Imaging Anomalous Nematic Order and Strain in Optimally Doped ${\mathrm{BaFe}}_2(\mathrm{As},\mathrm{P}{)}_2$

We present the strain and temperature dependence of an anomalous nematic phase in optimally doped ${\mathrm{BaFe}}_2(\mathrm{As},\mathrm{P}{)}_2$. Polarized ultrafast optical measurements reveal broken fourfold rotational symmetry in a temperature range above $T_c$ in which bulk probes do not detect a phase transition. Using ultrafast microscopy, we find that the magnitude and sign of this nematicity vary on a $50–100\mu \mathrm{m}$ length scale, and the temperature at which it onsets ranges from 40 K near a domain boundary to 60 K deep within a domain. Scanning Laue microdiffraction maps of local strain at room temperature indicate that the nematic order appears most strongly in regions of weak, isotropic strain. These results indicate that nematic order arises in a genuine phase transition rather than by enhancement of local anisotropy by a strong nematic susceptibility. We interpret our results in the context of a proposed surface nematic phase.

Figure 1

Crystal structure of P:Ba122 and photomodulation results at optimal doping. (a) Crystal structure of P:Ba122. (b) Pump-probe response $\mathrm{\Delta }R/R$ as a function of time at a fixed position, with probe polarization parallel to the Fe-Fe directions $a$ (solid lines) and $b$ (dotted lines). Red, black, and blue traces correspond to $T=28$, 14, and 7 K, respectively, spanning the apparent superconducting transition temperature. (c) Time and temperature dependence of the $C_4$-odd photomodulation response $\delta \varphi \equiv (\mathrm{\Delta }{R}_b-\mathrm{\Delta }{R}_a)/R$. (d) Temperature dependence of the maximum-amplitude value of $\mathrm{\Delta }R(t)/R$ for probe polarization along $a$ (red) and $b$ (blue), illustrating near-perfect antisymmetry under a $\pi /2$ rotation of the probe polarization, abrupt onset of broken $C_4$ symmetry, and competition between superconductivity and nematic order.

Figure 2

Spatial variation ($13\mu \mathrm{m}$ resolution) of optical anisotropy (a) and $ab$-plane strain (b)–(d) on a $390\times 260\mu \mathrm{m}$ region of an optimally doped P:Ba122 crystal mounted on Cu. (a) Photomodulation proxy for nematic order, $\delta {\varphi }_M$. (b) Transverse strain anisotropy ${ϵ}_{bb}-{ϵ}_{aa}$ in the Fe-Fe basis. (c) Transverse unit cell dilation $\mathrm{Tr}{\mathit{ϵ}}^{(t)}$. (d) Transverse equivalent strain ${ϵ}_{\text{eq}}^{(t)}=(2{ϵ}_{ij}^{(t)}{ϵ}_{ij}^{(t)}/3{)}^{1/2}$. Superimposed lines are parallel to the Fe-Fe directions and are located at the same positions in each image to facilitate a visual comparison of features. Optical data were collected at $T=5\mathrm{K}$, strain data at room temperature.

Figure 3

Comparison of spatial variation ($13\mu \mathrm{m}$ resolution) and temperature dependence of nematic order for piezo-mounted (uniaxially strained) and Cu-mounted (biaxially strained) crystals. (a) Spatial variation of photomodulation proxy for nematic order, $\delta {\varphi }_M$, on the piezo-mounted crystal, which is uniaxially strained as indicated. (b) Histograms showing the distribution of $\delta {\varphi }_M$ for both crystals. (c) Spatial variation of $\delta {\varphi }_M$ on the Cu-mounted crystal, with open circles indicating positions at which temperature dependence data were collected and a black line marking a region of null $\mathrm{\Delta }R/R$ response separating regions of opposite nematic sign. (d) Temperature dependence of $\delta {\varphi }_M$ for the piezo-mounted crystal while warming (right-pointed triangles) and cooling (left-pointed triangles). The black line is a Curie-Weiss fit with $T_{\mathrm{CW}}=19\mathrm{K}$ (solid on the fitted domain, dashed at lower temperatures). Inset: Standardized fit residuals. (e) Temperature dependence of $\delta {\varphi }_M$ for the Cu-mounted crystal far from the boundary at the point marked $A$ (open squares) and near the boundary at the point marked $B$ (circles). Apparent nematic transition temperatures are indicated. Inset: Scatter plot of the nematic transition temperature as a function of distance from the domain boundary indicated by the black line in (c); correlation is positive with $p$ value $<{10}^{-2}$.