Nematic magnetoelastic effect contrasted between $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ and FeSe

To elucidate the origin of nematic order in Fe-based superconductors, we report a Raman scattering study of lattice dynamics, which quantify the extent of $C_4$-symmetry breaking, in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and FeSe. FeSe possesses a nematic ordering temperature $T_{\mathrm{s}}$ and orbital-related band-energy split below $T_{\mathrm{s}}$ that are similar to those in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, but unlike ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ it has no long-range magnetic order. We find that the $E_g$ phonon-energy split in FeSe becomes substantial only well below $T_{\mathrm{s}}$, and its saturated value is much smaller than that in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. Together with reported results for the $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ family, the data suggest that magnetism exerts a major influence on the lattice.

Figure 1

Thick arrows indicate displacement of Fe atoms in the $B_{2g}$ and $B_{3g}$ phonon modes in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and FeSe. As and Se atoms are omitted for clarity. The vertical Fe-Fe bonds are highlighted as being more rigid than the horizontal ones.

Figure 2

(a) Raman spectra measured on ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and FeSe single crystals. The inset shows temperature dependence of the spectrum of FeSe near 130 ${\mathrm{cm}}^{-1}$, vertically offset for clarity. (b) Temperature dependence of phonon-energy split in FeSe, plotted together with band-energy split observed with photoemission at the Brillouin-zone $M$ point and spin-lattice relaxation rate increase below 90 K observed with NMR. Data are normalized at 20 K for comparison.

Figure 3

Structural phase transition temperature (a), magnetic ordering temperature (b), and an empirical combination (see text) of magnetic and orbital energies (c) plotted vs $E_g$ phonon-energy split for FeSe and $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$)${}_2{\mathrm{As}}_2$ [56].

Figure 4

Raman spectra measured on three representative surface spots of FeSe with different local stress.