  We present magnetostriction and magnetization measurements of a cobalt
ferrite Co0.8Fe2.2O4 single crystal. We observe unusual behaviour in the
magnetic hard axis of the single crystal which manifests in a jump of the
magnetization curve at a critical field. This first order magnetization process
(FOMP) which is explained as an anisotropy driven transition is visible at
temperatures lower than 150 K. By analyzing the anisotropy constants we found
that the higher order anisotropy constant K2 dominates the anisotropy energy.
In the magnetostriction measurements the FOMP is clearly visible as a huge jump
in the [111] direction, which can be explained by means of a geometric model.
