Nonlinear and time-resolved optical study of the 112-type iron-based superconductor parent ${\mathrm{Ca}}_{1-x}{\mathrm{La}}_x{\mathrm{FeAs}}_2$ across its structural phase transition

The newly discovered 112-type ferropnictide superconductors contain chains of As atoms that break the tetragonal symmetry between the $a$ and $b$ axes. This feature eliminates the need for uniaxial strain that is usually required to stabilize large single domains in the electronic nematic state that exists in the vicinity of magnetic order in the iron-based superconductors. We report detailed structural symmetry measurements of 112-type ${\mathrm{Ca}}_{0.73}{\mathrm{La}}_{0.27}{\mathrm{FeAs}}_2$ using rotational anisotropy optical second-harmonic generation. This technique is complementary to diffraction experiments and enables a precise determination of the point-group symmetry of a crystal. By combining our measurements with density functional theory calculations, we uncover a strong optical second-harmonic response of bulk electric dipole origin from the Fe and Ca $3d$-derived states that enables us to assign $C_2$ as the crystallographic point group. This makes the 112-type materials high-temperature superconductors without a center of inversion, allowing for the possible mixing of singlet and triplet Cooper pairs in the superconducting state. We also perform pump-probe transient reflectivity experiments that reveal a 4.6-THz phonon mode associated with the out-of-plane motion of As atoms in the FeAs layers. We do not observe any suppression of the optical second-harmonic response or shift in the phonon frequency upon cooling through the reported monoclinic-to-triclinic transition at 58 K. This allows us to identify $C_1$ as the low-temperature crystallographic point group but suggests that structural changes induced by long-range magnetic order are subtle and do not significantly affect electronic states near the Fermi level.

Figure 1

Structure of ${\mathrm{Ca}}_{1-x}{\mathrm{La}}_x{\mathrm{FeAs}}_2$ and experimental setup. (a) Crystal structure of ${\mathrm{Ca}}_{1-x}{\mathrm{La}}_x{\mathrm{FeAs}}_2$ in the monoclinic phase $\left(T>T_S\right)$. Zigzag As chains run along the $b$ axis. The space group of the crystal, $P{2}_1$ (point group $C_2)$, is noncentrosymmetric and possesses a single symmetry element: a twofold screw axis along b. (b) Iron atomic planes above and below the structural transition temperature $T_S$ (distortions from a perfect square lattice are exaggerated for clarity). Below $T_S$ the crystal loses its screw axis and becomes triclinic. (c) Simplified schematic of the RA-SHG experimental setup. A laser beam (800 nm; red), incident from the left, passes through a dichroic mirror and is focused by a lens onto the sample. The reflected second harmonic (400 nm; blue) is recollimated by the lens and reflects off the mirror into a charge-coupled device (CCD) detector. Additional optics used for polarization compensation are omitted for clarity but are described in Ref. [22]. By rotating the position of the incident laser beam about the central optical axis, the scattering plane rotates by an angle $\varphi$ about the sample surface normal, simultaneously tracing out a circle on the CCD. Bottom right inset shows linear polarizations in $\left(P\right)$ and out of $\left(S\right)$ the scattering plane. (d) Electrical resistivity (top) and magnetic susceptibility (bottom) measurements showing clear anomalies at the structural and magnetic transition temperatures, respectively. (e) Partial and total density of states of ${\mathrm{CaFeAs}}_2$ as computed by DFT. States near the Fermi level have predominantly Fe $3d$ character, mixing with Ca $3d$ orbitals well above $E_F$. Vertical arrows show the relative scale of the electronic energy bands and the fundamental $\left(\omega \right)$ and second-harmonic $\left(2\omega \right)$ photons.

Figure 2

RA-SHG data for ${\mathrm{Ca}}_{0.73}{\mathrm{La}}_{0.27}{\mathrm{FeAs}}_2$ taken at 70 K. Raw CCD images for (a) $P_{\mathrm{in}}-P_{\mathrm{out}}$, (b) $P_{\mathrm{in}}-S_{\mathrm{out}}$, (c) $S_{\mathrm{in}}-P_{\mathrm{out}}$, and (d) $S_{\mathrm{in}}-S_{\mathrm{out}}$ polarization geometries. (e)–(h) Corresponding rotational anisotropy polar plots extracted from the CCD images. A single intensity scale is maintained across the figures and relative intensities are accurately depicted. Solid curves show a global fit to the data assuming a $C_2$ point group, as discussed in the text.

Figure 3

Temperature dependence of RA-SHG for ${\mathrm{Ca}}_{0.73}{\mathrm{La}}_{0.27}{\mathrm{FeAs}}_2$. Rotational anisotropy curves for (a) $P_{\mathrm{in}}-P_{\mathrm{out}}$, (b) $P_{\mathrm{in}}-S_{\mathrm{out}}$, (c) $S_{\mathrm{in}}-P_{\mathrm{out}}$, and (d) $S_{\mathrm{in}}-S_{\mathrm{out}}$ polarization geometries taken from 30 to 80 K in 10-K steps. Curves are normalized by their respective average values in order to remove the effects of long-term laser power drift. There is no detectable change in anisotropy with temperature across the structural phase transition.

Figure 4

Pump-probe transient reflectivity measurements of ${\mathrm{Ca}}_{0.73}{\mathrm{La}}_{0.27}{\mathrm{FeAs}}_2$, showing the time-resolved relative change in reflectivity after the pump pulse above and below the structural phase transition. Inset shows the corresponding Fourier transform (FT) of the reflectivity after subtracting a long time-scale exponential response, as discussed in the text. A phonon resonance at 4.6 THz is present in both measurements.