# Spin-orbit coupling induced two-electron relaxation in silicon donor pairs

## TL;DR

This paper theoretically identifies a dominant spin-orbit coupling-based relaxation mechanism in silicon donor pairs, revealing its dependence on donor configuration, temperature, and magnetic field, with implications for spintronics and quantum computing.

## Contribution

It uncovers a previously overlooked relaxation process in silicon donor pairs driven by spin-orbit coupling, electron-phonon, and inter-donor interactions, with detailed symmetry analysis.

## Key findings

- Relaxation rate scales from J^5 to J^4 with exchange interaction J.
- Dependence on donor alignment and triplet spin orientation.
- Relaxation occurs without magnetic field, with crossover behavior at high Zeeman energies.

## Abstract

We unravel theoretically a key intrinsic relaxation mechanism among the low-lying singlet and triplet donor-pair states in silicon, an important element in the fast-developing field of spintronics and quantum computation. Despite the perceived weak spin-orbit coupling (SOC) in Si, we find that our discovered relaxation mechanism, combined with the electron-phonon and inter-donor interactions, dominantly drives the transitions in the two-electron states over a large range of donor coupling regime. The scaling of the relaxation rate with inter-donor exchange interaction $J$ goes from $J^5$ to $J^4$ at the low to high temperature limits. Our analytical study draws on the symmetry analysis over combined band, donor envelope and valley configurations. It uncovers naturally the dependence on the donor-alignment direction and triplet spin orientation, and especially on the dominant SOC source from donor impurities. While a magnetic field is not necessary for this relaxation, unlike in the single-donor spin relaxation, we discuss the crossover behavior with increasing Zeeman energy in order to facilitate comparison with experiments.