Spin-density-wave-induced anomalies in the optical conductivity of AFe2As2, (A=Ca, Sr, Ba) single-crystalline iron pnictides

We report the complex dielectric function of high-quality $A\textrm{Fe}_2\textrm{As}_2$, ($A$=Ca, Sr, Ba) single crystals with $T_{\mathrm{N}}\approx150\ \textrm{K}$, $200\ \textrm{K}$, and $138\ \textrm{K}$, respectively, determined by broadband spectroscopic ellipsometry at temperatures $10\leq T\leq300\ \textrm{K}$ and wavenumbers from $100\ \textrm{cm}^{-1}$ to $52000\ \textrm{cm}^{-1}$. In $\textrm{CaFe}_2\textrm{As}_2$ we identify the optical spin-density--wave gap $2\Delta_{\mathrm{SDW}}\approx1250\ \textrm{cm}^{-1}$. The $2\Delta_{\mathrm{SDW}}/(k_{\mathrm{B}}T_{\mathrm{N}})$ ratio, characterizing the strength of the electron-electron coupling in the spin-density--wave state, amounts to $\approx12$ in $\textrm{CaFe}_2\textrm{As}_2$, significantly larger than the corresponding values for the $\textrm{SrFe}_2\textrm{As}_2$ and $\textrm{BaFe}_2\textrm{As}_2$ compounds: 8.7 and 5.3, respectively. We further show that, similarly to the Ba-based compound, two characteristic SDW energy gaps can be identified in the infrared-conductivity spectra of both $\textrm{SrFe}_2\textrm{As}_2$ and $\textrm{CaFe}_2\textrm{As}_2$ and investigate their detailed temperature dependence in all three materials. This analysis reveals the existence of an anomaly in $\textrm{CaFe}_2\textrm{As}_2$ at a temperature $T^*\approx80\ \textrm{K}$, well below the N\'eel temperature of this compound, which implies weak coupling between the two SDW subsystems. The coupling between the two subsystems evolves to intermediate in the Sr-based and strong in the Ba-based material. The temperature dependence of the infrared phonons reveals clear anomalies at the corresponding N\'eel temperatures of the investigated compounds. In $\textrm{CaFe}_2\textrm{As}_2$, the phonons exhibit signatures of SDW fluctuations above $T_N$ and some evidence for anomalies at $T^*$. (full abstract in PDF)