  This study investigated the dynamics of an electron--nuclear spin-coupled
system using three Al$_x$Ga$_{1-x}$As bulk samples with different aluminum
concentrations $x$ of 0, 0.05, and 0.15. The time-resolved Kerr rotation
technique was primarily used. The samples with $x=$ 0.05 and 0.15 exhibited an
anomalously large nuclear magnetic field of $\sim$1.1 T, which was twice the
applied magnetic field. This observation is unusual for bulk semiconductors,
which typically exhibit weak hyperfine interactions. Further investigations
revealed a long nuclear field formation time, which indicated clear two-stage
formation dynamics. Thus, this study concluded that slow nuclear spin diffusion
owing to the nuclear quadrupole interaction facilitates the formation process
of the nuclear field.
