Phonon softening near the structural transition in BaFe${}_2$As${}_2$ observed by inelastic x-ray scattering

In this work we present the results of an inelastic x-ray scattering experiment detailing the behavior of the transverse acoustic [110] phonon in BaFe${}_2$As${}_2$ as a function of temperature. When cooling through the structural transition temperature, the transverse acoustic phonon energy is reduced from the value at room temperature, reaching a maximum shift near inelastic momentum transfer $\vec{q}=0.1$. This softening of the lattice results in a change of the symmetry from tetragonal to orthorhombic at the same temperature as the transition to long-range antiferromagnetic order. While the lattice distortion is minor, the anisotropy in the magnetic exchange constants in pnictide parent compounds is large. We suggest mechanisms of electron-phonon coupling to describe the interaction between the lattice softening and the onset of magnetic ordering.

Figure 1

(a) Comparison of 300 K, 140 K, and 130 K phonon spectra at $\vec{q}=0.1$. (b) Comparison of 300 K and 130 K phonon spectra at $\vec{q}=0.05$. The dotted line shows the Bragg peak measurement at $T=130$ K, $\vec{Q}$ $=$ (2,2,0)${}_O$. All spectra are Bose factor corrected and normalized to one. Errors are statistical errors propagated through Bose correction.

Figure 2

Energy of transverse acoustic phonon as a function of temperature for $\vec{Q}=(\vec{H}-\vec{q},\vec{K}+\vec{q})$ for $H=K=2$ and $\vec{q}=$ (a) 0.15, (b) 0.12, (c) 0.10, and (d) 0.08 in orthorhombic reciprocal lattice units. Dotted line indicates $T_S$. Error bars are statistical errors propagated through Bose correction and peak averaging. Two softenings are observed, one at $T_S$ and additional softening at low $\vec{q}$ at low temperature.

Figure 3

(a) Dispersion of TA phonon at 300 K, 140 K, 130 K, and 57 K. Dotted line indicates a linear fit to the 300 K data. (b) Central peak width as a function of $\vec{q}$ for $T=300$ K, 130 K, and 57 K. Thick dashed line at $E=2.3$ meV indicates the width of the Bragg peak measured at $\vec{Q}=(2,2,0)$ $T=130$ K. Dotted line on 300 K data represents the fitted peak width. Error bars are statistical errors propagated through Bose correction and the curve fitting procedure.