Stress-induced nematicity in ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ studied by Raman spectroscopy

We use polarized Raman scattering to study the structural phase transition in ${\mathrm{EuFe}}_2{\mathrm{As}}_2$, the parent compound of the 122-ferropnictide superconductors. The in-plane lattice anisotropy is characterized by measurements of the side surface with different strains induced by different preparation methods. We show that while a fine surface polishing leaves the samples free of residual internal strain, in which case the onset of the $C_4$ symmetry breaking is observed at the nominal structural phase transition temperature $T_S$, cutting the side surface induces a permanent fourfold rotational symmetry breaking spanning tens of degrees above $T_S$.

Figure 1

(a) The orientation of the measured surface (blue rectangle) and the definition of the axis. The light polarization $c$ is defined along the longest axis of the crystal and the polarizations $a$ and $b$ are the longer and shorter nearest Fe-Fe directions, respectively. The X and Y axes are at 45 deg from $a$ and $b$. (b) Raman susceptibility ${\chi }^{\prime \prime }$ from the side surface and the $ab$ surface. (c) and (d) Atomic displacements of the two $E_g$ modes in the high-temperature tetragonal phase. (e) and (f) Atomic displacements of the $B_{2g}$  and $B_{3g}$  phonons in the low-temperature phase derived from the lower-energy branch of the two degenerate $E_g$  phonons in the high-temperature phase shown in (c).

Figure 2

(a) Raman susceptibility measured with the $ac$ polarization configuration at different temperatures on a surface made by a razor blade cut (blue curve) and a surface made by sandpaper polishing (red curve). The three peaks at 19.4, 29.2, and $95.4 {\mathrm{cm}}^{-1}$  marked with stars are laser plasma lines. The two peaks at 181 and $208 {\mathrm{cm}}^{-1}$  marked with pound signs are the $A_{1g}$ and $B_{1g}$ phonon modes. (b) and (c) Temperature- dependent phonon spectra measured with the $ac$ polarization. The blue and red curves are the fits to Lorentz functions. (d) and (e) Microscopic images of the cut surface and the polished surface, respectively. The reference for the space scaling of the images is given in (e).

Figure 3

(a) Phonon energy from the cut surface (blue) and polished surface (red) by fitting to the Lorentz function using Eqs. (1) and (2) above and below $T_S$, respectively. The dashed vertical line indicates $T_S$. (b) Phonon energy anisotropy and lattice anisotropy order parameter as a function of temperature. The temperature is scaled by $T_S$. (c) Phonon linewidth from the two different surfaces. The solid curves are guide lines to the eye. (d) Comparison of the $E_g$  mode extra broadening and $B_{2g}/B_{3g}$  mode splitting for the two surfaces. The vertical error bars are from the fitting error. The temperature error is $\pm 5$ K.