Transient electronic anisotropy in overdoped $\mathrm{NaF}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{o}}_x\mathrm{As}$ superconductors

By combining polarized pump-probe spectroscopic and Laue x-ray diffraction measurements, we have observed nonequivalent transient optical responses with the probe beam polarized along the $x$ and $y$ axes in overdoped $\mathrm{NaF}{\mathrm{e}}_{1\text{–}x}\mathrm{C}{\mathrm{o}}_x\mathrm{As}$ superconductors. Such transient anisotropic behavior has been uncovered in the tetragonal phase with the doping level and temperature range far from the borders of static nematic phases. The measured transient anisotropy can be well explained as a result of nematic fluctuation driven by an orbital order with energy splitting of the $d_{xz}$- and $d_{yz}$-dominant bands. In addition, the doping level dependence and the pressure effect of the crossover temperature show significant differences between the transient nematic fluctuation and static nematic phase, implying spin and orbital orders may play different roles in static and transient nematic behaviors.

Figure 1

Polarization-dependent differential reflectivity $\mathrm{\Delta }R/R\left(t\right)$ recorded from $\mathrm{NaF}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{o}}_x\mathrm{As}$ ($x\approx 0.05$, $T_c\approx 16\mathrm{K}$). (a) Schematic diagram of the probe polarization with respect to the in-plane lattice axes. The square and rectangle represent the tetragonal and orthorhombic lattice, respectively. Different colors indicate the Fe/Co atoms at different planes. (b), (c) Polar plot of polarization dependence of $\mathrm{\Delta }R/R\left(t\right)$ recorded at 8 and 26 K, respectively. (d), (e) Time-resolved traces of $\mathrm{\Delta }R/R\left(t\right)$ recorded with different probe polarizations at 8 and 26 K, respectively. (f), (g) Polarization-dependent amplitudes of fast and slow components of data (d), (e) fitted to a biexponential decay component, respectively.

Figure 2

Temperature dependence of anisotropic response in $\mathrm{NaF}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{o}}_x\mathrm{As}$ ($x\approx 0.05$). (a) Time-resolved kinetics of differential reflectivity probed with polarization angles $\theta =0^{\circ }$ and $\theta ={90}^{\circ }$ at different temperatures, respectively. (b) The anisotropic part $[\mathrm{\Delta }R/R_{\mathrm{ani}}=\mathrm{\Delta }R/R(0^{\circ })-\mathrm{\Delta }R/R(90^{\circ })]$ is plotted as a function of time delay and temperature. (c) The signal difference at a time delay of 5 ps is plotted vs temperature. (d) Temperature-dependent amplitudes and (e) lifetime parameters of the fast and slow components of data (b) fitted to the biexponential decay function, respectively.

Figure 3

Polarization-dependent transient reflectivity of $\mathrm{NaF}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{o}}_x\mathrm{As}$ samples with different dopings [(a), (b) $x\approx 0.03$, (c), (d) 0.04, and (e), (f) 0.05] recorded below and above the transition temperature from anisotropic to isotropic phases. (g) A diagram showing the possible mechanism responsible for the transient anisotropic response. The electric dipole-allowed transitions involving specific orbitals are schematically shown when the probe is polarized along the $x$ and $y$ axes, respectively (see text).

Figure 4

Doping-level-dependent crossover temperature ($T^{*}$) of the transient nematic response in $\mathrm{NaF}{\mathrm{e}}_{1-x}\mathrm{C}{\mathrm{o}}_x\mathrm{As}$ is shown in the phase diagram obtained by static measurements (SDW: spin-density-wave phase; SC: superconducting phase). $T_c$, $T_M$, $T_S$, and $T_{\mathrm{nem}}$ are literature values of the transition temperatures for superconductivity [38], SDW [61, 79], structure transition [61], and nematic phases [38] obtained by transport measurements. The superconducting transition temperatures of the samples obtained from this work are also included.