Magneto-elastic coupling in detwinned Sr(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ by inelastic x-ray scattering

We present phonon dispersion measurements from detwinned single crystals of \linebreak Sr(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ with different doping levels(x=0 and 0.08) using inelastic x-ray scattering with 1.5 meV resolution at SPring-8. The crystals were detwinned by application of in-plane uniaxial stress. This allowed us to measure single domain phonon structure in the magnetically ordered state. We clearly identified the change in the phonon dispersion induced by the onset of magnetic order, with phonon energies depending on orientation of the phonon wave vector relative to the Fe moment. We compare our results to $\it ab$-$\it initio$ pseudo potential calculations: Magnetic calculations give better agreement than non-magnetic calculations, but in most parts of the Brillouin zone investigated, they overestimate the magnitude of the mode splitting and in fact often fail to predict even the correct sign of the splitting.