Polar State induced by Block-type Lattice Distortions in BaFe2Se3 with Quasi-One-Dimensional Ladder Structure

TL;DR

This study investigates the temperature-dependent crystal structures of BaFe2Se3, revealing a polar low-temperature phase with block-type lattice distortions and a loss of inversion symmetry, linked to electronic and magnetic property changes.

Contribution

It provides detailed structural analysis of BaFe2Se3's low-temperature phase, highlighting the role of block-type lattice distortions and symmetry breaking in its properties.

Findings

Low-temperature phase has Pmn2_1 space group with broken inversion symmetry.

Emergence of macroscopic polarization along the rung direction.

Structural transition affects electronic and magnetic properties.

Abstract

Temperature dependent crystal structures of the quasi-one-dimensional ladder material BaFe2Se3 are examined. Combining the optical second harmonic generation (SHG) experiments and neutron diffraction measurements, we elucidate the crystal structure with Pmn2_1 space group in the low-temperature phase below Ts2 = 400 K, further above Neel temperature. This low-temperature phase loses the spatial inversion symmetry, where a resultant macroscopic polarization emerges along the rung direction. The transition is characterized by block-type lattice distortions with the magneto-striction mechanism. Change in the electrical resistivity and the magnetic susceptibility across the polar-nonpolar transition also suggests a modification of the electronic states reflecting the structural instability. Consistency and discrepancy with the existing theory are discussed.

Full text

The crystal structure of BaFe2Se3 is composed of edge-shared FeSe4 tetrahedra forming a quasi-one-dimensional ladder structure of Fe atoms (Fig. 1(a)). The structure can be regarded as the case one-third of the Fe atom stripes are removed from the two-dimensional square lattice of Fe atoms, reminding us of a close relationship with iron-based superconductors Caron et al. (2011); Lei et al. (2011); Krzton-Maziopa et al. (2012); Lv et al. (2013). Superconductivity has been observed quite recently under high pressures in BaFe2Se3 Ying et al. (2017); Zhang et al. (2018). The material is frequently argued in comparison with a related material BaFe2S3, which also becomes superconducting under pressures Takahashi et al. (2015); Yamauchi et al. (2015); Arita et al. (2015); Suzuki et al. (2015); Patel et al. (2016); however these two compounds have a striking difference in the crystal structure. Whereas BaFe2S3 has the $Cmcm$ space group in the whole temperature range measured (Fig. 1 (b)), BaFe2Se3 exhibits a structural phase transition at 660 K (= $T_{s1}$) from the high-temperature $Cmcm$ space group to low-temperature $Pnma$ space group Svitlyk et al. (2013), which induces small distortions both in intra and inter ladder structures (Fig. 1 (c)). Below $T_{s1}$, Fe-Fe bonds along the leg direction become staggered in the anti-phase manner between the two adjacent legs, and the ladder planes are slightly rotated from the principal axes of the orthorhombic structure. At around 400 K (= $T_{s2}$), the second structural transition occurs, which is evidenced by a shift of ($h00$) reflection in the X-ray diffraction profile and a sharp peak in the differential scanning calorimetry signal Svitlyk et al. (2013). However, the nature of this structural transition is uncovered, which is the central question of this study.

With further cooling BaFe2Se3, an antiferromagnetic order develops below the Néel temperature ($T_{\rm N}$) of 220$\sim$255 K. The magnetic structure was determined to be a block-type one with the magnetic easy axis along the layer direction, which is distinct from the stripe-type magnetic ordering with the magnetic easy axis of the rung direction in BaFe2S3 Luo et al. (2013); Lovesey et al. (2015). Block-type magnetically ordered phase is theoretically predicted to have large ferroelectric polarizations reflecting the broken inversion symmetry Dong et al. (2014). The related important point is that the block-type magnetic structure within $Pnma$ involves basis functions over separate irreducible representations (irreps) to form the corepresentation Nambu et al. (2012), which puzzles us in the light of the second-order fashion of the magnetic transition. Therefore, the actual crystal structure is expected to have lower symmetry than $Pnma$ even in the paramagnetic phase ($T_{\rm N}<T<T_{s2}$).

In this study, we performed the optical second harmonic generation (SHG) measurements for BaFe2Se3. Together with re-analysis on powder neutron diffraction profiles, we show that the phase transition at 400 K is the structural transition from unpolar $Pnma$ to polar $Pmn2_{1}$ space group. The transition is triggered by block-type lattice distortions through the spin-lattice coupling, and the resultant $Pmn2_{1}$ structure can compatibly accommodate the block-type magnetic structure. Indeed linear spin-wave calculations with assuming this space group well account for observed magnetic excitations Mourigal et al. (2015). Relationship between our experimental findings and electronic nematic transitions widely observed in the iron-based superconductors will be discussed.

High-quality single crystals of BaFe2Se3 were grown by the melt-growth method. Stoichiometric amounts of elemental Ba shots, Fe powders, and Se powders in a carbon crucible were sealed into an evacuated quartz ampoule. The ampoule was slowly heated up to 1373 K, kept for 48 hrs, and slowly cooled to room temperature. The powder X-ray diffraction using the Cu-$K_{\alpha}$ radiation indicates no trace of impurity phases. The electrical resistivity was measured by the standard four-probe method. The magnetic susceptibility was collected by using a superconducting quantum interference device magnetometer with applying magnetic field along the $a$ (leg direction) and $b$ (layer direction) axes below room temperature, and only along the $a$ axis above room temperature. For the optical measurements, the oriented crystals were polished by a sand-paper and Al2O3 fine powders. The SHG experiments were performed in the experimental setup shown in Fig. 3(a). Incident pulsed light with a wavelength of 800 nm (1.55 eV) and the pulse duration of 130 fs at a repetition rate of 1 kHz is generated by using a Ti:sapphire regenerative amplifier system, and is irradiated on the sample. The laser power is $\sim$1 mW and the spot size is typically $\sim$200 $\mu$m. The reflected light with twice energy is detected by a photomultiplier tube. Optical measurements at low temperatures were performed by using He and N2 flow cryostats.

Figure 2 summarizes fundamental physical properties of BaFe2Se3. The electrical resistivity ($\rho$) shown in Fig. 2(a) exhibits the Arrhenius-type temperature dependence with small excitation energy of 0.2 eV, which is consistent with the energy gap observed in the optical conductivity spectra shown in Supplemental Materials sup . The $\rho$ curve shows an anomaly at the second structural transition temperature of $T_{s2}$, as can be clearly seen from the dip-like feature in the temperature derivative of log$\rho$, indicating that the insulating behavior is enhanced in the low-temperature phase. Temperature dependence of the magnetic susceptibility ($\chi$) taken under the magnetic field of 1 T is shown in Fig. 2(b). Besides the reported anomaly corresponding to the antiferromagnetic transition at $T_{\rm N}$ = 220 K, we observe a clear anomaly at $T_{s2}$, suggesting a large change in electronic states is likely across $T_{s2}$.

To obtain further insights into the structural transition at $T_{s2}$, we performed optical SHG experiments. The SHG is the second-order nonlinear optical phenomena, in which photons with twice the energy of initial photons are generated from samples. The SHG intensity ($I$) is represented by $I(2\omega)\propto|\mu_{0}\frac{\partial^{2}\vec{P}}{\partial t^{2}}+\mu_{0}(\nabla\times\frac{\partial\vec{M}}{\partial t})|^{2}$, which consists of an electric dipole contribution $P_{i}(2\omega)=\varepsilon_{0}\chi^{{\rm polar}}_{ijk}E_{j}(\omega)E_{k}(\omega)$ and a magnetic dipole contribution $M_{i}(2\omega)=\varepsilon_{0}c\chi^{{\rm axial}}_{ijk}E_{j}(\omega)E_{k}(\omega)$, where $P$, $M$, and $E$ stand for the electric polarization, magnetic dipole moment and electric field, respectively Fiebig et al. (2005). The tensors $\chi^{\rm polar}_{ijk}$ and $\chi^{\rm axial}_{ijk}$ are the third-rank SHG tensors having polar and axial characteristics, respectively. The SHG tensors are governed by the point group of the system, and the particularly important is that polar tensors can be finite only in noncentrosymmetric systems. For example, in the centrosymmetric $mmm$ symmetry (the point group of $Cmcm$ and $Pnma$ space groups), all the components in $\chi^{{\rm polar}}$ should be zero, whereas $\chi^{\rm axial}_{abc}$, $\chi^{\rm axial}_{bca}$, and $\chi^{\rm axial}_{cab}$ components of $\chi^{\rm axial}$ can be finite.

We first performed experiments in a configuration shown in Figs. 3(a) and 3(b): the incident laser is irradiated on the (010) surface and the reflected SHG light normal to the surface is detected; the polarization of the initial light ($\phi_{\omega}$) and that of the reflected SHG light ($\phi_{2\omega}$) were analyzed by linear polarizers. The advantage of this setup is that magnetic-dipole contributions ($\chi^{\rm axial}_{abc}$, $\chi^{\rm axial}_{bca}$, and $\chi^{\rm axial}_{cab}$) expected for the $mmm$ point group are undetectable due to the symmetrical reason. Nevertheless, as can be seen from Fig. 2(c), when $\phi_{\omega}$ = 90*∘* and $\phi_{2\omega}$ = 0*∘*, we observe that the SHG intensity begins to develop below $T_{s2}$, strongly indicating the inversion symmetry being broken in the low-temperature phase. Indeed, the detailed analysis presented in the following revealed that the observed signal reflects the $\chi^{\rm polar}_{caa}$ component in the $mm2$ point group.

Here, we discuss the point group below $T_{s2}$ by analyzing the polarization dependence of the SHG signal. Figures 3(d) and 3(f) show the SHG signal in the $\phi_{\omega}$ - $\phi_{2\omega}$ plane, which are collected in the experimental configuration of Figs. 3(a) and 3(b). At 450 K, as shown in Fig. 3(d), there is negligibly small SHG signal observed in accordance with the centrosymmetric $Pnma$ symmetry (Fig. 3(c)). At 200 K, on the other hand, one can see clear polarization dependences: the strong signal is discernible at ($\phi_{\omega}$, $\phi_{2\omega}$) = (0*∘, 0∘) and (90∘, 0∘*) (Fig. 3(f)). We here postulate that the point group of the low-temperature phase is $mm2$, which is the subgroup of $mmm$. The symmetry operation lost in lowering the point group is the inversion operation, so that $mm2$ is a noncentrosymmetric point group. Then, in $mm2$, $\chi^{\rm polar}_{caa}$, $\chi^{\rm polar}_{ccc}$, and $\chi^{\rm polar}_{aac}$ components can be finite, whereas axial tensors have the same component as in the case of $mmm$ ($\chi^{\rm axial}_{abc}$, $\chi^{\rm axial}_{bca}$, and $\chi^{\rm axial}_{cab}$ can be excited in the present configuration). Taking care that axial tensors cannot be detected in the current experimental setup, one can simulate the SHG pattern by changing the sign and magnitude of the polar tensor components. The simulated pattern with $\chi^{\rm polar}_{caa}$ : $\chi^{\rm polar}_{ccc}$ : $\chi^{\rm polar}_{aac}$ = −2.0 : 1.0 : 0 well reproduces the experimentally observed polarization dependence (Fig. 3(e)).

We next performed similar experiments for the (011) surface: the polarization of the initial light ($\phi_{\omega}$) and that of the reflected SHG light ($\phi_{2\omega}$) are defined as shown in Fig. 3(g). In contrast to the results for the (010) surface, the SHG signals exhibit characteristic polarization dependences even at 450 K (Fig. 3(i)), which is above the second structural transition temperature. This SHG pattern is well reproduced by putting the axial tensor components in the $mmm$ point group to be $\chi_{bca}^{\rm axial}$ + $\chi_{cab}^{\rm axial}$: $\chi_{abc}^{\rm axial}$ = $-$1.0 : 1.0 (Fig. 3(h)). We stress here that the axial tensor contributions can be allowed even in centrosymmetric crystals. When the temperature is decreased down to 200 K, the strong signal appears at ($\phi_{\omega}$, $\phi_{2\omega}$) = (90*∘, 0∘*) in addition to signals observed at 450 K (Fig. 3(k)). The observed SHG pattern can be well reproduced by simulations under the assumption of the point group of $mm2$ with the rung direction as the two-fold rotation axis (Fig. 3 (j)); here, we set $\chi^{\rm axial}_{abc}$ : $\chi^{\rm axial}_{bca}$ +$\chi^{\rm axial}_{cab}$ : $\chi^{\rm polar}_{caa}$ : $\chi^{\rm polar}_{ccc}$ : $\chi^{\rm polar}_{cbb}$ + $\chi^{\rm polar}_{bcb}$ = 1 : $-$1 : $-$0.78 : 0.39 : $-$0.67. We thus conclude that the phase below $T_{s2}$ has the point group of $mm2$ with the polar axis as the rung direction.

Herein, let us identify the crystal structure below $T_{s2}$. To do this, we first list up possible space groups. Since any discontinuity or thermal hysteresis is not observed in physical quantities across the transition, the phase transition at $T_{s2}$ is considered to be of the second-order; therefore, we consider the maximal subgroup of $Pnma$. We then list up three candidate space groups, $Pmc2_{1}$, $Pmn2_{1}$, and $Pna2_{1}$; these respectively lose one of three orthogonal mirror/glide operations associated with the layer, rung, and leg directions. Among them, $Pmn2_{1}$ is the most plausible one, because the SHG results indicate that the polar axis is along the rung direction. We then re-analyze the powder neutron diffraction profiles collected at $T$ = 300 K temperature, yielding better convergence in the $Pmn2_{1}$ model than in others. The obtained structural parameters are shown in Table I in the Supplemental Materials sup . Importantly, the $Pmn2_{1}$ model is compatible with the block-type magnetic structure below $T_{\rm N}$. Actually, the powder neutron diffraction profiles below $T_{\rm N}$ can be well fitted by the $Pmn2_{1}$ structure model and the block-type magnetic structure model with the magnetic wave vector of (1/2, 1/2, 1/2). Here, the magnetic structure is represented by a single irrep $\Gamma_{1}$ (Table II of Supplemental Materials sup ) in consistent with the second-order nature of the magnetic transition. The resultant magnetic space group is $Pmn2_{1}1^{\prime}$, so that the time-reversal symmetry is preserved by combining the translation operation even below $T_{\rm N}$ (Fig.1 (d)). Therefore, the polar-$c$ and axial-$c$ tensors do not become finite upon the magnetic order, justifying the analysis of the SHG results.

The observed polar state in BaFe2Se3 is almost in accordance with the theoretical proposals by Dong, $et$ $al$ Dong et al. (2014). According to the theory, the block-type magnetic ordering is stabilized by an electronic origin in a realistic band structures Luo et al. (2013). As a result, there appears uniform displacements of Se atoms perpendicular to the local ladder plane, bearing the macroscopic polarization along the rung direction, which is in consistent with our experimental results. The microscopic mechanism of this magneto-elastic coupling is argued to be the so-called exchange striction. The mechanism is known to affect in the up-up-down-down-type antiferromagnetic phase of a conventional multiferroic material $o$-YMnO3  Sergienko et al. (2006); Picozzi et al. (2007). The large lattice distortions induced at around $T_{\rm N}$ shown in ref. Nambu et al. (2012) strongly support this scenario.

However, there is an apparent incompatibility between the theory and our experimental results. Whereas the theory predicts emergence of polarization below $T_{\rm N}$, our results indicate that polar lattice distortions emerge below $T_{s2}$, which is much higher than $T_{\rm N}$. This kind of successive structural and magnetic phase transitions, which are closely related with each other from the symmetry point of view, are reminiscent of the iron-based superconductors including Co-doped BaFe2As2 Chu et al. (2009); Fernandes et al. (2014). Among them, the high temperature structural transition has been considered to be originating from an orbital order or electronic nematic order, since the rotational symmetry is broken in the electronic system Chu et al. (2012); Kasahara et al. (2012); Fernandes et al. (2014); Sun et al. (2016). It is possible that a similar mechanism is involved in BaFe2Se3, in which prominent quantum fluctuations inherent in the reduced spatial dimensionality results in a large separation of the two transition temperatures. We also note that the isostructural compound BaFe2S3 exhibits a broad anomaly in the electrical resistivity at around 200 K, which is higher than the antiferromagnetic transition temperature of 120 K. This could be also due to the possible orbital order Yamauchi et al. (2015). In the iron-based superconductors, not only antiferromagnetic fluctuations but also structural (orbital) fluctuations are expected to have key roles for the formation of superconducting state. Such possibility shall be also pursued for the superconducting states under pressure in BaFe2S3 and BaFe2Se3, which will open a research field of the superconducting multiferroics.

In conclusion, we observed the optical second harmonic generation signals below the structural transition temperature of 400 K in quasi-one-dimensional ladder material BaFe2Se3. Combined with neutron diffraction results, we uncovered the detailed crystal structure in the low temperature phase, which has the polar $Pmn2_{1}$ space group. In the viewpoint of the symmetry, BaFe2Se3 is therefore multiferroics with both polarity and antiferromagnetic order. The structural phase transition is driven by the block-type lattice distortions through the magneto striction mechanism. Considerable change in the electrical resistivity and magnetic susceptibility across the polar-nonpolar phase transition suggests that electronic states are largely modified by this structural instability.