Thermopower as a Sensitive Probe of Electronic Nematicity in Iron Pnictides

We study the in-plane anisotropy of the thermoelectric power and electrical resistivity on detwinned single crystals of isovalent substituted ${\mathrm{EuFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$. Compared to the resistivity anisotropy, the thermopower anisotropy is more pronounced and clearly visible already at temperatures much above the structural and magnetic phase transitions. Most remarkably, the thermopower anisotropy changes sign below the structural transition. This is associated with the interplay of two contributions due to anisotropic scattering and orbital polarization, which dominate at high and low temperatures, respectively.

Figure 1

Schematic phase diagram of ${\mathrm{EuFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$, based on 19, 20. The ordering temperatures of ${\mathrm{Eu}}^{2+}$ magnetic moments have been omitted for clarity, as they are not important in the context of this study. Open diamond (red), solid diamond (green), and solid circle (blue) symbols denote structural ($T_s$), antiferromagnetic ($T_N$), and superconducting (SC) phase transitions shown in Figs. 2, 5. The upper and lower cartoons illustrate the anisotropic scattering [18] and orbital polarization [12] scenario for the in-plane resistivity behavior, respectively. See text.

Figure 2

Electrical resistivity (a) and (c) and thermoelectric power (b) and (d) of ${\mathrm{EuFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$ along the orthorhombic $a$ and $b$ axes, indicated by blue and red, respectively. Solid arrows indicate structural phase transition ($T_s$) as determined by peak position of temperature derivative of resistivity anisotropy (see Fig. 3). The antiferromagnetic transition ($T_N$) is obtained from the (lower) kink of the resistivity data along the $b$ axis and denoted by the dashed arrows.

Figure 3

Temperature dependence of the normalized electrical resistivity anisotropy $({\rho }_b-{\rho }_a)/({\rho }_b+{\rho }_a)$ for ${\mathrm{EuFe}}_2({\mathrm{As}}_{0.95}{\mathrm{P}}_{0.05}{)}_2$ (a) and ${\mathrm{EuFe}}_2({\mathrm{As}}_{0.91}{\mathrm{P}}_{0.09}{)}_2$ (b), as well as respective temperature derivatives (c) and (d). Solid arrows indicate $T_s$ as determined from minima in (c) and (d).

Figure 4

Temperature dependence of the TEP anisotropy $\Delta S=S_b(T)-S_a(T)$ for ${\mathrm{EuFe}}_2({\mathrm{As}}_{0.95}{\mathrm{P}}_{0.05}{)}_2$ (a) and ${\mathrm{EuFe}}_2({\mathrm{As}}_{0.91}{\mathrm{P}}_{0.09}{)}_2$ (b). Solid and dashed arrows indicate $T_s$ and $T_N$, respectively, as determined from the electrical resistivity (cf. Fig. 1 and resistivity anisotropy, Fig. 3). Plus ($+$) and minus ($-$) symbols indicate sign of thermopower anisotropy.

Figure 5

Temperature dependence of the electrical resistivity (a) and TEP (b) for ${\mathrm{EuFe}}_2({\mathrm{As}}_{0.77}{\mathrm{P}}_{0.23}{)}_2$ [(a) and (b) denote in-plane tetragonal (110) directions perpendicular and parallel to the applied uniaxial pressure, which in the orthorhombic notation would correspond to the respective main axes; however, there is no orthorhombic phase in this sample]. For (b) data along the tetragonal (110) axis without uniaxial pressure are shown [27]. The inset in (a) displays the resistivity anisotropy in the normal state. Dashed lines are intended as guides to the eye and the arrow indicates transition into the SC state.