  We revisit the electronic structure of BaFe$_2$As$_2$, the archetypal parent
compound of the Fe-based superconductors, using angle-resolved photoemission
spectroscopy (ARPES). Our high-resolution measurements of samples detwinned by
the application of a mechanical strain reveal a highly anisotropic 3D Fermi
surface in the low temperature magnetic phase. By comparison of the observed
dispersions with ab-initio calculations, we argue that overall it is magnetism,
rather than orbital ordering, which is the dominant effect, reconstructing the
electronic structure across the Fe 3d bandwidth. Finally, we measure band
dispersions directly from within one domain without applying strain to the
sample, by using the sub-micron focused beam spot of a nano-ARPES instrument.
