Ab initio calculation of the spin lattice relaxation time T1 for nitrogen-vacancy centers in diamond

Abstract

We investigate the fundamental mechanism of spin-phonon coupling in the negatively charged nitrogen-vacancy center (NV-) in diamond in order to calculate the spin lattice relaxation time T1 and its temperature dependence from first principles. Starting from the dipolar spin-spin interaction between two electrons, we couple the spins of the electrons to the movements of the ions and end up with an effective spin-phonon interaction potential Vs-ph. Taking this time-dependent potential as a perturbation of the system, a Fermi's golden rule expression for transition rates is obtained which allows us to calculate the spin lattice relaxation time T1. We find that the temperature dependence of T1 is determined by the the zero-temperature transition rate Γ0. We simulate the color center ab initio to extract the figures necessary to quantify Γ0. We calculate the local phonon modes of the color center within the harmonic approximation using the small displacement method and extract the phononic density of states and band structure by diagonalizing the dynamical matrix. We show that our model allows us to calculate T1 in good agreement with experimental observations.