Periodic optical pumping of semiconductor systems like gallium arsenide grants insight into the spin dynamics and coupling of electrons and nuclei. Nuclear-induced frequency focusing occurs when spin-polarized nuclei alter the Larmor spin precession frequency of the electrons to approach discrete values. These discrete values are integer or half-integer multiples of a quantity that is proportional to the repetition rate of the optical pulses. In earlier work, we presented a numerical model based on the optical Stark effect that captures the interplay of electron and nuclear spins in bulk gallium arsenide. In this paper, we report the observation of nuclear-induced frequency focusing in our material and show that this behavior can help to explain the peak deformations that we observe to persist in subsequent peaks in a magnetic-field scan measurement of Kerr rotation when the field scan is paused for an extended time interval. We demonstrate that extending our model to account for a distribution of electron spins with different Overhauser fields allows us to reproduce these observations as well as additional phenomena, including changes in Kerr rotation amplitude, from our previous work.
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