centers in diamond*

We investigate on 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. Starting from the dipolar spin-spin interaction between two electrons, we couple the spins of the electron to the movements of the ions and end up with an effective spin-phonon interaction potential. Taking this time dependent potential as a perturbation of the system leads to Fermi's golden rule for transition rates which allows to calculate the spin lattice relaxation time T₁. We simulate the color center with the Vienna Ab Initio Simulation Package (VASP) to extract the figures necessary to quantify T₁.
Our theory leads to three different types of first order processes for spin-phonon interaction in analogy with electron-photon interaction:
An excitation of a spin is accompanied by the absorption of a phonon with the matching frequency of the spin transition.
A deexcitation of a spin due to induced emission of a phonon.
A temperature independent contribution where a spin relaxes spontaneously and a phonon is emitted.
A comparison with experimental data is presented.