Origin of the Resistivity Anisotropy in the Nematic Phase of FeSe

The in-plane resistivity anisotropy is studied in strain-detwinned single crystals of FeSe. In contrast to other iron-based superconductors, FeSe does not develop long-range magnetic order below the tetragonal-to-orthorhombic transition at $T_s\approx 90\mathrm{K}$. This allows for the disentanglement of the contributions to the resistivity anisotropy due to nematic and magnetic orders. Comparing direct transport and elastoresistivity measurements, we extract the intrinsic resistivity anisotropy of strain-free samples. The anisotropy peaks slightly below $T_s$ and decreases to nearly zero on cooling down to the superconducting transition. This behavior is consistent with a scenario in which the in-plane resistivity anisotropy is dominated by inelastic scattering by anisotropic spin fluctuations.

Figure 1

(a) Polarized light image of an FeSe single crystal at 7 K, revealing orthorhombic domains oriented along the tetragonal [100] direction (parallel to the sample sides). For detwinning, the sample is cut along the [110] tetragonal direction as indicated by the green lines. Enlarged are the views of the area indicated by the white box in (a) and corresponding RGB histograms taken at (b) 92, (c) 80, and (d) 10 K. The change below $T_s$ is most pronounced in the red channel (b)–(d) and the temperature evolution of its histograms is shown in panel (e). The peak splitting $\omega$ was analyzed using a fit to two Gaussians [lines in (e)] and the normalized nematic order parameter, ${\varphi }_{\text{image}}=\omega (T)/{\omega }^{T\to 0}$, is shown in panel (f) and compared with the results of angle-resolved photoemission spectroscopy (ARPES) measurements [32] and the orthorhombic lattice distortion $\delta =(a-b)/(a+b)$ from our x-ray diffraction measurements.

Figure 2

(a) Temperature-dependent resistivity of FeSe measured in a free-standing state, ${\rho }_t$ (black curve), and under two values of uniaxial tensile strain, ${ϵ}_a={ϵ}_1$, ${ϵ}_2$, representing a fully detwinned state, ${\rho }_a$ (blue and purple curves). The resistivity along the orthorhombic $b$ direction was calculated as ${\rho }_b=2{\rho }_t-{\rho }_a$ (green curve). The insets show the whole temperature range and the schematics of the horseshoe detwinning device. (b) Resistivity anisotropy $\mathrm{\Delta }\rho \equiv {\rho }_a-{\rho }_b$ for the two values of strain, ${ϵ}_1$ and ${ϵ}_2$. Their difference $\mathrm{\Delta }\rho ({ϵ}_1)-\mathrm{\Delta }\rho ({ϵ}_2)$ is proportional to the strain-derivative $d\mathrm{\Delta }\rho /d{ϵ}_a$ (dashed orange line). The latter was used to extract the intrinsic (strain-free) in-plane anisotropy of the resistivity $\mathrm{\Delta }\rho ({ϵ}_a=0)\approx \mathrm{\Delta }\rho ({ϵ}_2)-(d\mathrm{\Delta }\rho /d{ϵ}_a){ϵ}_2$ in the orthorhombic phase (red line).

Figure 3

(a) Elastoresistivity coefficients $2m_{66}$ and $m_{11}-m_{12}$ of FeSe measured using crossed samples glued to a piezostack, shown schematically in the left inset. The right inset shows the inverse of $2m_{66}-2m_{66,0}$ demonstrating nearly perfect Curie-Weiss–like behavior, $2m_{66}=A/(T-T_0)+2m_{66,0}$ with $2m_{66,0}=-2.6$ and $T_0=83\mathrm{K}$. (b) Scaling of $2m_{66}=1/{\rho }_t[d\mathrm{\Delta }\rho /d({ϵ}_a-{ϵ}_b)]$ with the resistivity anisotropy $\mathrm{\Delta }\rho ({ϵ}_2)$ measured in detwinned samples. Here, we assume that $\mathrm{\Delta }\rho ({ϵ}_2)$ is induced by the applied strain above $T_s$, so that $\mathrm{\Delta }\rho ({ϵ}_2)={ϵ}_2(d\mathrm{\Delta }\rho /d{ϵ}_a)$ and use the identity $d({ϵ}_a-{ϵ}_b)/d{ϵ}_a=1+{\nu }_{\mathrm{FeSe}}$ to transform between the two quantities. The inset shows the Poisson ratio of FeSe, ${\nu }_{\mathrm{FeSe}}$, determined from the ultrasound data of Ref. [37] (solid line), and extrapolated to 250 K and below $T_s$ (dashed lines).

Figure 4

Experimental temperature-dependent resistivity anisotropy in the zero-strain limit [from Fig. 2, red symbols], $\mathrm{\Delta }\rho (T)$, compared to the product of the temperature-dependent experimentally determined order parameter ${\varphi }_{\text{image}}$ of Fig. 1 and the isotropic resistivity ${\rho }_t$ of Fig. 2 (black circles). The blue line shows the results of a model calculation where $\mathrm{\Delta }\rho$ is determined by the product of a mean-field-type nematic order parameter $\varphi (T)$ and a temperature dependent function $\mathrm{\Upsilon }(T)$ resulting from inelastic scattering promoted by spin fluctuations (see inset).