Coexistence and Competition of Magnetism and Superconductivity on the Nanometer Scale in Underdoped ${\mathrm{BaFe}}_{1.89}{\mathrm{Co}}_{0.11}{\mathrm{As}}_2$

We report muon spin rotation ($\mu \mathrm{SR}$) and infrared spectroscopy experiments on underdoped ${\mathrm{BaFe}}_{1.89}{\mathrm{Co}}_{0.11}{\mathrm{As}}_2$ which show that bulk magnetism and superconductivity (SC) coexist and compete on the nanometer length scale. Our combined data reveal a bulk magnetic order, likely due to an incommensurate spin density wave (SDW), which develops below $T^{\mathrm{mag}}\approx 32\mathrm{K}$ and becomes reduced in magnitude (but not in volume) below $T_c=21.7\mathrm{K}$. A slowly fluctuating precursor of the SDW seems to develop already below the structural transition at $T^s\approx 50\mathrm{K}$. The bulk nature of SC is established by the $\mu \mathrm{SR}$ data which show a bulk SC vortex lattice and the IR data which reveal that the majority of low-energy states is gapped and participates in the condensate at $T\ll T_c$.

Figure 1

(a) $T$ dependence of the in-plane resistivity $\rho$ and (b) the zero-field-cooled (zfc) magnetic volume susceptibility ${\chi }_V$ of ${\mathrm{BaFe}}_{1.89}{\mathrm{Co}}_{0.11}{\mathrm{As}}_2$ with $H=10\mathrm{Oe}$ parallel to the $c$ axis. Inset: Derivative of $\rho (T)$ showing the change in slope around $T^s\approx 50\mathrm{K}$.

Figure 2

(a) ZF-$\mu \mathrm{SR}$ time spectra (symbols) showing a rapid depolarization below about 40 K. Solid lines show fits with Eq. (1). (b) TF-$\mu \mathrm{SR}$ spectra (symbols) at $H_{\mathrm{ext}}=300\mathrm{mT}$ plotted in a rotating reference frame (${\omega }_{\mathrm{RRF}}=39.5\mathrm{MH}z$). Solid lines show fits with Eq. (2). (c) $T$ dependence of the depolarization rates ${\lambda }_f^{\mathrm{TF}}$ and ${\lambda }_f^{\mathrm{ZF}}$. (d) TF-$\mu \mathrm{SR}$ line shapes showing the distribution of local magnetic fields $p(B_{\mu })$ during a so-called pinning experiment as described in the text.

Figure 3

$T$-dependent spectra of (a) the FIR reflectivity $R(\omega )$ and (b) the in-plane optical conductivity ${\sigma }_1(\omega )$ of ${\mathrm{BaFe}}_{1.89}{\mathrm{Co}}_{0.11}{\mathrm{As}}_2$ with $T_c=21.7\mathrm{K}$. Solid circles show ${\sigma }^{\mathrm{dc}}$ as obtained from Fig. 1a.

Figure 4

$T$-dependent spectral changes for UD ${\mathrm{BaFe}}_{1.89}{\mathrm{Co}}_{0.11}{\mathrm{As}}_2$ and OP ${\mathrm{BaFe}}_{1.87}{\mathrm{Co}}_{0.13}{\mathrm{As}}_2$ as obtained with IR ellipsometry. (a) and (b) Difference of the optical conductivity between 25 and 50 K and between 5 and 25 K, respectively. (c) $T$ dependence of the spectral weight between 600 and $1400{\mathrm{cm}}^{-1}$. $T_c$ is marked by the solid arrows. The vertical axes are scaled to show the common trends above 50 K.