero-field splitting (ZFS) along specific normal mode potential energy surfaces. Dynamic ZFSs provide a powerful means to independently evaluate contributions from spin-allowed and/or -forbidden excited states to spin–phonon coupling terms. Furthermore, ratios between various intramolecular coupling terms for a given mode drive spin conversion processes in transition metal complexes and can be used to analyze mechanisms of ISC. Variations in geometric structure strongly influence the relative intramolecular linear spin–phonon coupling terms and will thus define the overall spin state dynamics. While of general importance for understanding magnetization dynamics, this study links the phenomenon of spin–phonon coupling across fields of single molecule magnetism, quantum materials/qubits, and transition metal photophysics.

Spin-Phonon Relaxation in Magnetic Molecules: Theory, Predictions and Insights

“…Taking analytical derivatives of D one obtains an expression equivalent to Eq. 196, pointing once again to the energy of excited electronic states as the key variable influencing spin-phonon coupling [100]. In the case of transition metals with very large anisotropy, electronic excited states are generally so close to the ground state that the perturbation theory used to describe D in the ligand field approach breaks down.…”