  The relative high fluxes of the Galactic ultra-luminous X-ray pulsar Swift
J0243 allow a detailed study of its spin-down regime in quiescence state, for a
first time. After the 2017 giant outburst, its spin frequencies show a linear
decreasing trend with some variations due to minor outbursts. The linear
spin-down rate is $\sim-1.9\times10^{-12}$ Hz/s during the period of lowest
luminosity, from which one can infer a dipole field $\sim1.75\times10^{13}$ G.
The $\dot{\nu}-L$ relation during the spin-down regime is complex, and the
$\dot{\nu}$ is close to 0 when the luminosity reaches both the high end
($L_{38}\sim0.3$) and the lowest value ($L_{38}\sim0.03$). The luminosity of
zero-torque is different for the giant outburst and other minor outbursts. It
is likely due to different accretion flows for different types of outburst, as
evidenced by the differences of the spectra and pulse profiles at a similar
luminosity for different types of outburst (giant or not). The pulse profile
changes from double peaks in the spin-up state to a single broad peak in the
low spin-down regime, indicating the emission beam/region is larger in the low
spin-down regime. These results show that accretion is still ongoing in the low
spin-down regime for which the neutron star is supposed to be in a propeller
state.
