Polar state induced by block-type lattice distortions in ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ with quasi-one-dimensional ladder structure

A stripe-type magnetic structure and related orbital ordering are universally observed in iron-based superconductors. As an exception, the quasi-one-dimensional ladder material ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$, which shows pressure-induced superconductivity, exhibits a block-type antiferromagnetic ordering. The research of the electronic and structural properties in ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ at ambient conditions is important to reveal the origin of multiorbital superconductivity. Here, we report the temperature-dependent crystal structure of ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$, combining optical second harmonic generation experiments and neutron diffraction measurements. We elucidate the crystal structure with the $Pmn{2}_1$ space group in the low-temperature phase below $T_{s2}=400$ K, further above the Néel temperature. This low-temperature phase loses spatial inversion symmetry, where a resultant macroscopic polarization emerges along the rung direction. The transition is characterized by block-type lattice distortions possibly accompanied by polar orbital ordering.

Figure 1

(a) Crystal structure of ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$ in the $Pmn{2}_1$ phase. The principle axes ($a$, $b$, and $c$) are defined under the $Pmn{2}_1$ notation. Red arrows indicate the electric polarization induced below $T_{s2}$. (b)–(d) Schematic drawings of the local ladder structure with the space group of (b) $Cmcm$, (c) $Pnma$, (d) $Pmn{2}_1$, and (e) $Pmn{2}_1{1}^{\prime }$. Preserved symmetry operations are also shown. The possible pattern of the orbital ordering is depicted in (d) and (e). The block-type magnetic structure is also shown in (e) with white circles (up spins) and crosses (down spins).

Figure 2

Temperature dependence of the physical properties of ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$. (a) Electrical resistivity ($\rho$) with applying the current parallel to the leg direction (left), and the temperature derivative of $log\rho$ (right). (b) Magnetic susceptibility ($\chi$) under the external magnetic field ($H$) of 1 T applied along the layer (open) and leg (solid) directions. (c) Second harmonic generation (SHG) intensity in the experimental setup shown in Figs. 3 and 3. Below the structural transition temperature of $T_{s2}\sim 400$ K, the SHG intensity due to the breaking of the spatial inversion symmetry develops.

Figure 3

Polarization dependence of the SHG intensity for ${\mathrm{BaFe}}_2{\mathrm{Se}}_3$. (a) Experimental geometry of SHG measurements. The incident laser beam with the linear polarization is irradiated normal to the (010) or (011) surface, and the reflected SHG is detected by a photomultiplier tube after analyzing the polarization. (b), (g) Relationship between crystal axes and the polarization angle of the incident light ${\varphi }_{\omega }$ and that of SHG ${\varphi }_{2\omega }$. Polarization dependence of (c), (e) simulated and (d), (f) observed SHG signals at 200 and 450 K for the (010) plane. Polarization dependence of (h), (j) simulated and (i), (k) observed SHG signals at 200 and 450 K for the (011) plane. In the simulations, the $mmm$ and $mm2$ point groups are respectively assumed for 450 and 200 K data. In the right panel of (f) and (k), ${\varphi }_{2\omega }$ dependences of the SHG intensity collected at ${\varphi }_{\omega }$ = ${90}^{\circ }$ are shown.