  Surface magnetism and its correlation with the electronic structure are
critical to understand the gapless topological surface state in the intrinsic
magnetic topological insulator MnBi$_2$Te$_4$. Here, using static and time
resolved angle-resolved photoemission spectroscopy (ARPES), we find a
significant ARPES intensity change together with a gap opening on a Rashba-like
conduction band. Comparison with a model simulation strongly indicates that the
surface magnetism on cleaved MnBi$_2$Te$_4$ is the same as its bulk state. The
coexistence of surface ferromagnetism and a gapless TSS uncovers the novel
complexity of MnBi$_2$Te$_4$ that may be responsible for the low quantum
anomalous Hall temperature of exfoliated MnBi$_2$Te$_4$.
