Effect of magnetism on lattice dynamics in ${\mathrm{SrFe}}_2{\mathrm{As}}_2$ using high-resolution inelastic x-ray scattering

Phonon spectra of detwinned ${\mathrm{SrFe}}_2{\mathrm{As}}_2$ crystals, as measured by inelastic x-ray scattering, show clear anisotropy accompanying the magnetostructural transition at 200 K. We model the mode splitting using magnetic DFT calculations, including a phenomenological reduction in force-constant anisotropy that can be attributed to magnetic fluctuations. This serves as a starting point for a general model of phonons in this material applicable to both the antiferromagnetically ordered phase and the paramagnetic phase. Using this model, the measured splitting in the magnetic phase below $T_N$, and the measured phonon linewidth, we set a lower bound on the mean magnetic fluctuation frequency above $T_N$ at 210 K.

Figure 1

Anisotropy of phonon structure of detwinned ${\mathrm{SrFe}}_2{\mathrm{As}}_2$. (a),(b) Typical $2\theta$ scan of the tetragonal (3 3 0) and $\left(3\overline{3}0\right)$ reflections for twinned and detwinned crystals below $T_{s,N}$. (c),(d) IXS spectra for twinned and detwinned crystals at $\mathit{q}=(-0.5,\pm 0.5,0)$ measured below $T_{s,N}$. Solid lines are fits to the data. (e) IXS spectra measured at relatively twin-free section of twinned crystal. (f) Comparison of IXS spectra measured on the twinned crystal and a superposition of two IXS spectra measured on the detwinned crystal. (g) Schematic showing the directions in reciprocal space where the IXS scans were measured.

Figure 2

(a),(b) Temperature dependence of IXS spectra of detwinned ${\mathrm{SrFe}}_2{\mathrm{As}}_2$ at $\mathit{Q}=(3-q,3+q,0)$ (red) and $\mathit{Q}=(3-q,-3-q,0)$ (blue) corresponding to the two $\mathrm{\Gamma }\text{−}M$ directions.

Figure 3

(a)–(c) Comparison of the measured dispersion for detwinned ${\mathrm{SrFe}}_2{\mathrm{As}}_2$ and various DFT calculations at $\mathit{Q}=(3-q,\pm (3+q),0)$. In (b) magnetic and (c) rescaled magnetic calculations, there are two inequivalent $\mathrm{\Gamma }\text{−}M$ directions pointing along the AFM and the FM ordered directions, shown in red and blue, respectively. Lines represent calculated phonon dispersions weighted by the structure factor, whereas the data points represent experimental phonon energies. (d)–(g) Comparison of the measured mode splitting for detwinned ${\mathrm{SrFe}}_2{\mathrm{As}}_2$ and DFT calculations at $\mathit{Q}=(3-q,\pm (3+q),0)$. Mode 1 is the TA mode, modes 2, 3, and 4 have, respectively, $E_u,B_{1g}$, and $E_u$ symmetry at $\mathrm{\Gamma }$ in the tetragonal structure $\left(I4/mmm\right)$.