Spin relaxation due to Spin-phonon coupling in Molecular spin qubit*

A promising molecular spin qubit, comprising a Lu(II) compound characterized by a large clock transition and an extended electron spin lifetime, has garnered considerable attention in recent years. A huge hyperfine interaction plays an important role in this spin qubit. We investigate how changes in the hyperfine interaction between the electron and the Lu nucleus, induced by phonon motion, impact spin relaxation. We employ first-principles calculations to obtain the variance in hyperfine interaction resulting from phonon motion. The phonon dispersion and modes are treated using the frozen phonon method. Subsequently, we solve the Redfield theory equation of motion in a second quantization framework to determine the electron spin relaxation time. Temperature dependence of the spin relaxation time is also obtained. The calculated relaxation time is in good agreement with experimental data at low temperatures.