Complete characterization of GaAs gradient-elastic tensors and reconstruction of internal strain in GaAs/AlGaAs quantum dots using nuclear magnetic resonance

Abstract

Recently, we have calibrated the diagonal components ${S}_{11}={S}_{xxxx}$ of the GaAs gradient elastic tensor ${S}_{ijkl}$ using nuclear magnetic resonance (NMR) and photoluminescence spectroscopy of GaAs/AlGaAs quantum dot structures in Faraday geometry [E. A. Chekhovich et al., Phys. Rev. B 97, 235311 (2018)]. Here we measure quantum dot NMR spectra in oblique magnetic fields giving access to the off-diagonal components ${S}_{yzyz}$. We find the ratios ${S}_{yzyz}/{S}_{xxxx}\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}+1.{98}_{\ensuremath{-}0.27}^{+0.21}$ for $^{75}\mathrm{As}$ and $\ensuremath{\approx}\ensuremath{-}0.{40}_{\ensuremath{-}0.31}^{+0.23}$ for $^{69}\mathrm{Ga}$. Combined with our previous results, we find all independent nonzero components of ${S}_{ijkl}$: $Q{S}_{xxxx}\ensuremath{\approx}+0.758\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ V, $Q{S}_{yzyz}\ensuremath{\approx}+1.51\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ V for $^{75}\mathrm{As}$ and $Q{S}_{xxxx}\ensuremath{\approx}\ensuremath{-}0.377\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ V, $Q{S}_{yzyz}\ensuremath{\approx}+0.151\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ V for $^{69}\mathrm{Ga}$, where $Q$ is the corresponding nuclear quadrupolar moment. Our results show that earlier nuclear acoustic resonance experiments [R. K. Sundfors, Phys. Rev. B 10, 4244 (1974)] most likely overestimated the GaAs gradient elastic tensors, especially for $^{69}\mathrm{Ga}$. We further use NMR spectroscopy in oblique fields for assumption-free measurement of the intrinsic strain in GaAs/AlGaAs quantum dots. We find deviations of the strain principle directions from the sample growth axis, which vary between individual quantum dots.