  We present a first-principles study of 180-degree ferroelectric domain walls
in tetragonal barium titanate. The theory is based on an effective Hamiltonian
that has previously been determined from first-principles
ultrasoft-pseudopotential calculations. Statistical properties are investigated
using Monte Carlo simulations. We compute the domain-wall energy, free energy,
and thickness, analyze the behavior of the ferroelectric order parameter in the
interior of the domain wall, and study its spatial fluctuations. An abrupt
reversal of the polarization is found, unlike the gradual rotation typical of
the ferromagnetic case.
