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Modification of the gap at the Dirac point (DP) in antiferromagnetic (AFM)axion topological insulator MnBi$_2$Te$_4$ and its electronic and spinstructure has been studied by angle- and spin-resolved photoemissionspectroscopy (ARPES) under laser excitation with variation of temperature(9-35~K), light polarization and photon energy. We have distinguished both alarge (62-67~meV) and a reduced (15-18~meV) gap at the DP in the ARPESdispersions, which remains open above the N\'eel temperature($T_\mathrm{N}=24.5$~K). We propose that the gap above $T_\mathrm{N}$ remainsopen due to short-range magnetic field generated by chiral spin fluctuations.Spin-resolved ARPES, XMCD and circular dichroism ARPES measurements show asurface ferromagnetic ordering for large-gap sample and significantly reducedeffective magnetic moment for the reduced-gap sample. These effects can beassociated with a shift of the topological DC state towards the second Mn layerdue to structural defects and mechanical disturbance, where it is influenced bya compensated effect of opposite magnetic moments.

Nature of the Dirac gap modulation and surface magnetic interaction in axion antiferromagnetic topological insulator MnBi$_2$Te$_4$