Superorders and acoustic modes folding in BiFeO$_3$/LaFeO$_3$ superlattices

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.