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The detailed behavior of the in-plane infrared-active vibrational modes hasbeen determined in AFe$_2$As$_2$ (A$\,=\,$Ca, Sr, and Ba) above and below thestructural and magnetic transition at $T_N=$172, 195 and 138 K, respectively.Above $T_N$, two infrared-active $E_u$ modes are observed. In all threecompounds, below $T_N$ the low-frequency $E_u$ mode is observed to split intoupper and lower branches; with the exception of the Ba material, the oscillatorstrength across the transition is conserved. In the Ca and Sr materials, thehigh-frequency $E_u$ mode splits into an upper and a lower branch; however, theoscillator strengths are quite different. Surprisingly, in both the Sr and Bamaterials, below $T_N$ the upper branch appears be either very weak or totallyabsent, while the lower branch displays an anomalous increase in strength. Thefrequencies and atomic characters of the lattice modes at the center of theBrillouin zone have been calculated for the high-temperature phase for each ofthese materials. The high-frequency $E_u$ mode does not change in position orcharacter across this series of compounds. Below $T_N$, the $E_u$ modes arepredicted to split into features of roughly equal strength. We discuss thepossibility that the anomalous increase in the strength of the lower branch ofthe high-frequency mode below $T_N$ in the Sr and Ba compounds, and the weak(silent) upper branch, may be related to the orbital ordering and a change inthe bonding between the Fe and As atoms in the magnetically-ordered state.

Vibrational anomalies in AFe$_\mathbf{2}$As$_\mathbf{2}$ (A$\,=\,$Ca, Sr, and Ba) single crystals