The multi-orbital Hubbard model is known to host various ordered states such as antiferromagnetism, ferromagnetism and orbital-order. Here we propose an engineered system - an ultrathin SrVO$_3$ film - to realize all said orders upon carrier doping, achievable with realistic gate-voltages. As a central observation we find that throughout the phase diagram, dominant non-local fluctuations lead to a momentum differentiation of the self-energy, particularly the scattering rate. In contrast to the pseudogap behavior in the one-band Hubbard model, here in the multi-band case the differentiation is between momenta on the occupied and unoccupied side of the Fermi surface. Our work, based on the dynamical vertex approximation, hence complements the understanding of spectral signatures of nearby second order phase transitions and calls to reexamine the momentum differentiation in other systems using methods beyond dynamical mean-field theory.
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