In-plane anisotropy of electrical resistivity in strain-detwinned SrFe${}_2$As${}_2$

Intrinsic, in-plane anisotropy of electrical resistivity was studied on mechanically detwinned single crystals of SrFe${}_2$As${}_2$ above and below the temperature of the coupled structural/magnetic transition, $T_{\mathrm{TO}}$. Resistivity is smaller for electrical current flow along the orthorhombic $a_o$ direction (direction of antiferromagnetically alternating magnetic moments) and is larger for transport along the $b_o$ direction (direction of ferromagnetic chains), which is similar to CaFe${}_2$As${}_2$ and BaFe${}_2$As${}_2$ compounds. A strongly first-order structural transition in SrFe${}_2$As${}_2$ was confirmed by high-energy x-ray measurements, with the transition temperature and character unaffected by moderate strain. For small strain levels, which are just sufficient to detwin the sample, we find a negligible effect on the resistivity above $T_{\mathrm{TO}}$. With the increase of strain, the resistivity anisotropy starts to develop above $T_{\mathrm{TO}}$, clearly showing the relation of anisotropy to an anomalously strong response to strain. Our study suggests that electronic nematicity cannot be observed in the FeAs-based compounds in which the structural transition is strongly first order.

Figure 1

(Top) Schematic of the sample mounted on a “horseshoe” with strain applied through the potential wires by adjusting a push screw. The wires were insulated from the horseshoe by thin fiberglass boards. (Second panel from top) Zoom of the central area of the sample, overlaid with a spatial map, taken at 6 K, of the percentage of domain population with orthorhombic distortion along the strain (domains O2, O4 in the schematic presentation of the x-ray Laue pattern, third panel) as determined from the integrated x-ray intensity over all four possible domains, with actual x-ray data shown in Fig. 3. Thick dashed lines at potential contacts show the area above the soldered contact. (Bottom) Polarized optical microscopy images of the strained (left, area A in top panel) and unstrained (right, area B in top panel) areas at 5 K, revealing mechanical detwinning on the surface of the sample between potential contacts.

Figure 2

(Top) Temperature dependence of resistivity measured along the tetragonal [110]${}_T$ direction in twinned (${\rho }_t$, black curves) and strain-detwinned (${\rho }_{\mathit{ao}}$, red curves) states for sample #1 grown from Sn flux and sample #3 grown from FeAs flux with subsequent annealing ($A$-FeAs). The blue line shows calculated temperature-dependent resistivity for sample #1 in the direction transverse to the strain, ${\rho }_{\mathit{bo}}\equiv 2\times {\rho }_t-{\rho }_{\mathit{ao}}$ (Ref. 6). The green line shows temperature-dependent resistivity for another Sn-grown sample #2, partially detwinned by application of stress with preferable orientation of domains in the $b$ orthorhombic direction. (Bottom) Zoom of the temperature-dependent resistivity for sample #3 in the vicinity of the structural transition as a function of relative displacement of the horseshoe sides (in arbitrary but monotonically increasing units). The free-standing sample was measured before being mounted on the horseshoe. Fixing the sample to the horseshoe creates some strain, even without any additional displacement from the push screw (Strain 000) and partially detwins it. The pressure value for the highest displacement was estimated as in MPa range. The red curve (015 displacement) shows resistivity in the detwinned state, showing a sharp transition with no features above $T_{\mathrm{TO}}$. With further increase of strain the feature at the transition broadens and reveals strain-induced resistivity anisotropy in nominally tetragonal phase.

Figure 3

Temperature evolution of the (220)${}_T$ peak (in the tetragonal phase crystallographic notation) of high-energy x-ray Laue patterns in the strain-free (twinned, left column of images) and strained (right column of images) parts of the crystal, as shown in Fig. 1. At 6 K, the base temperature of our experiment (top), four peaks in the twinned part of the crystal correspond to four equivalent crystallographic directions of distortion in four equivalent domains, with very close to equal populations ranging between 23% and 26% of the full integrated peak intensity. In the strained portion of the crystal, the intensity is distributed very unevenly, with the dominant spot comprising $~$96% of the integrated peak intensity, the second spot approximately 4%, while the other two peaks go below our resolution limit ($~$0.1%). The orthorhombic peaks are observed all the way to the temperature of the structural, orthorhombic to tetragonal, phase transition. Phase coexistence of the orthorhombic and tetragonal peaks at 200 K (second panel) clearly illustrates that (1) the structural transition remains at the same temperature and is first order; (2) the domain population clearly changes with temperature. The phase coexistence disappears abruptly within a 1 K step, as seen in both the strained and unstrained regions of the sample (bottom panels) in the 201 K image, where the orthorhombic peaks are completely gone.

Figure 4

Temperature dependence of the structural order parameter $\delta =\frac{(a_o-b_o)}{(a_o+b_o)}$ as determined from the analysis of the (220)${}_T$ spot splitting in single domain and twinned areas of the SrFe${}_2$As${}_2$ single crystal. The positions of the peaks were determined from the fit of the pixel profile to a Gaussian, as shown in the inset for strained area at three characteristic temperatures. The solid line shows anisotropy of electrical resistivity (right scale), normalized to match the magnitude of the structural order parameter at low and high temperature. Anisotropy peaks below the transition and finds a very small residual value above the transition, coinciding within error bars with the magnitude of the strain-induced lattice distortion.

Figure 5

Temperature dependence of resistivity anisotropy, ${\rho }_{\mathit{bo}}/{\rho }_{\mathit{ao}}-1$ in three $A$Fe${}_2$As${}_2$ compounds. The anisotropy monotonically increases with ionic radius of the rare-earth element, peaks at or slightly below the structural transition, and then remains relatively constant. Notable anisotropy above the transition is observed only in the $A=\text{Ba}$ compound, with a weakly first-order character of the structural transition.