  We predict breakdown of the electric dipole approximation at nonlinear Cooper
minimum in direct two-photon $K-$shell atomic ionisation by circularly
polarised light. According to predictions based on the electric dipole
approximation, we expect that tuning the incident photon energy to the Cooper
minimum in two-photon ionisation results in pure depletion of one spin
projection of the initially bound $1s$ electrons, and hence, leaves the ionised
atom in a fully oriented state. We show that by inclusion of electric
quadrupole interaction, dramatic drop of orientation purity is obtained. The
low degree of the remaining ion orientation provides a direct access to
contributions of the electron-photon interaction beyond the electric dipole
approximation in the two-photon ionisation of atoms and molecules. The
orientation of the photoions can be experimentally detected either directly by
a Stern-Gerlach analyzer, or by means of subsequent $K\alpha$ fluorescence
emission, which has the information about the ion orientation imprinted in the
polarisation of the emitted photons.
