Magnetism-dependent phonon anomaly in LaFeAsO observed via inelastic x-ray scattering

The phonon dispersion was measured at room temperature along ($0,0,L$) in the tetragonal phase of LaFeAsO using inelastic x-ray scattering. Spin-polarized first-principles calculations imposing various types of antiferromagnetic order are in better agreement with the experimental results than nonmagnetic calculations, although the measurements were made well above the magnetic ordering temperature, $T_N$. Splitting observed between two $A_{1g}$ phonon modes at 22 and 26 meV is only reproduced in spin-polarized calculations. Magnetostructural effects similar to those observed in the $A$Fe${}_2$As${}_2$ ($A=\text{Ca}$,Sr,Ba,Eu) materials are present in LaFeAsO. The inclusion of Fe spin is necessary to find reasonable agreement of the calculations with the measured spectrum well above $T_N$. On-site Fe and As force constants show significant softening compared to nonmagnetic calculations, however an investigation of the real-space force constants associates the magnetoelastic coupling with a complex renormalization instead of softening of a specific pairwise force.

Figure 1

Energy scan at constant $Q$ at (a) $Q=(0.0,0,8.3)$ and (b) $Q=(0.0,0,8.5)$ measured at room temperature on LaFeAsO. Experimental data are given by solid green points. The black line is a fit using a pseudo-Voigt function.

Figure 2

Contour plots of the calculated dynamical structure factor along $(0,0,L)$. Values range from blue (no intensity) to red (high intensity), and have been multiplied by the energy to improve visibility of the optical modes. The white dots show the experimentally determined frequencies, as described in the text, with the intensity (also multiplied by the energy) shown by the size of the dot. (a) Nonmagnetic calculation, (b) Spin-polarized (SP) calculation with SDW ordering, (c) SP calculation with checkerboard ordering, and (d) SP calculation with striped ordering.

Figure 3

Dynamical structure factor calculation of constant-$Q$ line scan at $Q=(0,0,8.5)$. The dotted red line corresponds to nonmagnetic calculations of the dynamical structure factor. The solid yellow line corresponds to spin-polarized calculations imposing the SDW AFM ordering observed at lower temperatures. The black dashed line and blue dashed-dotted lines correspond to spin-polarized calculations with a striped (ferromagnetic along $c$) and checkerboard ordering, respectively. The elastic peak has been subtracted from the experimental data, shown in green circles, and is normalized to the average of the four calculations. The inset zooms in on the anomalous modes near 24 meV.

Figure 4

Different AFM order used in the calculations. La atoms are light blue, O atoms are green, As atoms are purple, and Fe atoms are brown. The red and blue arrows show up and down spin, respectively. (a) Expanded nonmagnetic unit cell, (b) experimentally observed SDW, (c) checkerboard ordering, and (d) striped ordering aligned ferromagnetically along the $c$ axis.