Effects of Anisotropic Charge on Transverse Optical Phonons in NiO

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.