Effects of anisotropic charge on transverse optical phonons in NiO: Inelastic x-ray scattering spectroscopy study

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 $\sim 1\text{meV}$ 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.

Figure 1

(Color online) (a) The $\theta$ scan around the (333) Bragg peak. The bar indicates the expected peak position of $\left\{33\overline{3}\right\}$. (b) IXS spectra at $\left|q\right|=\left(0.1,0.1,0.1\right)$. LA denotes longitudinal-acoustic phonon. ${\text{TA}}_{\text{s}}$ (${\text{LA}}_{\text{s}}$) indicates the Stokes line of TA (LA) while ${\text{TA}}_{\text{a}}$ (${\text{LA}}_{\text{a}}$) does the anti-Stokes line. (c) The enlarged view of (b) at around the TO phonons. Dotted lines are results of curve fitting and the bars show the peak positions.

Figure 2

(Color online) (a) Phonon dispersion of NiO in the $\left|q\right|=\left[\text{qqq}\right]$ direction, which is determined theoretically (lines), and experimentally (the dots). (b) Simulated TO-phonon distribution in the vicinity of $\left|Q\right|=\left(333\right)$ (solid line). Dotted line shows the spectrum broadened by a 0.4 meV resolution function. (c) The band structure along [qqq] and $\left[\text{qq}\overline{\text{q}}\right]$ obtained by $\text{LSDA}+U$. Solid lines are the valence bands, which are used in calculating the Berry’s phase of polarization.

Figure 3

(Color online) (a) TO-phonon dispersion in the [111] and $\left[11\overline{1}\right]$ directions. Dotted lines are results of curve fitting. (b) Comparison of ${\text{TO}}_{\perp }$ and ${\text{TO}}_{\left[112\right]}$ phonon modes between experimental (marks) and theoretical (lines) results. The calculations are based on the shell model with (solid and dotted lines)/without (dashed lines) effective charge anisotropy. (c) Simulated TO-phonon distribution for the effective charge anisotropy in the vicinity of $\left|Q\right|=\left(333\right)$.