Observation of Incipient Charge Nematicity in ${\mathrm{Ba}(\mathrm{Fe}{}_{1-X}\mathrm{Co}{}_X)}_2\mathrm{As}{}_2$

Using electronic Raman spectroscopy, we report direct measurements of charge nematic fluctuations in the tetragonal phase of strain-free ${\mathrm{Ba}(\mathrm{Fe}{}_{1-x}\mathrm{Co}{}_x)}_2\mathrm{As}{}_2$ single crystals. The strong enhancement of the Raman response at low temperatures unveils an underlying charge nematic state that extends to superconducting compositions and which has hitherto remained unnoticed. Comparison between the extracted charge nematic susceptibility and the elastic modulus allows us to disentangle the charge contribution to the nematic instability, and to show that charge nematic fluctuations are weakly coupled to the lattice.

Figure 1

(a) Sketch of the phase diagram of ${\mathrm{Ba}(\mathrm{Fe}{}_{1-x}\mathrm{Co}{}_x)}_2\mathrm{As}{}_2$. $T_s$, $T_N$, and $T_c$ are the structural, magnetic, and superconducting (SC) transition temperatures, respectively. (b) Tetragonal FeAs layer, with the $x$ and $y$ axes defined along the Fe-Fe bonds. (c) Momentum-space structure of the form factor ${\gamma }_{\mathbf{k}}^{\mu }$ for $x^2-y^2$ and $xy$ symmetries [23]. (d) Temperature dependent Raman response $({\chi }^{x^2-y^2}{)}^{\prime \prime }$ and $({\chi }^{xy}{)}^{\prime \prime }$ in a strain-free $\mathrm{BaFe}{}_2\mathrm{As}{}_2$ single crystal with $T{}_s=138\mathrm{K}$. The incoming and outgoing photon polarizations ($e_I$ ,$e_S$) used for each symmetry configuration are depicted in the insets. The sharp peaks are due to phonon excitations. The electronic Raman continuum in $x^2-y^2$ symmetry displays a low frequency quasielastic peak (QEP) that is superimposed on a weaker and broad continuum that extends to energies above $1000{\mathrm{cm}}^{-1}$ and is essentially temperature independent in the tetragonal phase (see Supplemental Material [24]). In the orthorhombic phase, this broad continuum shows a suppression below $500{\mathrm{cm}}^{-1}$ in both symmetries because of the Fermi surface reconstruction induced by the simultaneous magnetic order [25].

Figure 2

(a) Temperature dependent Raman conductivity ${({\chi }^{x^2-y^2})}^{\prime \prime }/\omega$ for $x=0$ (parent), $x=0.02$ (strongly underdoped), $x=0.045$ (underdoped), $x=0.065$ (optimally doped), $x=0.10$ (overdoped), and $x=0.20$ (strongly overdoped). The structural transition temperature is indicated for the three underdoped compositions. The $x=0.065$ composition corresponds to optimal superconducting transition temperature ($T_c=24.5\mathrm{K}$ where no structural transition was detected. (b) Evolution of the static charge nematic susceptibility, ${\chi }_0^{x^2-y^2}$, as a function of temperature and doping. The structural transition temperature $T_s$ and the superconducting transition temperature $T_c$ are indicated in red squares and blue triangles, respectively.

Figure 3

(a) Temperature dependence of the inverse nematic charge susceptibility, ${({\chi }_0^{x^2-y^2})}^{-1}$, in the tetragonal phase ($T>T_s$) as a function of Co composition. The lines are Curie-Weiss fits for each composition (see text). (b) ($x$, $T$) phase diagram showing the orthorhombic (Ortho) and superconducting (SC) phases. The mean-field transition temperature extracted from the Curie-Weiss fit, $T_0$, is shown as green squares (the green line is a linear fit of its doping dependence). The corresponding structural transition temperature $T_s$ (red squares), magnetic transition temperature $T_N$ (white circles), and superconducting transition temperature $T_c$ (blue triangles) are also indicated [26].

Figure 4

Temperature dependence of the experimental shear modulus (data of Ref. [31], in purple), together with the expected temperature dependence of the shear modulus due to the coupling between the charge nematic and orthorhombic order parameters using Eq. (3) (in black). The bare shear modulus was assumed to be temperature independent and the only adjustable parameter, $a={\lambda }^2/C_S^0$ (see text) was chosen to fit the shear modulus data at high temperatures ($a=0.8$). The temperature scale was normalized using the measured structural transition temperatures ($T_S=130\mathrm{K}$ in Ref. [31]).