  The combination of topology and magnetism is attractive to produce exotic
quantum matters, such as the quantum anomalous Hall state, axion insulators and
the magnetic Weyl semimetals. MnBi2Te4, as an intrinsic magnetic topological
insulator, provides a platform for the realization of various topological
phases. Here we report the intermediate Hall steps in the magnetic hysteresis
of MnBi2Te4, where four distinguishable magnetic memory states at zero magnetic
field are revealed. The gate and temperature dependence of the magnetic
intermediate states indicates the noncollinear spin structure in MnBi2Te4,
which can be attributed to the Dzyaloshinskii-Moriya interaction as the
coexistence of strong spin-orbit coupling and local inversion symmetry breaking
on the surface. Moreover, these multiple magnetic memory states can be
programmatically switched among each other through applying designed pulses of
magnetic field. Our results provide new insights of the influence of bulk
topology on the magnetic states, and the multiple memory states should be
promising for spintronic devices.
