Effect of Disorder on the Resistivity Anisotropy Near the Electronic Nematic Phase Transition in Pure and Electron-Doped ${\mathrm{BaFe}}_2{\mathrm{As}}_2$

We show that the strain-induced resistivity anisotropy in the tetragonal state of the representative underdoped Fe arsenides ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ and $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x{)}_2{\mathrm{As}}_2$ is independent of disorder over a wide range of defect and impurity concentrations. This result demonstrates that the anisotropy in the in-plane resistivity in the paramagnetic orthorhombic state of this material is not due to elastic scattering from anisotropic defects. Conversely, our result can be most easily understood if the resistivity anisotropy arises primarily from an intrinsic anisotropy in the electronic structure.

Figure 1

(a) Schematic diagram illustrating measurement of longitudinal elastoresistance, $(\mathrm{\Delta }R/R{)}_{xx}$ (i.e., current $\parallel {\epsilon }_{xx}$) and transverse elastoresistance $(\mathrm{\Delta }R/R{)}_{yy}$ (i.e., current $\perp$ ${\epsilon }_{xx}$ ) for the case of ${\epsilon }_{xx}$ aligned along the $[110{]}_T$ tetragonal crystallographic direction. Gold rectangles indicate position of electrical contacts for standard four-point measurement. Actual crystal dimensions are typically $0.5\times 0.1\mathrm{mm}$, compared with the PZT stack which has lateral dimensions $9.15\times 5.2\mathrm{mm}$ (b) Representative data showing the induced resistivity anisotropy ($N\sim (\mathrm{\Delta }R/R{)}_{xx}-(\mathrm{\Delta }R/R{)}_{yy}$) as a function of strain ${\epsilon }_{xx}$ at several temperatures above $T_s$ for ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ with RRR $\sim 5$. Black lines show linear fits for each temperature from which the elatoresistivity coefficient $m_{66}$ is extracted.

Figure 2

(a) Temperature dependence of the normalized resistivity, $\rho /\rho (300\mathrm{K})$ for ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ with RRR $\sim 5$ (as grown samples, shown by green data points) and RRR $\sim 15.5$ (annealed samples, pink data points). (b) Temperature-dependence of the elastoresistivity coefficients $-2m_{66}$ for the same samples shown in (a). $T_{s/N}$ values determined from $d\rho /dT$ are indicated by dashed and solid vertical lines for as-grown and annealed samples respectively.

Figure 3

Phase diagrams of $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ (red) and $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x{)}_2{\mathrm{As}}_2$ (blue). Squares, circles and triangles indicate $T_s$, $T_N$, and $T_c$ respectively. $T_s$ and $T_N$ were determined from $d\rho /dT$ of free standing samples. $T_c$ was defined by the midpoint of the superconducting transitions. The two sets of compositions demonstrated in this Letter (2.5% Co, 1.7% Ni, and 3.4% Co, 2.1% Ni) are denoted by dotted lines.

Figure 4

Comparison of elastoresistivity coefficients for Co and Ni doped samples with identical $T_N$ values. (a),(b) Temperature dependence of the normalized resistance, $\rho /\rho (300\mathrm{K})$ and the elastoresistivity coefficient $-2m_{66}$, respectively, for samples from Set 1 ($T_N=95\mathrm{K}$). (c),(d) Similar data data for samples from Set 2 ($T_N=80\mathrm{K}$). Solid and dashed vertical lines indicate $T_s$ and $T_N$, respectively, for each composition. For both sets of samples, $m_{66}$ is identical for the Co and Ni doped samples, despite the significant difference in impurity scattering.