  Phonon dispersion of detwinned NiO is measured using inelastic x-ray
scattering. It is found that, near the zone center, the energy of the
transverse optical phonon mode polarized parallel to the antiferromagnetic
order is ~1 meV lower than that of the mode polarized perpendicular to the
order, at room temperature. This is explained via anisotropic polarization of
the Ni and O atoms, as confirmed using a Berry's phase approach with
first-principles calculations. Our explanation avoids an apparent contradiction
in previous discussions focusing on Heisenberg interaction.
