Low Temperature Relaxation of Donor Bound Electron Spins in $^{28}$Si:P

TL;DR

This study investigates the extremely long spin relaxation times of donor electrons in isotopically enriched silicon at low temperatures, revealing temperature-dependent relaxation mechanisms and validating theoretical predictions about phonon interactions.

Contribution

It provides detailed measurements of spin relaxation times in $^{28}$Si:P at low temperatures, highlighting the transition from linear to T$^9$ dependence and confirming phonon-related relaxation processes.

Findings

Spin relaxation times exceed 20 hours at low temperatures.

Relaxation rate increases linearly below 1 K and transitions to T$^9$ dependence between 2-4 K.

Validation of phonon-mediated relaxation processes in isotopically enriched silicon.

Abstract

We measure the spin-lattice relaxation of donor bound electrons in ultrapure, isotopically enriched, phosphorus-doped $^{28}$Si:P. The optical pump-probe experiments reveal at low temperatures extremely long spin relaxation times which exceed 20 h. The $^{28}$Si:P spin relaxation rate increases linearly with temperature in the regime below 1 K and shows a distinct transition to a T$^9$ dependence which dominates the spin relaxation between 2 and 4 K at low magnetic fields. The T$^7$ dependence reported for natural silicon is absent. At high magnetic fields, the spin relaxation is dominated by the magnetic field dependent single phonon spin relaxation process. This process is well documented for natural silicon at finite temperatures but the $^{28}$Si:P measurements validate additionally that the bosonic phonon distribution leads at very low temperatures to a deviation from the linear temperature dependence of $\Gamma$ as predicted by theory.