A novel non-adiabatic spin relaxation mechanism in molecular qubits

The interaction of electronic spin and molecular vibrations mediated by spin–orbit coupling governs spin relaxation in molecular qubits. We derive an extended molecular spin Hamiltonian that includes both adiabatic and non-adiabatic spin-dependent interactions, and we implement the computation of its matrix elements using state-of-the-art density functional theory. The new molecular spin Hamiltonian contains a novel spin–vibrational orbit interaction with a non-adiabatic origin, together with the traditional molecular Zeeman and zero-field splitting interactions with an adiabatic origin. The spin–vibrational orbit interaction represents a non-Abelian Berry curvature on the ground-state electronic manifold and corresponds to an effective magnetic field in the electronic spin dynamics. We further develop a spin relaxation rate model that estimates the spin relaxation time via the two-phonon Raman process. An application of the extended molecular spin Hamiltonian together with the spin relaxation rate model to Cu(II) porphyrin, a prototypical S = 1/2 molecular qubit, demonstrates that the spin relaxation time at elevated temperatures is dominated by the non-adiabatic spin–vibrational orbit interaction. The computed spin relaxation rate and its magnetic field orientation dependence are in excellent agreement with experimental measurements.