Magnetoelastic coupling and charge correlation lengths in a twin domain of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ ($x=0.047$): A high-resolution x-ray diffraction study

The interplay between structure, magnetism, and superconductivity in single crystal Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ ($x=0.047$) has been studied using high-resolution x-ray diffraction by monitoring charge Bragg reflections in each twin domain separately. The emergence of the superconducting state is correlated with the suppression of the orthorhombic distortion around $T$${}_{\mathtt{C}}$, exhibiting competition between orthorhombicity and superconductivity. Above $T$${}_{\mathtt{S}}$, the in-plane charge correlation length increases with the decrease of temperature, possibly induced by nematic fluctuations in the paramagnetic tetragonal phase. Upon cooling, anomalies in the in-plane charge correlation lengths along $a$ (${\xi }_a$) and $b$ axes (${\xi }_b$) are observed at $T$${}_{\mathtt{S}}$ and also at $T$${}_{\mathtt{N}}$ indicative of strong magnetoelastic coupling. The in-plane charge correlation lengths are found to exhibit anisotropic behavior along and perpendicular to the in-plane component of stripe-type AFM wave vector (101)${}_{\mathrm{O}}$ below around $T$${}_{\mathtt{N}}$. The temperature dependence of the out-of-plane charge correlation length shows a single anomaly at $T$${}_{\mathtt{N}}$, reflecting the connection between Fe-As distance and Fe local moment. The origin of the anisotropic in-plane charge correlation lengths ${\xi }_a$ and ${\xi }_b$ is discussed on the basis of the antiphase magnetic domains and their dynamic fluctuations.

Figure 1

Schematic illustration in reciprocal space of (a) untwinned crystal in the ($\mathit{HK}$0)${}_{\mathrm{T}}$ plane at the high-temperature tetragonal phase and (b) uniformly rotated and separated anisotropic twin domains in the (${hk0)}_{\mathrm{O}}$ plane at the orthorhombic phase. The arrows show typical scans performed at Bragg reflections.

Figure 2

The temperature dependence of peak positions extracted from (a) ($h$08)${}_{\mathrm{O}}$ ($h$ domain, circles) and (0$k$8)${}_{\mathrm{O}}$ ($k$ domain, squares) scans, and (b) the $l$ scan for (00$l$)${}_{\mathrm{O}}$ reflection. The inset of (a) shows the orthorhombic distortion $\delta$ as a function of temperature. The inset of (b) shows the zoomed view on $l$ scan for (20$l$)${}_{\mathrm{O}}$ reflection. Linear and quadratic fits to the data above $T$${}_{\mathtt{S}}$ are included as solid lines. The dashed lines in (a) and (b) indicate the locations of structural, magnetic, and superconducting transition temperatures $T$${}_{\mathtt{S}}$, $T$${}_{\mathtt{N}}$, and $T$${}_{\mathtt{C}}$.

Figure 3

(a) A representative longitudinal scan of $\mathbf{Q}={\left(h08\right)}_{\mathrm{O}}$ at 150 K (above $T$${}_{\mathtt{S}}$) and 46 K (below $T$${}_{\mathtt{S}}$). The Q values and intensity were normalized for comparison. It can be seen that the peak widths broaden significantly below $T$${}_{\mathtt{S}}$. (b) The temperature evolution of FWHM of the Gaussian function ($2\omega$) for the longitudinal scan of ($h$08)${}_{\mathrm{O}}$ ($h$ domain).

Figure 4

The temperature dependence of (a) the intrinsic width $\kappa$ of the longitudinal scans of ($h$08)${}_{\mathrm{O}}$ ($h$ domain) and (0$k$8)${}_{\mathrm{O}}$ ($k$ domain) obtained from the Lorentzian function and (b) the in-plane charge correlation lengths along the $a$ axis (${\xi }_a$) and $b$ axis (${\xi }_b$). The inset of (a) shows a detailed view of $\kappa$ around $T$${}_{\mathtt{N}}$ and $T$${}_{\mathtt{S}}$. The anisotropy of the correlation length ${\eta }_{\xi }$ as a function of temperature is shown in the inset of (b). The dashed lines mark the locations of structural and magnetic transition temperatures $T$${}_{\mathtt{S}}$ and $T$${}_{\mathtt{N}}$.

Figure 5

Schematic pictures of two kinds of the antiphase magnetic domains, with boundaries along the (a) $a$ axis and (b) $b$ axis, respectively. The antiphase domains are pinned at $T$ $<$ $T$${}_{\mathtt{N}}$ but show the dynamic behavior in the region of $T$${}_{\mathtt{N}}$ $<$ $T$ $<$ $T$${}_{\mathtt{S}}$. The pink lines show the antiphase boundaries. $J$${}_{\mathtt{1}}$ represents the nearest-neighbor exchange couplings along the $a$ or $b$ direction, whereas $J$${}_{\mathtt{2}}$ represents the next-nearest-neighbor exchange couplings.

Figure 6

Temperature dependence of (a) the intrinsic width $\kappa$ of the $l$ scan for (008)${}_{\mathrm{O}}$ obtained from the Lorentzian function and (b) the out-of-plane charge correlation length along the $c$ axis (${\xi }_c$).The dashed line indicates the locations of $T$${}_{\mathtt{N}}$ and $T$${}_{\mathtt{S}}$.