Relaxation of Shallow Donor Electron Spin due to Interaction with Nuclear Spin Bath

TL;DR

This paper investigates how nuclear spins in silicon affect the relaxation and decoherence of shallow donor electron spins, like phosphorus, at low temperatures and magnetic fields, highlighting the nuclear spin bath's significant role.

Contribution

It provides a detailed calculation of electron spin relaxation times considering the nuclear spin bath, revealing the impact of nuclear spins on donor electron spin decoherence in silicon.

Findings

Nuclear spins significantly influence electron spin relaxation at low magnetic fields.

Calculated relaxation times $T_1$ and $T_2$ depend on external magnetic field strength.

Nuclear spin bath plays a crucial role in donor electron spin decoherence in silicon.

Abstract

We study the low-temperature dynamics of a shallow donor, e.g., $^{31}$P, impurity electron spin in silicon, interacting with the bath of nuclear spins of the $^{29}$Si isotope. For small applied magnetic fields, the electron spin relaxation is controlled by the steady state distribution of the nuclear spins. We calculate the relaxation times $T_1$ and $T_2$ as functions of the external magnetic field, and conclude that nuclear spins play an important role in the donor electron spin decoherence in Si:P at low magnetic fields.