  Generic conditions are established for producing a non-Fraunhofer response of
the critical supercurrent subject to an external magnetic field in
ferromagnetic Josephson junctions. Employing the quasiclassical Keldysh-Usadel
method, we demonstrate theoretically that an inhomogeneity in the magnitude of
the energy scales in the system, including Thouless energy, exchange field and
temperature gradient normal to the transport direction, influences drastically
the standard Fraunhofer pattern. The exotic non-Fraunhofer response, similar to
that observed in recent experiments, is described in terms of an intricate
interplay between multiple '0-pi'-states and is related to the appearance of
proximity vortices.
