“…1 (e) and (f) for Γ point in (e) and M point in (f), respectively. Note that the space group of Fe-X-Fe trilayer is P4/nmm, in which the glide-plane mirror symmetry operation {m z | 1 2 1 2 0} and inversion symmetry operation {i| 1 2 1 2 0} are essential [11,[36][37][38]. First, the Bloch states can be classified according to the parities of {m z | 1 2 1 2 0}, i.e., |d o/e,α or |d o/e , m l , m j with o, e, α, m l , m j denoting the odd or even parity of {m z | 1 2 1 2 0}, the αth d orbital, and two magnetic quantum numbers, respectively.…”