  Coupling at the interface of core/shell magnetic nanoparticles is known to be
responsible for the exchange bias (EB) and the relative sizes of core and shell
components are supposed to influence the associated phenomenology. In this
work, we have prepared core/shell structured nanoparticles with the total
averaged diameter around $\sim$ 27 nm and a wide range of shell thicknesses
through the controlled oxidation of Co nanoparticles well dispersed in an
amorphous silica host. Structural characterizations give compelling evidence of
the formation of Co$_3$O$_4$ crystallite phase at the shells surrounding the Co
core. Field cooled hysteresis loops display nonmonotonous dependence of the
exchange bias $H_E$ and coercive $H_C$ fields, that become maximum for a sample
with an intermediate shell thickness, at which lattice strain is also maximum
for both the phases. Results of our atomistic Monte Carlo simulations of the
particles with the same size and compositions as in experiments are in
agreement with the experimental observations and have allowed us to identify a
change in the contribution of the interfacial surface spins to the
magnetization reversal giving rise to the maximum in $H_E$ and $H_C$.
