  We proved the existence of a universal flexo-antiferrodistortive coupling as
a necessary complement to the well-known flexoelectric coupling. The coupling
is universal for all antiferrodistortive systems and can lead to the formation
of incommensurate, spatially-modulated phases in multiferroics. Our analysis
can provide a self-consistent mesoscopic explanation for a broad range of
modulated domain structures observed experimentally in multiferroics.
