  Hybrid multiferroics such as BiFeO$_3$ (BFO) and La$_{0.7}$Sr$_{0.3}$MnO$_3$
(LSMO) heterostructures are highly interesting functional systems due to their
complex electronic and magnetic properties. One of the key parameters
influencing the emergent properties is the quality of interfaces, where varying
interdiffusion lengths can give rise to different chemistry and distinctive
electronic states. Here we report high-resolution depth resolved chemical and
electronic investigation of BFO/LSMO superlattice using standing-wave hard
X-ray photoemission spectroscopy in the first-order Bragg as well as
near-total-reflection geometry. Our results show that the interfaces of BFO on
top of LSMO are atomically abrupt, while the LSMO on top of BFO interfaces show
an interdiffusion length of around 1.2 unit cells. The two interfaces also
exhibit different chemical gradients, with the BFO/LSMO interface being
Sr-terminated by a spectroscopically distinctive high binding energy component
in Sr 2p core-level spectra, which is spatially contained within 1 unit cell
from the interface. From the electronic point of view, unique valence band
features were observed for bulk-BFO, bulk-LSMO and their interfaces. Our X-ray
optical analysis revealed a unique electronic signature at the BFO/LSMO
interface, which we attribute to the coupling between those respective layers.
Valence band decomposition based on the Bragg-reflection standing-wave
measurement also revealed the band alignment between BFO and LSMO layers. Our
work demonstrates that standing-wave hard x-ray photoemission is a reliable
non-destructive technique for probing depth-resolved electronic structure of
buried layers and interfaces with sub-unit-cell resolution. Equivalent
investigations can be successfully applied to a broad class of material such as
perovskite complex oxides with emergent interfacial phenomena.
