Mechanisms of $S-T_+$ coupling in singlet-triplet qubits

Semiconductor quantum dots provide a unique environment for studying a variety of problems, from few-particle systems to the central spin problem. Investigating these systems furthers our understanding of fundamental physics and advances efforts to achieve semiconductor spin-based quantum information processing. We study two electron spins in a semiconducting double quantum dot and measure the spin singlet to $m_s=1$ triplet ($S-T_+$) avoided crossing. Our results suggest that several processes, including the hyperfine interaction between the electrons and the host nuclei and spin-orbit coupling in the quantum dots, compete to drive the $S-T_+$ transition. This work gives insight into the poorly understood nuclear dynamics in these systems and provides a path forward for improving nuclear pumping efficiency and therefore coherence times in semiconducting spin qubits.