Hysteretic behavior in the optical response of the underdoped Fe-arsenide $\text{Ba(}{\text{Fe}}_{1-x}{\text{Co}}_x{\text{)}}_2{\text{As}}_2$ in the electronic nematic phase

We use a new technique that allows in situ variation of uniaxial stress to probe the polarization dependence of the optical reflectivity of the representative underdoped iron-arsenide $\text{Ba(}{\text{Fe}}_{1-x}{\text{Co}}_x{\text{)}}_2{\text{As}}_2$ through the tetragonal-to-orthorhombic structural transition and with respect to their electronic nematic phase. These measurements reveal a hysteretic behavior of the anisotropic optical response to uniaxial stress in the orthorhombic state associated with twin boundary motion, whereas the pressure-induced anisotropy of the optical response is reversible in the tetragonal state.

Figure 1

Ferroelastic tetragonal-to-orthorhombic structural transition in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$: (a) Schematic phase diagram, emphasizing the underdoped regime. These materials tend to form dense structural twin domains as they are cooled through the ferroelastic tetragonal-to-orthorhombic transition at $T_s$. As illustrated schematically in the inset to (a), uniaxial pressure $p$ (black arrows) affects the relative population of twins oriented with the (elongated) $a$ axis parallel (green domain) and perpendicular (blue domain) to the applied stress. (b) illustrates two types of temperature and pressure cycles used for our experiments, which we refer to as zero-pressure-cooled (ZPC) pressure-loop experiments (blue arrows) and pressure-cooled (PC) fixed-$p$ experiments (green arrow), respectively. For the ZPC $p$-loop experiment the $p$ dependence of the optical anisotropy is measured following an initial cooling in zero pressure (blue stars). For the PC fixed-$p$ experiment, the sample is cooled to 10 K (i.e., $T\ll T_s$) at fixed $p$ and then the optical anisotropy (green stars) is collected upon warming at the same $p$ (dark-red arrows).

Figure 2

Representative data of the optical reflectivity of BaFe${}_2$As${}_2$ for the zero-pressure-cooled experiments: (a) Reflectivity [$R\left(\omega \right)$] measured at 10 K and $p=0.8$ bars, displaying the optical anisotropy in the MIR spectral range. The inset shows $R\left(\omega \right)$ up to the visible and ultraviolet range with a logarithmic frequency scale. Above 3000 cm${}^{-1}$ the spectra for both polarization directions merge together [33]. (b)–(g) $p$ dependence of $R_{\mathrm{ratio}}\left(\omega \right)$ (see text) at 10, 120, and 140 K for increasing (b)–(d) and decreasing $p$ (e)–(g). Values of $R_{\mathrm{ratio}}\left(\omega \right)$ (see text and Fig. 3) are determined at 1500 cm${}^{-1}$ (vertical dashed line). Applied stress is given in bars and corresponds to $p$ of He gas inside the volume of the pressure device [33].

Figure 3

Optical anisotropy ($\Delta R_{\mathrm{ratio}}$) of BaFe${}_2$As${}_2$ as a function of pressure at representative temperatures: (a)–(h) Solid and open symbols denote increasing and decreasing $p$, respectively, for $p$-loop measurements following an initial ZPC protocol. Our measurements show that in the orthorhombic phase the optical anisotropy exhibits a hysteretic behavior due to twin boundary motion, while in the tetragonal phase a reversible linear response to applied $p$ is recovered [Fig. 1]. Data from PC fixed-$p$ measurements are shown by brown and green stars for $p=0.3$ and 0.8 bars, respectively. Additional gray stars indicate measurements for which the sample was initially prepared by $p$ cooling to 10 K with $p=0.8$ bars, at which temperature $p$ was released. The optical anisotropy was then measured as a function of $T$ while warming under conditions of $p=0$ bars (i.e., PC-ZPW experiment). Dashed and dotted lines are drawn to guide the eye. Arrows [blue in (a) and orange in (f)] sketch the $p$-increasing/decreasing and $p$-sweeping loops at 10 K ($T<T_s$) and 135 K ($T\ge T_s$), respectively.

Figure 4

Temperature dependence of the pressure-induced optical anisotropy in BaFe${}_2$As${}_2$: (a) $T$ dependence of $\Delta R_{\mathrm{ratio}}$ at fixed $p$, from data along the virgin curve (Fig. 3), compared to the dc anisotropy ratio $\Delta \rho /\rho$, obtained from transport results in the case of samples constantly held under uniaxial pressure [10]. The dotted lines are guides to the eyes. (b) $T$ dependence of $\Delta R_{\mathrm{ratio}}/p$. The dashed line corresponds to a Curie-like behavior (see text). The vertical double-dotted-dashed line defines the transition temperature $T_s$.