  We investigate within mean-field theory the influence of a one-dimensional
optical lattice and of trapped degenerate fermions on the critical rotational
frequency for vortex line creation in a Bose-Einstein condensate. We consider
laser intensities of the lattice such that quantum coherence across the
condensate is ensured. We find a sizable decrease of the thermodynamic critical
frequency for vortex nucleation with increasing applied laser strength and
suggest suitable parameters for experimental observation. Since 87Rb-40K
mixtures may undergo collapse, we analyze the related question of how the
optical lattice affects the mechanical stability of the system.
