  We revealed the anomalous temperature behavior of the giant dielectric
permittivity and unusual frequency dependences of the pyroelectric response of
the fine-grained ceramics prepared by the spark plasma sintering of the
ferroelectric BaTiO3 nanoparticles. The temperature dependences of the
electro-resistivity indicate the frequency-dependent transition in the
electro-transport mechanisms between the lower and higher conductivity states
accompanied by the maximum in the temperature dependence of the loss angle
tangent. The pyroelectric thermal-wave probing revealed the existence of the
spatially inhomogeneous counter-polarized ferroelectric state at the opposite
surfaces of the ceramic sample. We described the anomalous temperature behavior
of the giant dielectric response and losses using the core-shell model for
ceramic grains and modified Maxwell-Wagner approach. We assume that core shells
and grain boundaries, which contain high concentration of space charge carriers
due to the presence of graphite inclusions in the inter-grain space, can
effectively screen weakly conductive ferroelectric grain cores. The
superparaelectric-like state with a giant dielectric response can appear in the
paraelectric shells and inter-grain space due to the step-like thermal
activation of localized polarons in the spatial regions, agreeing with
experimentally observed frequency-dependent transition of the electro-transport
mechanism. The obtained results can be the key for the description of complex
electrophysical properties inherent to the strongly inhomogeneous media with
electrically coupled insulating ferroelectric nanoregions and semiconducting
superparaelectric-like regions.
