We first focus on the change of crystal lattice symmetry in XRD measurements. Figure 2a shows the X-ray profiles for 220T reflection at 300, 120, and 32 K for *x* = 0.51, where the suffix "T" signifies the indexing in the tetragonal system. Though the 220T 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 220T, 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 220T peak, our result reveals a breaking of lattice *C*4 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 LaFeAsO1–*x*Hx from the As K-edge EXAFS measurement for *x* = 0.51, 0.45, 0.42, and 0.37. Figure 3a, b shows the representative *k*2-weighted EXAFS oscillation *k*2χ(*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 *P*4/*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 sphere26,27. 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 *k*2*χ*dif(*q*) = *k*2*χ*(*q*)(*T*)−*s*0*k*2*χ*(*s*1*q*)(250 K), where *s*0 and *s*1 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 *k*2*χ*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 Δ*R* in the shell. Based on the relation Δ*R* = π/(2*q*beat)26, we can estimate Δ*R* 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 Δ*R*; this was not observed in PP119,20. Note that Δ*R* 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 *k*2*χ*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 diagram15,16,18. 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(As1-*x*Px)2 and Sr1-*x*NaxFe2As2, nematic states arise at specific doping levels from parent to superconducting phase, while breaking *C*4 magnetic and/or lattice symmetries28,29. 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 *C*4 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 LaFeAsO1-*x*Hx 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 mixtures1,31. In contrast, the superconductivity in LaFeAsO1‒xHx 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 breaking33,34. Since polar structure is also observed in SmFeAsO1‒xHx with *T*c = 55 K35,36, 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‒xHx 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 *C*4 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.