Electrodynamic response in the electronic nematic phase of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$

We perform, as a function of uniaxial stress, a temperature-dependent optical-reflectivity investigation of the parent Fe-arsenide compound ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ over a broad spectral range, from the far infrared up to the ultraviolet, across the coincident structural tetragonal-to-orthorhombic and spin-density-wave (SDW) phase transitions at $T_{s,N}=135$ K. Our results provide knowledge to the complete electrodynamic response of the title compound over a wide energy range as a function of both tunable variables. For temperatures below $T_{s,N}$, varying the uniaxial stress in situ affects the twin domain population and yields hysteretic behavior of the optical properties as the stress is first increased and then decreased, whereas for temperatures above $T_{s,N}$ the stress-induced optical anisotropy is reversible, as anticipated. In particular, by analyzing the low-frequency infrared response, we obtain detailed insight to the effects determining the intrinsic anisotropy of the (metallic) charge dynamics in the orthorhombic state, and similarly the induced one due to applied uniaxial stress at higher temperatures in the tetragonal phase. The low-frequency optical conductivity thus allows establishing a link to the $dc$ transport properties and reveals that they are determined almost exclusively by changes in the Drude weight, therefore by the anisotropy in the Fermi surface parameters. Finally, we show that the spectral weight distribution in the SDW state occurs for energies below approximately 1 eV, and therefore points towards a correlation mechanism due to Hund's coupling rather than on-site Coulomb interactions.

Figure 1

In-plane reflectivity $\left[R\right(\omega \left)\right]$ of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ at selected $T$ and $p$. (a) Temperature evolution of $R\left(\omega \right)$ in the FIR-UV range (semilogarithmic scale) for twinned samples (i.e., at 0 bar). The vertical dashed line marks the upper frequency limit of the HR extrapolation (see text). (b)–(u) display the pressure dependence of the optical anisotropy in $R\left(\omega \right)$ up to 2500 ${\mathrm{cm}}^{-1}$ collected at 0, 0.4, 0.8 and released 0 bar [denoted by “(r)”] and at selected $T$: (b)–(e) 140, (f)–(i) 135, (j)–(m) 120, (n)–(q) 70, and (r)–(u) 10 K, compared to the data collected at 160 K for equivalent $p$.

Figure 2

In-plane optical conductivity of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ at selected $T$ and $p$. (a) Temperature evolution of ${\sigma }_1\left(\omega \right)$ in the FIR-UV range (semilogarithmic scale) at 0 bar (i.e., twinned sample) [57]. (b)–(u) display the pressure evolution of the anisotropy in ${\sigma }_1\left(\omega \right)$ up to 2500 ${\mathrm{cm}}^{-1}$ at 0, 0.4, 0.8 [57] and released 0 bar [denoted by “(r)”] and at selected $T$: (b)–(e) 140, (f)–(i) 135, (j)–(m) 120, (n)–(q) 70, and (r)–(u) 10 K, compared to the data at 160 K for equivalent $p$. We apply the same legend convention as in Fig. 1.

Figure 3

Fit components of the optical conductivity along the $b$ axis in ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, at 10 K and 0 bar (see also Fig. 2(g) in Ref. [57]), considered within the Drude-Lorentz approach [Eq. (1)]. Apart from the optical phonon (OP) contribution, an equivalent set of fit components is considered along the $a$ axis. (Inset) Temperature dependence of $\rho \left(T\right)={\left[{\sigma }_1(\omega =0,T)\right]}^{-1}$ from the fit (see text) of the optical conductivity at 0.8 bar (i.e., at saturation). Each resistivity curve has been normalized at 200 K. The dashed line indicates the transition temperature $T_{s,N}$, while the dotted lines are guide to the eyes.

Figure 4

Pressure and temperature dependence of the parameters describing the Drude components [57]. The panels show: [(a), (b), (e), and (f)] the plasma frequency (${\omega }_{pN/B}$) and [(c), (d), (g), and (h)] the scattering rate (${\mathrm{\Gamma }}_{N/B}$) of the broad ($B$) and narrow ($N$) Drude term along the $a$ and $b$ axes, respectively. The dots indicate the fitted ($p,T$) points, which have been interpolated using a first-neighbor interpolation procedure to generate the color maps. The dashed line indicates the transition temperature $T_{s,N}$. Released pressures are denoted by “(r).”

Figure 5

Relative variation $\left[\mathrm{\Delta }SW\right(p,T)=SW(p,T)-SW(0\mathrm{bar},T\left)\right]$ of the squared oscillator-strengths with respect to the $p$ = 0 bar situation (twinned sample) for selected fit components (Fig. 3) as a function of $p$ and $T$ along both axes: (a) and (b) Drude terms ($S{W}_{\mathrm{Drude}}={\omega }_{pN}^2+{\omega }_{pB}^2$), (c) and (d) FIR-MIR-NIR ($S{W}_{\text{FIR-NIR}}=S_{\mathrm{FIR}}^2+S_{\mathrm{MIR}}^2+S_{\mathrm{NIR}}^2$), and (e) and (f) visible-UV ranges ($S{W}_{\mathrm{VIS}}={\sum }_{j=1}^2{S}_j^2$). The dots indicate the fitted points for various combinations of $p$ and $T$, which have been interpolated using a first-neighbor interpolation procedure to generate the color maps. The dashed line indicates the transition temperature $T_{s,N}$. Released pressures are denoted by “(r).”

Figure 6

(a) Ratio of the integrated spectral weight ($SW$) [Eq. (2)] between both axes at 160 K as a function of the cutoff frequency ${\omega }_c$ and applied uniaxial stress $p$, demonstrating that $SW$ at this temperature is isotropic for all $p$ and ${\omega }_c$. This is further true at all $T\ge 160$ K. (b)–(s) Pressure and temperature dependence of $SW$, normalized by the corresponding quantity at 160 K for both $a$ and $b$ axes, as well as of the ratio $S{W}_a/S{W}_b$ [72] estimated at the cutoff frequencies (b)–(d) ${\omega }_c$ = 250, (e)–(g) 500, (h)–(j) 1000, (k)–(m) 2000, (n)–(p), 4000 and (q)–(s) 10000 ${\mathrm{cm}}^{-1}$. The dots indicate the experimental ($p,T$) points, which have been interpolated using a first-neighbor interpolation procedure to generate the color maps. The dashed line indicates the transition temperature $T_{s,N}$. Released pressures are denoted by “(r).”

Figure 7

Color maps of the $p$ dependence of the real part ${\sigma }_1\left(\omega \right)$ of the optical conductivity along the $a$ and $b$ axis [57] as well as of $\mathrm{\Delta }{\sigma }_1(\omega ,p;T)={\sigma }_1^a(\omega ,p;T)-{\sigma }_1^b(\omega ,p;T)$ up to 2500 ${\mathrm{cm}}^{-1}$ at (a)–(c) 160, (d)–(f) 140, (g)–(i) 135, (j)–(l) 120, and (m)–(o) 10 K. Data have been interpolated using a first-neighbor interpolation procedure to generate the color maps. Released pressures are denoted by “(r).”

Figure 8

Pressure and temperature dependence of the fit parameters for the FIR HO (see also Supplemental Material of Ref. [57]). The panels show the peak frequency ${\omega }_0$ [(a) and (b)], the width $\gamma$ [(c) and (d)] and the strength $S$ [(e) and (f)] for the $a$ and $b$ axis, respectively. The dots indicate the fitted ($p,T$) points, which have been interpolated using a first-neighbor interpolation procedure to generate the color maps. The dashed line indicates the transition temperature $T_{s,N}$. Released pressures are denoted by “(r).”

Figure 9

Pressure and temperature dependence of the fit parameters for the MIR HO (see also Supplemental Material of Ref. [57]). The panels show the peak frequency ${\omega }_0$ [(a) and (b)], the width $\gamma$ [(c) and (d)], and the strength $S$ [(e) and (f)] for the $a$ and $b$ axes, respectively. The dots indicate the fitted ($p,T$) points, which have been interpolated using a first-neighbor interpolation procedure to generate the color maps. The dashed line indicates the transition temperature $T_{s,N}$. Released pressures are denoted by “(r).”

Figure 10

Pressure and temperature dependence of the fit parameters for the NIR HO (see also Supplemental Material of Ref. [57]). The panels show the peak frequency ${\omega }_0$ [(a) and (b)], the width $\gamma$ [(c) and (d)], and the strength $S$ [(e) and (f)] for the $a$ and $b$ axes, respectively. The dots indicate the fitted ($p,T$) points, which have been interpolated using a first-neighbor interpolation procedure to generate the color maps. The dashed line indicates the transition temperature $T_{s,N}$. Released pressures are denoted by “(r).”

Figure 11

Pressure and temperature dependence of the accumulated $SW$ within the Drude-Lorentz fit components. The panels in the upper two rows display ${\sum }_{i=0}^{j}S{W}_i$ for the $a$ (a)–(d) and $b$ axis (e)–(h), normalized by the same quantity at 160 K. $S{W}_i$ may be the squared plasma frequency ${\omega }_{pN/B}^2$ of the narrow and broad Drude term and/or the squared HO strength $S^2$. The third row (i-l) displays the ratio ${\sum }_{i=0}^{j}S{W}_i^a/{\sum }_{i=0}^{j}S{W}_i^b$, highlighting the anisotropy of the accumulated $SW$ upon progressively adding the various fit components ($i=0$: narrow and $i=1$: broad Drude terms, $i=2$: FIR, $i=3$: MIR and $i=4$: NIR HO). The dots indicate the fitted ($p,T$) points, which have been interpolated using a first-neighbor interpolation procedure to generate the color maps. The dashed line indicates the transition temperature $T_{s,N}$. Released pressures are denoted by “(r).”