Ab initio calculation of the spin lattice relaxation time $T_1$ for nitrogen-vacancy centers in diamond

TL;DR

This paper presents a first-principles method to calculate the spin lattice relaxation time $T_1$ for nitrogen-vacancy centers in diamond, linking spin-phonon interactions with temperature dependence and matching experimental data.

Contribution

The study introduces a novel ab initio approach to compute $T_1$ for NV centers, integrating spin-phonon coupling and phonon mode analysis from first principles.

Findings

Calculated $T_1$ agrees with experimental results.

Established a first-principles framework for spin relaxation in NV centers.

Analyzed phonon modes relevant to spin relaxation.

Abstract

We investigate the fundamental mechanism of spin phonon coupling in the negatively charged nitrogen vacancy center $(\mathrm{NV}^-)$ in diamond in order to calculate the spin lattice relaxation time $T_1$ 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 $V_{s-ph}$. Taking this time dependent potential as a perturbation of the system, a Fermi's golden rule expression for transition rates is obtained which allows to calculate the spin lattice relaxation time $T_1$. We simulate the color center with the Vienna Ab initio Simulation Package (VASP) to extract the figures necessary to quantify $T_1$. We investigate on 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 bandstructure by diagonalizing the dynamical matrix using the phononpy package. We show that our model allows to calculate $T_1$ in good agreement with experimental observations.