  Recently evidence has emerged in the topological superconductor
Fe-chalcogenide FeTe1-xSex for time-reversal symmetry breaking (TRSB), the
nature of which has strong implications on the Majorana zero modes (MZM)
discovered in this system. It remains unclear however whether the TRSB resides
in the topological surface state (TSS) or in the bulk, and whether it is due to
an unconventional TRSB superconducting order parameter or an intertwined order.
Here by performing in superconducting FeTe1-xSex crystals both
surface-magneto-optic-Kerr effect (SMOKE) measurements using a Sagnac
interferometer and bulk magnetic susceptibility measurements, we pinpoint the
TRSB to the TSS, where we also detect a Dirac gap. Further, we observe surface
TRSB in non-superconducting FeTe1-xSex of nominally identical composition,
indicating that TRSB arises from an intertwined surface ferromagnetic (FM)
order. The observed surface FM bears striking similarities to the
two-dimensional (2D) FM found in 2D van der Waals crystals, and is highly
sensitive to the exact chemical composition, thereby providing a means for
optimizing the conditions for Majorana particles that are useful for robust
quantum computing.
