Scaling laws of electron and hole spin relaxation in indirect band gap (In,Al)As/AlAs quantum dots

We investigate the electron and heavy hole spin dynamics as a function of magnetic field in ensembles of indirect band gap (In,Al)As/AlAs quantum dots (QDs) with type-I band alignment. Employing a comprehensive model that accounts for both the exciton level quartet and the magnetic-field-driven redistribution of excitons between these states via spin relaxation processes, we extract the electron (${\tau }_{se}$) and heavy hole (${\tau }_{sh}$) spin relaxation times as a function of magnetic field for QDs of varying sizes. Our analysis reveals that both ${\tau }_{se}(B)$ and ${\tau }_{sh}(B)$ exhibit power-law scaling behavior, yet the scaling exponents for electrons and heavy holes show markedly different evolution with QD size. For QDs with a diameter of about 9 nm, we find ${\tau }_{se}(B)\propto B^{-5}$ and ${\tau }_{sh}(B)\propto B^{-3}$. Remarkably, increasing the QD diameter to about 16 nm results in a drastic change of the scaling laws, with both ${\tau }_{se}(B)$ and ${\tau }_{sh}(B)$ following a $\propto B^{-9}$ dependence. We discuss the underlying mechanisms responsible for this size-dependent transformation of the magnetic field scaling behavior of carrier spin relaxation.