Illuminating Ligand Field Contributions to Molecular Qubit Spin Relaxation via T₁ Anisotropy

Abstract

Electron spin relaxation in paramagnetic transition metal complexes constitutes a key limitation on the growth of molecular quantum information science. However, there exist very few experimental observables for probing spin relaxation mechanisms, leading to a proliferation of inconsistent theoretical models. Here we demonstrate that spin relaxation anisotropy in pulsed electron paramagnetic resonance is a powerful spectroscopic probe for molecular spin dynamics across a library of highly coherent Cu(II) and V(IV) complexes. Neither the static spin Hamiltonian anisotropy nor contemporary computational models of spin relaxation are able to account for the experimental T1 anisotropy. Through analysis of the spin–orbit coupled wave functions, we derive an analytical theory for the T₁ anisotropy that accurately reproduces the average experimental anisotropy of 2.5. Furthermore, compound-by-compound deviations from the average anisotropy provide a promising approach for observing specific ligand field and vibronic excited state coupling effects on spin relaxation. Finally, we present a simple density functional theory workflow for computationally predicting T₁ anisotropy. Analysis of spin relaxation anisotropy leads to deeper fundamental understanding of spin–phonon coupling and relaxation mechanisms, promising to complement temperature-dependent relaxation rates as a key metric for understanding molecular spin qubits.