In this work we develop an atomistic spin dynamics model for the ideal
Mn
50
Al
50
τ
-phase by means of first-principles calculations. The model is applied to study the domain wall and antiphase boundary phenomenology. In particular, it allows us to obtain the dependence on the interfacial exchange coupling of the nucleation and depinning fields, as well as the macroscopic magnetization profile across the antiphase boundary. We find that microscopic antiferromagnetic exchange coupling stronger than
10
meV
could unavoidably lead to the formation of a domain wall at the antiphase boundary.
