  Double quantum dot systems in the spin blockade regime exhibit leakage
currents that have been attributed to the Hyperfine interaction. We model
weakly coupled double-dot transport using a rate equation approach which
accounts for Hyperfine flip-flop transitions. The rate equations allow us to
obtain self-consistently the time evolution for electronic charge occupations
and for the nuclei polarizations in each dot. We analyze the current in the
spin blockade region as a function of magnetic field and observe hysteretic
behavior for fields corresponding to the crossing between triplet and singlet
states.
