  We present a family of discrete breathers, which exists in a nonlinear
polarizability model of ferroelectric materials. The core-shell model is set up
in its non-dimensionalized Hamiltonian form and its linear spectrum is
examined. Subsequently, seeking localized solutions in the gap of the linear
spectrum, we establish that numerically exact and potentially stable discrete
breathers exist for a wide range of frequencies therein.
  In addition, we present nonlinear normal mode, extended spatial profile
solutions from which the breathers bifurcate, as well as other associated
phenomena such as the formation of phantom breathers within the model.
  The full bifurcation picture of the emergence and disappearance of the
breathers is complemented by direct numerical simulations of their dynamical
instability, when the latter arises.
