  We investigate the spin tunnelling of spin-1 Bose-Einstein condensates in a
linearly sweeping magnetic field with a mean-field treatment. We focus on the
two typical alkali Bose atoms $^{87}Rb$ and $^{23}Na$ condensates and study
their tunnelling dynamics according to different sweeping rates of external
magnetic fields. In the adiabatic (i.e., slowly sweeping) and sudden (i.e.,
fast sweeping) limits, no tunnelling is observed. For the case of moderate
sweeping rates, the tunnelling dynamics is found to be very sensitive on the
sweeping rates with showing a chaotic-like tunnelling regime. With magnifying
the regime, however, we find interestedly that the plottings become resolvable
under a resolution of $10^{-4}$ G/s where the tunnelling probability with
respect to the sweeping rate shows a regular periodic-like pattern. Moreover, a
conserved quantity standing for the magnetization in experiments is found can
dramatically affect the above picture of the spin tunnelling. Theoretically we
have given a reasonable interpretation to the above findings and hope our
studies would bring more attention to spin tunnelling experimentally.
