First‐order magnetization processes (FOMP) and spin reorientation phase transitions are known to occur in hexaferrites as well as in rare‐earth transition‐metal compounds. This complex phenomenology has been described using high‐order terms in the anisotropy energy expansion. In order to understand the microscopic origin of these high‐order anisotropy constants in hexaferrites we have made a detailed analysis of the magnetic properties of BaZn1.1Co0.9Fe16O27which shows, at the same temperature, easy cone anisotropy and a FOMP. We have found good agreement between the experimental data and the predictions of a simple two sublattice model which takes into account the effect of the competition between the exchange and the difference in the anisotropy of the sublattices. This strongly supports the hypothesis that such a competition and the subsequent noncollinear order are the origin of the observed large high‐order anisotropy constants in hexaferrites as in intermetallic compounds.