Correlated vortex pinning in slightly orthorhombic twinned Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ single crystals: Possible shift of the vortex-glass/liquid transition

The interest in twin-boundary (TB) planes as a source of vortex pinning has been recently renewed with the discovery of the new iron-arsenide pnictide superconductors. In the family of compounds Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ a structural transition from a tetragonal to orthorhombic lattice takes place for compounds with $x<x_{\mathrm{cr}}\sim 0.065$. Approaching the critical doping, domain structure shrinks with sizes ultimately becoming comparable to vortex cores. In this work we investigate the changes in anisotropy produced by subtle differences in the Co doping level, in the neighborhood of the structural transition, in good-quality single crystals. Using a scaling approach we are able to determine the angular regions where correlated or uncorrelated disorder prevails. In the tetragonal samples ($x>x_{\mathrm{cr}}$) there is no twinning and we find good agreement with the expected scaling function under uncorrelated disorder, with small anisotropy values similar to those reported in the literature. We show that in the orthorhombic samples ($x<x_{\mathrm{cr}}$), TBs act as correlated disorder in a broad angular range. We propose that the observed angular dependence could be due to an increase in the vortex liquid-glass transition temperature.

Figure 1

Sharp ac transitions without significative enlargement with increasing dc and ac fields are observed. (a) Normalized in-phase ${\chi }^{\prime }$ and out-of-phase ${\chi }^{\prime \prime }$ at $H=0$, for samples with various Co doping, as a function of $T$ recorded with different ac amplitudes. (b) ${\chi }^{\prime }\left(T\right)$ and ${\chi }^{\prime \prime }\left(T\right)$ for a larger crystal with $x=0.062$ at various dc fields. (c) ZFC and FC $M\left(T\right)$ curves at $H=5000$ Oe. Arrows in (b) and (c) identify examples of typical points plotted in the phase diagram of Fig. 5 in curves recorded at $H=5000$ Oe (black dots). Inset: Sketch of the experimental geometry, where the gray rectangle represents a sample cross section.

Figure 2

Example of ${\chi }^{\prime }\left(T\right)$ curves recorded in slow cooling T ramps at (a) various dc fields H and (b) various orientations of the dc field $\theta$, in an untwinned sample. A Savitzky-Golay filter has been applied in order to smooth the high-frequency uncorrelated random noise in the temperature and susceptibility voltage signals. The ${\chi }^{\prime }$ values corresponding to the intersection between the vertical dashed lines ($T=21$ K) with each ${\chi }^{\prime }\left(T\right)$ curve have been used to build the curves shown in Fig. 3 (black squares).

Figure 3

Examples of curves obtained by ex-tracting data for recorded ${\chi }^{\prime }\left(T\right)$ curves (a) ${\chi }^{\prime }\left(H\right)$ at fixed T and $\theta$ in two samples. (b) ${\chi }^{\prime }\left(\theta \right)$ curves at fixed T and H in untwinned ($x=0.067$ and $x=0.074$) and twinned ($x=0.062$) samples. A dramatic change caused by TBs is observed. Continuous and dotted lines in panel (a) show the interpolation functions ${\chi }^{\prime }\left(H\right)$ and the corresponding confidence bands. Dashed line connecting both panels schematizes the definition of $H_1\left(\theta \right)$ in the scaling procedure (Fig. 4). Inset: ${\chi }^{\prime }\left(T\right)$ curves in the twinned samples corresponding to 3 directions of the dc field $H=1500$ Oe. Around $\theta =0$ the full curves shift to higher temperatures.

Figure 4

Examples of the resulting $H_1\left(\theta \right)/H_2$ for samples with different Co doping, $H_1\left(\theta \right)$ being defined as the “effective field” for which $\chi ({\theta }_1,H_1\left(\theta \right))=\chi (\theta ,H_2)$. The chosen angles ${\theta }_1$ are indicated with vertical dashed lines. Continuous lines show the scaling function obtained for untwinned samples [panels (b) and (c)] in the region $\theta <{\theta }_c$ (see text). In the twinned sample [panel (a)] TBs act as sources of correlated disorder in a broad angular range.

Figure 5

Inset: Magnetization loops $M\left(H\right)$ at fixed $T$ in a twinned sample. Main panel: Phase diagram built with magnetization (full symbols) and ac susceptibility (open symbols) results in two twinned samples (gray and black symbols). Examples of the definition of the plotted quantities are shown in the inset and in Fig. 1b. The IL (up and down triangles) coincides approximately with ${\chi }_{\max }^{\prime \prime }$ (open circles) and lies near the onset of the diamagnetic signal (squares). The rectangle in the right bottom corner indicates the region where angular measurements have been performed.