Nematic magnetoelastic effect contrasted between Ba(Fe${}_{1-x}$Co${}_x$)${}_2$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 BaFe${}_2$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 BaFe${}_2$As${}_2$, but unlike BaFe${}_2$As${}_2$ it has no long-range magnetic order. We find that the $E_g$ phonon-energy split in FeSe sets in only well below $T_{\mathrm{s}}$, and its saturated value is substantially smaller than that in BaFe${}_2$As${}_2$. Together with reported results for the Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ family, the data suggest that magnetism exerts a major influence on the lattice.