Polar nematic state in an iron-based superconductor LaFeAsO1-xHx

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Polar nematic state in an iron-based superconductor LaFeAsO_1-xH_x

https://doi.org/10.21203/rs.3.rs-77544/v1

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High critical temperature (T_c) superconductivity is generally considered to result from a fluctuation-mediated Cooper-pairing derived from a parent phase. The question of what type of fluctuation forms in materials thus plays a key role in understanding the mechanism of superconductivity. The iron-based superconductor LaFeAsO_1-xH_x possesses bipartite magnetic parent phases with centrosymmetric (x ~ 0) and non-centrosymmetric (x ~ 0.5) structures. The latter is an intriguing polar-metal phase induced by temperature and carrier doping. Here, we investigate average and local structures of LaFeAsO_1-xH_x using X-ray diffraction and extended X-ray absorption fine-structure measurements. We found lattice C₄ symmetry breaking far above the structural transition temperature, and the signature of a tiny split in As–Fe bond distances with broken spatial inversion symmetry in a wide temperature/doping range. The former reveals a nematic state, and the latter highlights a fluctuated state of polar structure which can be appropriately called polar nematic state.

Hard Condensed-matter Physics

Bipartite Magnetic Parent Phases

Phase Transitions

Superconductivity

Spatial inversion symmetry is intimately involved in the physics of matter, thereby its breaking can trigger exotic quantum phenomena. For example, metallic materials with polar crystallographic structure—polar metals—offer the opportunity to explore interesting physics such as unconventional superconductivity, nonreciprocal transport, and inverse Faraday effect^1–4. While over 60 polar metals have been reported to date⁵, a temperature-induced polar metal state as suggested by Anderson and Blount in 1965 is rare because screenings of conduction electrons hamper the formation of a macroscopic electrostatic field⁶. Shi et al. reported an example of a ferroelectric-like transition while maintaining the metallic behaviour in LiOsO₃⁷. On rising temperature or doping carrier, such a polar metal will recover its centrosymmetric structure; thus, one would expect a fluctuating state, a quantum critical point, and a nematic state adjacent to the polar metal phase^8–10.

Studies of high-T_c iron-based superconductors have experienced spectacular growth in condensed matter physics since their discovery^11–13. We believe that the most promising material for studying polar metals is an iron oxypnictide LaFeAsO_1 − xH_x, which is a hydrogen-substituted version of the prototype iron-based superconductor LaFeAsO_1‒xF_x¹⁴. The LaFeAsO_1 − xH_x exhibits a characteristic phase diagram via electron doping, as illustrated in Fig. 1. The diagram has two magnetic parent phases at x ~ 0 (PP1) and x ~ 0.5 (PP2), and two superconducting domes with T_c,max = 26 K at x ~ 0.08 (SC1) and T_c,max = 36 K at x ~ 0.35 (SC2)^15–18. Tetragonal-orthorhombic structural transitions at T_s1 (x ~ 0) and T_s2 (x ~ 0.5) precede magnetic transitions; the respective orthorhombic structures are centrosymmetric and non-centrosymmetric^18–20. The PP2 structure with the polar point group mm2 serves as a unique parent phase in high-T_c materials as the spatial inversion symmetry is broken by temperature¹⁸. Throughout this paper, we use the term "parent phase" to refer to the magnetic ordered state that breaks lattice C₄ symmetry. The source of SC2 has been discussed in terms of spin-fluctuation, orbital-fluctuation, and orbital-selective Mott state models^16,21−24. However, the nematicity or fluctuating state in highly electron doped LaFeAsO_1‒xH_x remains unexplored and warrants investigation.

In this paper, we analyse the average and local structures of LaFeAsO_1 − xH_x (0.35 ≤ x ≤ 0.51) by measuring synchrotron X-ray diffraction (XRD) and extended X-ray absorption fine-structure (EXAFS). Our XRD and EXAFS results led us to identify a polar nematic state: a broken lattice C₄ symmetry and a polar fluctuated structure that emerge at temperatures far above the parent phase. These phenomena arise from the dynamical and short-range fluctuation of the parent phase structure.

We first focus on the change of crystal lattice symmetry in XRD measurements. Figure 2a shows the X-ray profiles for 220_T reflection at 300, 120, and 32 K for x = 0.51, where the suffix "T" signifies the indexing in the tetragonal system. Though the 220_T profile is supposed to split into two peaks below the tetragonal-orthorhombic structural transition at T_s2 ~ 95 K, the profile was already broadened at 120 K. We regard the T_s2 transition as static and long-range order of the orthorhombic distortion, the temperature of which was estimated using the lattice constant¹⁸ and the resistivity¹⁶ anomalies. Moreover, the profile with a shoulder at 32 K exhibits inequivalent intensities of two reflections split from 220_T, manifesting the presence of polar structure below T_s2 (Supplementary Information, Fig. S1).

Figure 2b plots the temperature dependence of the profiles’ full width at half maximum H for x = 0.51, 0.45, 0.42, 0.40, and 0.35. H was obtained by fitting a profile to a single pseudo-Voigt function and normalising it to room temperature values. The H values rise significantly when cooled past the T_s2 transition for x = 0.51, 0.45, and 0.42. Note that they gradually increase far above T_s2. In contrast, the H values are nearly constant with temperature for x = 0.40 and 0.35. We here define the critical temperature T^* as the point deviating from the baseline formed from the averaged values of H above 250 K. The results are T^* = 240, 190, and 140 K for x = 0.51, 0.45, and 0.42, respectively. Since the T_s2 transition entails the broadening of the 220_T peak, our result reveals a breaking of lattice C₄ symmetry for x ≥ 0.42 despite a wide gap between T^* and T_s2. Considering the XRD measurement timescale of 10⁻¹⁵ s, the lowering of lattice symmetry in T_s < T < T^*might be viewed as a slower dynamical phenomenon. Another possible symmetry lowering for x = 0 above T_s1 = 175 K has been suggested in the narrow temperature range of 175 K < T < 200 K²⁵.

We proceed to examine the local structure of LaFeAsO_1–xH_x from the As K-edge EXAFS measurement for x = 0.51, 0.45, 0.42, and 0.37. Figure 3a, b shows the representative k²-weighted EXAFS oscillation k²χ(k) and R-space magnitude of the Fourier transformation (FT), respectively, at 9.7 and 250 K for x = 0.51. In the radial direction without phase-correction, the peak amplitudes around R = 2.1 and 2.9 Å correspond to As–Fe and As–La/As–O shells, respectively. We analysed the bond distances from the fit to the first As–Fe shell with an R-range of 1.85–2.30 Å based on the high-temperature P4/mmm structure. Figure 3c plots the temperature dependence of the As–Fe distances, which decrease on cooling within the high-temperature range (> 100 K). However, for x = 0.51, 0.45, and 0.42 the upturns in bond distances on cooling were observed at respective temperatures of 95, 90, and 30 K, which correspond closely to T_s2. The elongation of bond distance below T_s2 arises from the negative thermal expansion of the c-axis, as reported in previous XRD measurement¹⁸.

Next, we employed a Fourier-filtered back transformation in EXAFS, which enables the detection of unknown tiny distortions within a specific coordination sphere^26,27. Figure 4 illustrates the Fourier-filtered EXAFS amplitudes for As–Fe (1.60–2.45 Å) shells of R-spectra (EXAFS oscillations in Supplementary Information, Fig. S2). This examination found inflection points or “kinks” in each of profiles at the low temperature side. The amplitudes at the lowest temperature and at 250 K are plotted in the figure insets with solid blue and dashed black lines, respectively. The data at 250 K is normalised by the peak position and height of the object profiles used for the baseline. We define the difference amplitude between the object profiles and the baseline as the phenomenological formula k²χ_dif(q) = k²χ(q)(T)−s₀k²χ(s₁q)(250 K), where s₀ and s₁ are the scale factors (Supplementary Information, Fig. S3). We evaluated the kink positions q_beat indicated by arrows as the peaks in the wavenumber derivatives of k²χ_dif(q). The q_beat values were roughly 11.2, 11.0, 11.6, and 11.3 Å^-1 respectively for x = 0.51, 0.45, 0.42, and 0.37 at the lowest temperature. The kink is due to the beat produced from the phase difference of EXAFS oscillations with the difference of bond distances ΔR in the shell. Based on the relation ΔR = π/(2q_beat)²⁶, we can estimate ΔR of the As–Fe distances to be 0.140, 0.143, 0.135, and 0.139 Å for x = 0.51, 0.45, 0.42, and 0.37, respectively.

The uniform As–Fe distance in the high-temperature phase splits into two long and two short distances in PP2 along with the loss of inversion symmetry¹⁸, leading to a small ΔR; this was not observed in PP1^19,20. Note that ΔR at 32 K for x = 0.51 in PP2 was previously determined to be 0.14 Å from XRD study¹⁸, which agrees with our EXAFS result. We therefore ascribe the kinks in the EXAFS amplitude to the presence of local polar structure, and regard the k²χ_dif(q) as the fraction of the polar structure. The amplitude is largest at 30 K for x = 0.51 in PP2; its value drops with decreasing x and/or rising temperature, but can still be observed far outside of PP2.

Our results from XRD and EXAFS are summarised in Fig. 1 together with the previously observed phase diagram^15,16,18. The green area signifies the local distortion with broken inversion symmetry. The phase diagram shows that the lowering of lattice symmetry appears below T^*, and dynamical and short-range polar structure emerges over wide ranges in temperature and doping. Taking account of the gradual changes in H and beat amplitude, their transformations may be regarded as cross-over phenomena instead of a phase transition.

In the iron-based superconductors BaFe₂(As_1-xP_x)₂ and Sr_1-xNa_xFe₂As₂, nematic states arise at specific doping levels from parent to superconducting phase, while breaking C₄ magnetic and/or lattice symmetries^28,29. Hence, we view the lowering of lattice symmetry at temperatures T_s2 ≤ T ≤ T^* revealed by our XRD measurements as a nematic state. In the same way, we suggest that our nematic state involves an electronic or magnetic nematicity. Moreover, the local polar structure was identified over a wider temperature and doping range. Since the polar structure below T_s2 entails the breaking of lattice C₄ symmetry, both of these phenomena that occur above T_s2 should be intertwined. We thus propose that the T_s2 ≤ T ≤ T^* region can be called a polar nematic state, although it is difficult to identify the vanishing temperature for beat amplitude. Sakurai et al. reported NMR measurements for LaFeAsO_1-xH_x and pointed out an anisotropy of the electric-field gradient derived from a disproportionation of d-orbital electrons³⁰. This observation likely shares a close link with our result, given the possibility of the local polar structure being related to an orbital ordering or its fluctuation. Moreover, Onari et al. theoretically proposed that the second parent phase comes from a charge quadrupole order stemming from the disproportionation of d-orbital electrons²³.

Let us now consider the interplay between the local polar structure and the superconductivity. Lowering of lattice symmetry was unobserved via XRD for x = 0.40 and 0.35 in SC2, whereas the local polar structure was detected via EXAFS for x = 0.37. Since the orthorhombicity in PP2 rapidly reduces with decreasing x from x = 0.51¹⁸, the presence of a minute lattice distortion may have been experimentally undetectable via XRD. Regardless, the aforementioned electric-field gradient anisotropy from NMR³⁰ was evident even in the superconducting phase. Hence, we suggest that the polar nematic state is linked with the superconducting phase³⁰. We consider SC2 to be derived from PP2 by the introduction of holes, namely as x decreases from ~ 0.5. Thus, in relation to superconductivity, the polar structure may have an effect on T_c or the paring mechanism. As an example, noncentrosymmetric superconductors can give rise to exotic pairing states with spin-singlet and spin-triplet mixtures^1,31. In contrast, the superconductivity in LaFeAsO₁_‒_xH_x emerges after recovering inversion symmetry, where one might expect ﬂuctuation-related phenomena instead. Intriguing theories have been proposed by Anderson and Blount⁶, and Ydlium et al.³² positing that ferroelectric-like soft phonons enhance T_c or drives the superconductivity. Moreover, an odd-parity superconductivity derived from parity fluctuation has been predicted in the vicinity of inversion symmetry breaking^33,34. Since polar structure is also observed in SmFeAsO₁_‒_xH_x with T_c = 55 K^35,36, further insight awaits from the more detailed investigation of local physical properties in this system.

In conclusion, the average and local structures for highly electron doped LaFeAsO₁_‒_xH_x with bipartite parent phases were investigated using XRD and EXAFS measurements. The second parent phase (x ~ 0.5) entails the time-reversal and the spatial inversion symmetries broken. We have demonstrated that a dynamical state with broken lattice C₄ symmetry and polar structure—a polar nematic state—emerges in a wide temperature/doping range above the parent and the superconducting phases. This observation reported in this study is the intriguing result because the electronic, magnetic, and lattice instabilities should be weak generally in the highly electron-doped region. We conclude that EXAFS serves as a good probe for the detection of local polar structure that could help map further studies of nematicity.

Powder samples of LaFeAsO_1 − xH_x were prepared using a high-pressure solid-state reaction as described in a previous study¹⁵. Synchrotron XRD and As K-edge transmission EXAFS were carried out over the whole temperature range on beamlines BL-8A/8B/9C at the Photon Factory at the High Energy Accelerator Research Organization (KEK). For XRD measurements, a very fine powder sample was enclosed in a capillary with a diameter of 0.1 mm, which was irradiated with an X-ray beam. The sample was continuously rotated during the exposure. Two-dimensional XRD images were obtained using a diffractometer with a curved imaging plate (R-AXIS, Rigaku Corp.) at wavelength λ = 1.0993 Å. The images were integrated to yield 2θ-intensity data using the DISPLAY software (Rigaku). For EXAFS measurements, all crystalline reagents were fastidiously mixed with BN powder. This process is key to obtaining high-quality data up to the high-k region. EXAFS oscillations and R-space magnitude of the Fourier transformation were extracted from the raw data using the Athena program. The R-space data were fitted to the theoretical signals calculated by FEFF8 code using IFEFIT on the Arthemis platform³⁷.

Author Contributions

S.Maki, J.Y, S.I., Y.M, S. Matsuishi, H.H conceived the study. S.I. synthesised the samples. S.Maki, J.Y., H.A, H.S, R.K performed the synchrotron X-ray measurements. S.Maki, J.Y co-wrote the manuscript. All the authors discussed the results and the manuscript.

Acknowledgements

We thank Y. Kuramoto for fruitful discussions. This work was supported by the MEXT Elements Strategy Initiative to Form Core Research Center (JPMXP0112101001) and JSPS KAKENHI (No. 16K05434). The synchrotron XRD, EXAFS and neutron scattering experiments were performed with the approval of the Photon Factory Program Advisory Committee (No. 2013S2-002 and 2016S2-004) of IMSS, KEK. The crystal structures were created using the software VESTA ³⁸.

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Polar nematic state in an iron-based superconductor LaFeAsO_1-xH_x

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Polar nematic state in an iron-based superconductor LaFeAsO_1-xH_x

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