  Superlattices are materials created by the alternating growth of two
chemically different materials. The direct consequence of creating a
superlattice is the folding of the Brillouin zone which gives rise to
additional electronic bands and phonon modes. This has been successfully
exploited to achieve new transport and optical properties in semiconductor
superlattices, for example. Here, we show that multiferroic BiFeO$_3$/LaFeO$_3$
superlattices are more than just periodic chemical stacking. Using transmission
electron microscopy, X-ray diffraction and first-principles calculations, we
demonstrate the existence of a new order of FeO$_6$ octahedra, with a period
along the growth direction about twice that of the chemical supercell, i.e. a
superorder. The effect of this new structural order on the lattice dynamics is
studied with ultrafast optical pump-probe experiments. While a mode at 1.2 THz
is attributed solely to the chemical modulation of the superlattice, the
existence of another 0.7 THz mode seems to be explained only by a double
Brillouin zone folding in agreement with the structural description. Our work
shows that multiferroic BiFeO$_3$/LaFeO$_3$ superlattices can be used to tune
the spectrum of coherent THz phonons, and potentially that of magnons or
electromagnons.
