A comprehensive analysis of the giant in-plane uniaxial magnetic anisotropy of exchange biased molecular beam epitaxy grown Cu(1 1 0)/Ni 80Fe 20/Fe 50Mn 50 bilayers, discovered by Jungblut et al. (J. Appl. Phys. 75 (1994) 6659) is presented. Cu(1 1 0)/Ni 80Fe 20 samples have a uniaxial in-plane volume anisotropy with a [0 0 1] easy axis direction. Covering such ferromagnetic (F) layers with an antiferromagnetic (AF) Fe 50Mn 50 layer introduces an interface contribution to the uniaxial anisotropy that leads to an [1 1 ̄ 0] easy axis direction for F layer thicknesses below a critical value of 4 nm, and to an enhancement of the [0 0 1] anisotropy for larger thicknesses. The effect occurs only for Fe 50Mn 50 layers that are thicker than the minimum thickness that is required to obtain the exchange bias effect. From in situ low-energy electron diffraction (LEED) and scanning tunneling microscopy (STM) the Ni 80Fe 20 surface is shown to be corrugated, viz. in the form of elongated 2–4 monolayer high mesas at a distance of typically 4–8 nm in the [0 0 1] direction and a length along the [1 1 ̄ 0] direction of 25–60 nm. We show that this novel mesoscopic magnetic effect can be explained from the magnetically uncompensated nature of the AF (1 1 0) surface in combination with the corrugation of the F/AF interface. The spatially varying sign of the F–AF exchange coupling then leads to a preferred F layer magnetization direction that is perpendicular to the staggered AF magnetization. The remarkable change of sign of the interface anisotropy indicates that in the thin and thick F layer regimes the staggered AF magnetizations that are frozen in during the growth are different by a 90° rotation. We tentatively explain this from the kinetics of magnetic structure transformations in the bilayer during the growth process. The local exchange bias interaction parameter obtained from a quantitative analysis is J eb,loc ≈2.5–10 mJ/m 2 , which is close to the theoretical upper limit and is two orders of magnitude larger than the sample averaged interaction parameter, J eb, obtained from the exchange bias field. This provides the first direct experimental proof that the observed value of J eb of an AF/F bilayer can be the result of much larger but almost completely averaged out opposing local AF–F exchange interactions. The paper contains a brief overview of the recent developments in the field of mesoscopic magnetism.