  The central-spin problem, in which an electron spin interacts with a nuclear
spin bath, is a widely studied model of quantum decoherence. Dynamic nuclear
polarization (DNP) occurs in central spin systems when electronic angular
momentum is transferred to nuclear spins and is exploited in spin-based quantum
information processing for coherent electron and nuclear spin control. However,
the mechanisms limiting DNP remain only partially understood. Here, we show
that spin-orbit coupling quenches DNP in a GaAs double quantum dot, even though
spin-orbit coupling in GaAs is weak. Using Landau-Zener sweeps, we measure the
dependence of the electron spin-flip probability on the strength and direction
of in-plane magnetic field, allowing us to distinguish effects of the
spin-orbit and hyperfine interactions. To confirm our interpretation, we
measure high-bandwidth correlations in the electron spin-flip probability and
attain results consistent with a significant spin-orbit contribution. We
observe that DNP is quenched when the spin-orbit component exceeds the
hyperfine, in agreement with a theoretical model. Our results shed new light on
the surprising competition between the spin-orbit and hyperfine interactions in
central-spin systems.
