  Exchange bias (EB) shifts are commonly reported for the ferromagnetic
(FM)/antiferromagnetic (AFM) bilayer systems. While stoichiometric ordered
Sm$_{2}$NiMnO$_{6}$ (SNMO) and BaTiO$_{3}$ (BTO) are known to possesses FM and
diamagnetic orderings respectively, here we have demonstrated the cooling field
dependent EB and training effects in epitaxial SNMO/BTO/SNMO (SBS)
heterostructure thin films. The polarized Raman spectroscopy and magnetometric
studies reveal the presence of anti-site cation disorders in background of
ordered lattice in SNMO layers, which introduces Ni-O-Ni or Mn-O-Mn local AFM
interactions in long range Ni-O-Mn FM ordered host matrix. We have also
presented growth direction manipulation of the degree of cation disorders in
the SNMO system. Polarization dependent X-ray absorption measurements, duly
combined with configuration interaction simulations suggest charge transfer
from Ni/Mn 3\textit{d} to Ti 3\textit{d} orbitals through O 2\textit{p}
orbitals across the SNMO/BTO (SB) interfaces, which can induce magnetism in the
BTO spacer layer. The observed exchange bias in SBS heterostructures is
discussed considering the pinning of moments due to exchange coupling at SB (or
BTO/SNMO) sandwich interface.
