Ab-initio study of the relation between electric polarization and   electric field gradients in ferroelectrics
  The hyperfine interaction between the quadrupole moment of atomic nuclei and the electric field gradient (EFG) provides information on the electronic charge distribution close to a given atomic site. In ferroelectric materials, the loss of inversion symmetry of the electronic charge distribution is necessary for the appearance of the electric polarization. We present first-principles density functional theory calculations of ferroelectrics such as BaTiO3, KNbO3, PbTiO3 and other oxides with perovskite structures, by focusing on both EFG tensors and polarization. We analyze the EFG tensor properties such as orientation and correlation between components and their link with electric polarization. This work supports previous studies of ferroelectric materials where a relation between EFG tensors and polarization was observed, which may be exploited to study ferroelectric order when standard techniques to measure polarization are not easily applied. 
J. N. Gon\c{c}alves, A. Stroppa, J. G. Correia, T. Butz, S. Picozzi,   A. S. Fenta and V. S. Amaral
cond-mat.mtrl-sci cond-mat.other