Evolution of the Nematic Susceptibility in ${\mathrm{LaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{AsO}$

We report a systematic elastoresistivity study on ${\mathrm{LaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{AsO}$ single crystals, which have well separated structural and magnetic transition lines. All crystals show a Curie-Weiss–like nematic susceptibility in the tetragonal phase. The extracted nematic temperature is monotonically suppressed upon cobalt doping, and changes sign around the optimal doping level, indicating a possible nematic quantum critical point beneath the superconducting dome. The amplitude of the nematic susceptibility shows a peculiar double-peak feature. This could be explained by a combined effect of different contributions to the nematic susceptibility, which are amplified at separated doping levels of ${\mathrm{LaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{AsO}$.

Figure 1

(Color online). Schematic $T\text{−}x$ phase diagrams of three representative iron based superconductors [3, 27, 46, 47]: (a) $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$, (b) ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$, (c) ${\mathrm{LaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{AsO}$. The orange area is the antiferromagnetically ordered state, the green dome is the superconducting state, and the solid blue line shows the structural transition (with dashed line as a guide to the eye). The nematic order exists below the structural transition line and above the antiferromagnetically region.

Figure 2

(Color online). Elastoresistance measurements of the parent compound LaFeAsO. (a) The relative change of strain (${ϵ}_x=\mathrm{\Delta }{L}_x/L_x$) and sample resistivity ($\eta =\mathrm{\Delta }\rho /\rho$) according to the voltage applied to the piezo actuator at a fixed temperature $T=150\mathrm{K}$. The strain was measured along the current direction, which was aligned against the [110] axis of the crystal. (b) The relationship between ${ϵ}_x$ and $\eta$ at some representative temperatures. The nematic susceptibility was obtained from $\tilde{n}=-(\delta \eta /\delta {ϵ}_x)$ in the ${ϵ}_x=0$ limit. (c) The temperature dependence of $\tilde{n}$ is shown as blue open squares in the upper panel. The structural transition temperature determined in Ref. [48] is indicated by the green arrow. The red curve represents a Curie-Weiss fitting to data in the temperature range between the vertical dotted lines. Inset is a schematic of the experimental setup. The inverse nematic susceptibility $(\tilde{n}-{\tilde{n}}_0{)}^{-1}$ and the Curie constant $C=(\tilde{n}-{\tilde{n}}_0)(T-T^{\mathrm{nem}})$ are shown in the lower panel, indicating the fitting quality.

Figure 3

(Color online). Divergent nematic susceptibility in ${\mathrm{LaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{AsO}$ single crystals. Similar data as Fig. 2 for eleven samples of different doping levels ranging from underdoped to overdoped is shown in (a)–(k). Cobalt content $x$ is the nominal composition, which agrees well with the actual concentration determined by energy dispersive x-ray spectroscopy on crystals from the same batches. The temperatures between which Curie-Weiss fitting was performed were determined by minimizing the systematic deviation of the Curie constant (see Ref. [26]). The structural transition temperature is indicated by the green arrow and is extracted from Refs. [47, 49]. There is no arrow in Fig. 3 because the Co 4.2% sample was not studied in the Refs. [47, 49].

Figure 4

(Color online). Phase diagram and nematic susceptibility of ${\mathrm{LaFe}}_{1-x}{\mathrm{Co}}_x\mathrm{AsO}$. The white triangles, light blue diamonds, and green circles indicate $T_S$, $T_N$, and $T_c$ respectively, according to Refs. [46, 47, 49]. The orange area encloses the AFM ordered state, while the superconducting region is represented by the green area. The nematic critical temperature $T^{\mathrm{nem}}$ (red star) and the divergency coefficient (Curie constant) $C$ (magenta square, right axis, in log scale) are obtained by the Curie-Weiss fits of the nematic susceptibility data shown in Fig. 2 and Fig. 3. The error bars of them come from altering the fit range (see text). The dashed lines are guides to the eye. Evolution of the magnitude of $\tilde{n}$ is shown by the color plot, which shows a double-peak feature.