Microscopic theory of electron spin relaxation in N@C60

Abstract

Endohedral N@${\text{C}}_{60}$ exhibits an extremely long electron spin relaxation time and offers a great potential in storing and processing quantum information. Here, we present a microscopic theory of electron spin relaxation in N@${\text{C}}_{60}$. The theory combines (1) the spin-orbit interaction of $\text{N}\text{ }2p$ electrons, which mixes the ground-state $^{4}S$ with excited $^{2}P$ and $^{2}D$ states, and (2) the coupling between the $\text{N}\text{ }2p$ electrons and ${\text{C}}_{60}$ ${H}_{g}$ vibrations, which facilitates transitions between $^{2}P$ and $^{2}D$ states. The spin relaxation occurs via a two-phonon (Raman) process by absorbing a ${H}_{g}$ phonon and emitting another at the (approximately) same frequency. The theory consistently explains measured spin relaxation time ${T}_{1}$ and its temperature dependence, and predicts two independent spin decoherence ${T}_{2}$ constants for $\ifmmode\pm\else\textpm\fi{}3/2\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}1/2$ transitions.