Hyperfine-mediated transitions between a Zeeman split doublet in GaAs quantum dots: The role of the internal field

We consider the hyperfine-mediated transition rate between Zeeman split states of the lowest orbital level in a GaAs quantum dot. We separate the hyperfine Hamiltonian into a part which is diagonal in the orbital states and another one which mixes different orbitals. The diagonal part gives rise to an effective ~internal! magnetic field which, in addition to an external magnetic field, determines the Zeeman splitting. Spin-flip transitions in the dots are induced by the orbital-mixing part accompanied by an emission of a phonon. We evaluate the rate for different regimes of applied magnetic field and temperature. The rates we find are bigger than the spinorbit-related rates provided the external magnetic field is sufficiently low.