Evolution of the optical spectrum with doping in $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$

We investigated the optical spectrum of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ single crystals with various doping levels. It is found that the low-energy optical conductivity spectrum of this system can be decomposed into two components: a sharp Drude term and a broad “incoherent” term. For the compounds showing magnetic order, a gap appears predominantly in the incoherent component while an $s$-wave-like superconducting gap opens in both components for highly doped compounds. The Drude weight steadily increases as doping proceeds, consistent with electron doping in this system. On the other hand, the incoherent spectral weight is almost doping independent but its spectral feature is intimately connected with the magnetism. We demonstrate that the presence of two distinct components in the optical spectrum well explains the doping and temperature dependences of the dc resistivity.

Figure 1

(Color online) Temperature dependence of the in-plane resistivity for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ samples ($x=0$, 0.04, 0.06, and 0.08). A kink for $x=0$ corresponds to a magnetic transition at $T_{\text{N}}=138\text{K}$. For $x=0.04$, $T_{\text{N}}$ shifts down to $\sim 80\text{K}$. The compounds with $x=0.06$ and 0.08 show a sharp superconducting transition at $T_{\text{c}}=25$ and 20 K, respectively. The inset shows the schematic phase diagram of Co-doped ${\text{BaFe}}_2{\text{As}}_2$. Arrows indicate the compositions for which we study in the present work.

Figure 2

(Color online) (a) Optical conductivity spectrum and (b) $N_{\text{eff}}\left(\omega \right)$ of undoped ${\text{BaFe}}_2{\text{As}}_2$ at several temperatures below 150 K. Below $T_{\text{N}}=138\text{K}$, low-energy conductivity is suppressed and the suppressed weight is transferred to the higher-energy region up to $2000{\text{cm}}^{-1}$ as evidenced by $N_{\text{eff}}$ curves which merge at around $2000{\text{cm}}^{-1}$. An isosbestic point in ${\sigma }_1\left(\omega \right)$ is identified at $\omega =650{\text{cm}}^{-1}$.

Figure 3

(Color online) (a) Reflectivity spectra, (b) optical conductivity spectra, and (c) conductivity sum $N_{\text{eff}}\left(\omega \right)$ at $T=150\text{K}$ for various doping levels of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$. Solid squares in (b) indicate the values of the dc $\left(\omega =0\right)$ conductivity for each composition.

Figure 4

(Color online) Doping evolutions of (a) the optical conductivity spectrum and (b) the $N_{\text{eff}}$ spectrum at $T=30\text{K}$.

Figure 5

(Color online) Optical conductivity spectrum at $T=150\text{K}$ for (a) $x=0$, (b) 0.04, (c) 0.06, and (d) 0.08. Each spectrum is decomposed into a Drude term (blue hatched) and an incoherent term (red shaded). The green line indicates an interband component which is necessary to fit the data in the high energy region.

Figure 6

(Color online) Low-temperature optical conductivity spectrum and its decomposition for (a) $x=0$, (b) 0.04, (c) 0.06, and (d) 0.08. The data are at $T=5\text{K}$ for $x=0$ and 0.04, and at $T=30\text{K}$ for the others. A gap feature is seen in the incoherent term (red shaded) for $x=0$ and 0.04. An additional component (gray) is necessary to best fit the experimental result. For $x=0.06$ and 0.08, the incoherent term is almost unchanged as compared also with that at $T=150\text{K}$.

Figure 7

Spectral weights of (a) the Drude term and (b) the incoherent term plotted as a function of Co concentration at $T=150\text{K}$ (closed circles) and 30 K (open triangles).

Figure 8

Width of the Drude term $\left(1/\tau \right)$ is plotted as a function of temperature for (a) $x=0$, (b) 0.04, (c) 0.06, and (d) 0.08. For comparison, temperature dependence of resistivity is also shown (the right-hand scale). The scales of $1/\tau$ and resistivity are adjusted by taking into account the contribution of the incoherent component to the dc conductivity.

Figure 9

(Color online) Reflectivity spectrum and optical conductivity spectrum of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ for (a) (c) $x=0.06$ and (b) (d) 0.08 above and below the superconducting transition temperature $T_{\text{c}}$.

Figure 10

(Color online) Decomposition of the conductivity spectrum of $\text{Ba}{\left({\text{Fe}}_{0.94}{\text{Co}}_{0.06}\right)}_2{\text{As}}_2$ at $T=5\text{K}$. The experimental spectrum is best reproduced assuming a single SC gap of $80{\text{cm}}^{-1}$. The dashed lines indicate each component just above $T_{\text{c}}$.