  We report manifestly nonlinear dependence of quantum dot nuclear spin
polarization on applied magnetic fields. Resonant absorption and emission of
circularly polarized radiation pumps the resident quantum dot electron spin,
which in turn leads to nuclear spin polarization due to hyperfine interaction.
We observe that the resulting Overhauser field exhibits hysteresis as a
function of the external magnetic field. This hysteresis is a consequence of
the feedback of the Overhauser field on the nuclear spin cooling rate. A
semi-classical model describing the coupled nuclear and electron spin dynamics
successfully explains the observed hysteresis but leaves open questions for the
low field behaviour of the nuclear spin polarization.
