Doping dependence of the lattice dynamics in $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ studied by Raman spectroscopy

We report Raman scattering measurements on iron-pnictide superconductor $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ single crystals with varying cobalt $x$ content. Upon cooling through the tetragonal-to-orthorhombic transition, we observe a large splitting of the $E_g$ in-plane phonon modes involving Fe and As displacements. The splitting of the in-plane phonons at the transition is strongly reduced upon doping and disappears for $x=0.06$ qualitatively following the trend displayed by the Fe magnetic moment. The origin of the splitting is discussed in terms of magnetic frustration inherent to iron-pnictide systems and we argue that such enhanced splitting may be linked to strong spin-phonon coupling.

Figure 1

(Color online) Raman spectrum of ${\text{BaFe}}_2{\text{As}}_2$ at 305 K in the $\left(z^{\prime }{x}^{\prime }\right)$ configuration at $\lambda =514.52nm$. Inset: optical image of the undoped single-crystal ${\text{BaFe}}_2{\text{As}}_2$-geometry of the $\left(z^{\prime }{x}^{\prime }\right)$ configuration.

Figure 2

(Color online) Top panel: evolution with temperature of the Raman spectrum of ${\text{BaFe}}_2{\text{As}}_2$ in the $\left(z^{\prime }{x}^{\prime }\right)$ configuration. Inset: zoom on the ${\text{A}}_{1g}\left(\text{As}\right)$ mode. Bottom panel: evolution of the $B_{1g}\left(\text{Fe}\right)$ phonon linewidth with temperature. Inset: evolution of the $B_{1g}\left(\text{Fe}\right)$ phonon frequency with temperature.

Figure 3

(Color online) Top panel: evolution with temperature of the Raman spectrum of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ in the $z^{\prime }{x}^{\prime }$ configuration for $x=0$, $x=0.02$, $x=0.03$, $x=0.04$, $x=0.045$, and $x=0.06$. Bottom panel: evolution of the $E_g\left(\text{Fe},\text{As}\right)$ phonon frequency with temperature for the same dopings.

Figure 4

(Color online) Evolution of the amplitude of the $E_g$ phonon splitting with temperature for different doping $x=0$, $x=0.02$, $x=0.03$, $x=0.04$, and $x=0.045$. The dashed lines are fits using the order-parameter power law described in the text using $\beta =0.12$. Inset: evolution of the amplitude of the splitting at low temperature (20 K) and of the magnetic moment of Fe with $x$ doping (Refs. 11, 12, 21). The scales were chosen so as to normalize the splitting and the magnetic-moment amplitudes at $x=0$.

Figure 5

(Color online) Phase diagram of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$: temperatures of the structural $\left(T_s\right)$ and the superconducting $\left(T_c\right)$ transitions versus $x$ doping (Co content).

Figure 6

(Color online) In-plane Fe-As phonon displacement patterns in the orthorhombic phase with the positions of the Fe and As atoms projected in the $ab$ plane (Refs. 13, 24). The modes arise from the doubly degenerate $E_g$ mode in the tetragonal structure $\left(I4/mmm\right)$ which splits into nondegenerate $B_{2g}$ and $B_{3g}$ modes in the orthorhombic structure $\left(Fmmm\right)$. For As atoms, full and empty symbols are meant to differentiate between the As atoms located above and below the Fe plane. The Fe spins are drawn in black and display the stripelike magnetic pattern observed by neutron scattering in the orthorhombic phase (Ref. 12). The short-range exchange integrals involving next neighbors ($J_{1a}$ and $J_{1b}$) and nearest next-neighbors $\left(J_2\right)$ Fe spins are also depicted. Note that the superexchange path of $J_{1a}$ and $J_{1b}$ involves the As atoms.