Electron spin coherence of silicon vacancies in proton-irradiated 4H-SiC

We report ${T}_{2}$ spin coherence times for electronic states localized in Si vacancies in $4H\text{\ensuremath{-}}\mathrm{SiC}$. Our spin coherence study included two SiC samples that were irradiated with 2 MeV protons at different fluences (${10}^{13}$ and ${10}^{14}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$) in order to create samples with unique defect concentrations. Using optically detected magnetic resonance and spin echo, the coherence times for each sample were measured across a range of temperatures from 8 to 295 K. All echo experiments were done at a magnetic field strength of 0.371 T and a microwave frequency of 10.49 GHz. The longest coherence times were obtained at 8 K, being $270\ifmmode\pm\else\textpm\fi{}61\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$ for the ${10}^{13}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ proton-irradiated sample and $104\ifmmode\pm\else\textpm\fi{}17\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$ for the ${10}^{14}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ sample. The coherence times for both samples displayed unusual temperature dependencies; in particular, they decreased with temperature until 60 K, then increased until 160 K, then decreased again. This increase between 60 and 160 K is tentatively attributed to a motional Jahn-Teller effect. The consistently longer lifetimes for the ${10}^{13}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ sample suggest that a significant source of the spin dephasing can be attributed to dipole-dipole interactions between Si vacancies or with other defects produced by the proton irradiation. The lack of a simple exponential decay for our ${10}^{14}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ sample indicates an inhomogeneous distribution of defect spins.