We propose to investigate the uniaxial magnetic anisotropy and its temperature-dependent sign change (Morin transition) in epitaxial thin films of the prototypical antiferromagnet alpha-Fe2O3. The scenario is well established in bulk with a Morin transition temperature of 263 K, in thin films it is still a matter of debate. However, a deeper understanding is mandatory because of its interplay with the Dzyaloshinsky-Moriya interaction (DMI) between the Fe3+ moments, important for correctly describing the spin-Hall magnetoresistance (SMR) and its unexpected large amplitude as well as the magnon Hanle effect and its nonreciprocal behavior. The DMI breaks the inversion symmetry and leads to a finite canting of the antiferromagnetic sublattices, resulting in a tiny macroscopic magnetic moment in the (0001) plane. We will record the XMCD of this moment and the XMLD of the Néel order to quantify the DMI, to determine the Fe3+ canting angle, and to pinpoint the Morin transition temperature.