Iron pnictides comprise a new class of high-temperature (high-Tc) superconductors, which has been extensively studied since the discovery of the iron oxypnictide LaFeAsO (La1111; refs 8, 9, 10, 11, 12, 13, 14). The superconductivity appears as a result of carrier doping to the parent compound in place of the magnetic- and structural-ordered state2,9,15. A recent study reported an advanced doping method using a hydrogen anion instead of fluorine in La1111 that has surpassed the doping limit of fluorine, and uncovered the concealed second superconducting phase (SC2) with a higher Tc of 36 K at x 0.35, in addition to the first dome (SC1) with the maximum Tc of 26 K at x 0.1 (refs 7, 16). To investigate the origin of the two SC domes as well as the origin of the higher Tc in SC2, and to determine whether a certain hidden phase exists beyond the SC2 region, we have performed a multi-probe study in the range 0.40 ≤ x ≤ 0.51 using neutron, muon and X-ray beams.

Fig. 1a shows the neutron powder-diffraction pattern in the non-superconducting specimen with x= 0.51. Extra peaks were observed with indices (1/2, 1/2, n)T,M (n= 0, 1, 2) in the low-temperature region, where the subscripts T and M refer to the tetragonal cell and magnetic peak, respectively; these were determined to be unambiguously magnetic in origin because they were unobservable in the X-ray measurement. The (1/2, 1/2, 0)T,M reflection gradually gains intensity below the magnetic transition temperature TN= 89(1) K, estimated by the power law in the x = 0.51 sample, as shown in Fig. 1b, which indicates a continuous second-order transition. Similar magnetic peaks were also observed below TN 76 K for x= 0.45.

Figure 1: Pulsed neutron diffraction measurements of LaFeAsO1xHx.
figure 1

We prepared 1 g powder samples as described in ref. 7 (Supplementary Information). The powder diffraction measurements were performed on the low-angle detector bank of the Super HRPD at J-PARC for x= 0.51 and on the NOVA at J-PARC for x= 0.45. a, Magnetic reflections of (1/2, 1/2, n)T,M (n= 0, 1, 2) that were observed clearly at 10 K (for x= 0.51) (labelled in green) disappeared at 120 K. b, Temperature dependence of the integrated intensity of (1/2, 1/2, 0)T, M in x= 0.45 (orange) and 0.51 (green), normalized to the nuclear (0, 0, 2)T, N reflection (labelled in black in Fig. 1a). The data for x= 0.51 were fitted to the power law (TNT)2β, resulting in TN= 89(1) K and 2β= 0.58(5). The squared order parameter for x= 0.45 determined by μSR ( (muon frequency)2× (magnetic volume fraction)) is plotted (purple) after scaling to neutron data. The in-plane configuration of the Fe spin, determined by the Rietveld method17, for x= 0.45 as well as 0.51, is illustrated in the inset with the tetragonal unit cell aT× bT (solid line) in the high-temperature case and the magnetic unit cell 2aT× 2bT (broken line) in the low-temperature case. The error bars represent the statistical error in a and the uncertainty in the least-squares fitting of the peaks in b.

The in-plane magnetic structure is illustrated in the inset of Fig. 1b17. The ordering wavevector q= (1/2,1/2,0) was determined to correspond to the magnetic unit cell of × 2bT× cT, describing a tetragonal axis, which is consistent with the orthorhombic nuclear unit cell in the low-temperature case. The Fe spins are directed to a diagonal axis of the tetragonal cell, and form an antiferromagnetic collinear structure; this result reveals an exceptional stripe-type arrangement among the iron pnictides18,19,20,21. The spins couple ferromagnetically along the c axis. The magnetic moment in x= 0.51 at 10 K is estimated to be 1.21(1) μB per iron atom, which is significantly larger than the value of 0.63 μB for x= 0 (ref. 19). This observation that the long-range magnetic order emerges beyond SC2 is a remarkable finding because the d-electrons on the iron atoms should be delocalized by the large amount of carrier doping and, accordingly, the magnetic interaction is usually expected to be weak.

Fig. 2a shows the muon spin relaxation (μSR) time spectra for x= 0.45. The slow relaxation above 80 K is attributed to a paramagnetic state, whereas the line shapes below 80 K evolve into strongly damped oscillations with increasing amplitude on cooling, reflecting the development of the magnetically ordered volume fraction (MVF). The significant damping of the muon spin precession in contrast to a clear precession in x= 0 (ref. 22) indicates an inhomogeneity in the local magnetic fields, which is presumably due to the heavy doping effect (Supplementary Information).

Figure 2: Zero-field muon spin relaxation measurements.
figure 2

a, Time spectra of the muon polarization Pμ for x= 0.45, taken at PSI. The data exhibit significant damping in contrast to a clear muon spin precession in x= 0 (ref. 22), indicating an inhomogeneity in the local magnetic fields. b, Diagram of the muon spin relaxation process. The magnetic volume fraction (MVF) is estimated from the amplitude of the time-dependent asymmetry in the positron counts between the forward and backward counters. c, Temperature dependence of the MVF for samples in the range x= 0.40−0.51, conducted at J-PARC MUSE and PSI. d, Hydrogen concentration dependence of the MVF (blue) and the superconductivity (SC) shielding volume fraction (red). The error bars represent the statistical error in a and the uncertainty in the least-squares fittings of the spectra in c and d.

Fig. 2b is a diagram of the μSR process. The amplitude and frequency of the μSR signal reflect the MVF and the ordered moment of the magnetic region, respectively. Fig. 2c shows the temperature dependence of the resultant MVF. For x= 0.51, the magnetic ordering appears at TN= 92(7) K and the MVF becomes entire towards zero temperature. As the hydrogen content is reduced, the value of TN and the MVF decrease in unison. Fig. 2d shows the MVF and the superconductivity volume fraction (SVF) estimated from susceptibility measurements7, clearly indicating an inverse correlation between the MVF and the SVF. The approximate summation to unity suggests that antiferromagnetic static order and superconductivity coexist in the range 0.40 ≤ x ≤ 0.45 despite the absence of the coexistence state in the underdoped region15. The coexistence state is not attributed to the microscopic scale but to the mesoscopic scale in the spatial inhomogeneity, because if the coexistence state were due to the microscopic scale the MVF obtained by the μSR experiment would become entire even in the superconducting state (Supplementary Information). Further experimental work will clarify any intimate connection between superconductivity and magnetism in the heavier doping region23,24.

Fig. 3a shows the X-ray profiles of the (2, 2, 0)T reflections in the x= 0.45 and 0.51 samples. On cooling, the peak in the x= 0.51 sample was broadened, whereas the peak in x= 0.45 exhibited only slight broadening. No broadening of the (0, 0, l) reflections was observed in the x= 0.51 sample; therefore, the experimental findings imply that the tetragonal to orthorhombic (T–O) structural transition emerges clearly for x= 0.51.

Figure 3: Synchrotron X-ray diffraction measurements.
figure 3

Powder diffraction measurements for samples with x= 0.42, 0.45, 0.49 and 0.51 were performed on the beamlines of 8A/8B at KEK-PF. a, Representative profiles of the (2, 2, 0)T reflections for x= 0.45 and 0.51 at a wavelength of λ= 1.0993 Å. Peak broadening was observed in x= 0.51 below Ts 95 K, whereas there was slight broadening in x= 0.45. b, The temperature dependence of the lattice constants for x= 0.45 and 0.51. In x= 0.51, the aT- and cT-axes exhibit a split in length and an upturn with the T–O transition of Ts 95 K, respectively. In the orthorhombic phase, the values of bO and cO are divided by 2. The cell setting changes as aOcT, bOaT+ bT and cO= –aT+ bT (Fig. 1b inset). The orthorhombicity, ΔaT/aT= 0.41%, is smaller than that of the other iron pnictides (0.49%, LaFeAsO; 0.73%, BaFe2As2; refs 18, 20). c, Temperature dependence of the structural order parameter (OP) determined by neutron and X-ray diffraction, and the magnetic intensity of the (1/2, 1/2, 0)T, M reflection in x= 0.51. The error bars indicate the uncertainty in the least-squares fitting of the magnetic peaks in c.

Fig. 3b shows the temperature dependence of the lattice constants in samples with x= 0.45 and 0.51. In x= 0.51, the aT axis length splits in two below the T–O transition of Ts 95 K, and the cT axis length shows an upturn at Ts. In x= 0.45, although an apparent split between aT and bT does not exist, the cT axis anomaly appears to be similar to that in x = 0.51, which may be the result of insufficient coherence of the splitting of aT and bT in the low-temperature phase.

The resultant temperature dependence of the structural and magnetic order parameters is shown in Fig. 3c for x= 0.51. The small gap between the transition temperatures Ts and TN implies a strong correlation between structure and magnetism in comparison with the large gap of 20 K for x= 0. On the basis of a structural analysis25, the compound with x= 0.51 crystallizes below Ts in an orthorhombic Aem2 structure without inversion symmetry, in contrast to the universal Cmme structure with inversion symmetry observed in the 1111 materials (Supplementary Information). The Fe atom exhibits an off-centre deformation in the FeAs4 tetrahedron, as shown in the inset of Fig. 4. The present result provides us with an intriguing deduction that the unusual structural distortion, along with the loss of the inversion symmetry, which has not been found in large ensemble of the iron pnictides18,19,20,21, may profoundly affect the d-orbital levels of the iron atom26,27.

Figure 4: Magnetic, structural and superconducting phase diagram of LaFeAsO1xHx.
figure 4

The original parent compound with x= 0 exhibits a structural transition at Ts= 155 K, followed by an antiferromagnetic state (AF1) at TN= 137 K (ref. 18). With increasing x, two superconductivity domes appear: 0.05 ≤x≤ 0.20 (SC1) with Tc, max= 26 K, and 0.20 ≤x≤ 0.42 (SC2) with Tc, max= 36 K (ref. 7). Eventually, another antiferromagnetic phase (AF2) appears in the range 0.40 ≤x≤ 0.51. In the advanced parent compound at x= 0.51, structural and magnetic transitions occur at Ts 95 K and TN= 89 K, respectively. Ts’ indicates the c axis upturn temperature observed in X-ray measurements. The filled and open marks are obtained from the present and previous results, respectively7. The magnetic structures of AF1 (left) and AF2 (right) are shown with their magnetic moments m (ref. 19), where the solid lines represent the tetragonal cell. The displacements of the Fe and As atoms across the structural transitions are schematically described by the arrows on the FeAs4 tetrahedra from the view of the orthorhombic long axis, in which the Fe and As atoms move by 0.07 Å (0 Å) and 0.06 Å (0.01 Å) in x= 0.51 (x= 0), respectively. The error bars represent the uncertainty in the least-squares fitting routines.

Fig. 4 shows the phase diagram of LaFeAsO1−xHx, where the introduction of charge carriers via doping with hydrogen indeed controls the system (Supplementary Information). The features of the physical properties in x= 0.51 (x= 0) can be characterized as follows: the Fe-spin arrangement is a peculiar stripe-type (universal stripe-type)18,19; the magnetic moment is large, 1.21(1) μB (small, 0.63 μB); the gap between Ts and TN is 5 K (20 K); the structural symmetry is non-centrosymmetric (centrosymmetric); the magnetic and superconducting states coexist (the magnetic and superconducting states are exclusive) ; the behaviour of resistivity is as for a non-Fermi liquid (Fermi liquid)7. These findings strongly suggest the magnetic and electronic correlations are considerably developed in the right-hand region of the phase diagram.

We have thus far regarded the ‘undoped’ antiferromagnet with the structural transition adjacent to the superconducting state as the parent compound in the high-Tc superconductors. Hence, we now reveal that a newly discovered antiferromagnetic phase with a structural transition adhering to the superconducting phase is considered as the ‘doped’ parent phase. This behaviour is unexpected, because magnetic and electronic correlations are widely perceived as being weak in the region with heavy carrier doping. However, the magnetic and electronic correlations in the advanced parent phase at x 0.5 are indeed rather strong in comparison to the original parent phase at x 0. We think that a multi-band feature such as an orbitally selective Hund’s coupling or a Mott transition plays a crucial role so as to drive the emergence of the advanced parent phase, which is presumably stimulated by the half-integer number of the d6.5 state in x= 0.5 (refs 28, 29). In the iron pnictides, the ‘parent compound’ not only refers to the undoped material, but also more generally indicates a fingerprint at a certain critical point of the magnetic and electronic correlations. Yamakawa et al. proposed spin and orbital ordered states with the commensurate Fermi surface nesting at x= 0 and the incommensurate Fermi surface nesting at x 0.4 in LaFeAsO1−xHx from the theoretical calculation30; the latter inconsistency with the present result is presumably due to the sizeable electron correlation with the large magnetic ordered moment. A more sophisticated theory concerning the electron correlation, the multi-band picture, and the heavy doping effect in the crystal is required to specify the origin of the advanced parent phase.

We now discuss the origin of the two-dome SC phases. The electron doping to the d6 state of the x= 0 parent—that is, the chemical substitution of H to the O2− site—leads to the SC1 phase. From the viewpoint of the x 0.5 parent, the SC2 phase emerges through hole doping to the d6.5 state, by O2− substitution to the H site. Consequently, we can definitely state that the two SC domes are generated by carrier doping, starting from the left- and right-hand parent compounds towards the intermediate region of the phase diagram. Moreover, the Tc valley at x 0.2 is interpreted as a unique crossover region in this phase diagram.

The combination of the distinct feature of the structural instability with the loss of inversion symmetry and the localized nature of the d-electrons relative to the original parent compound plausibly result in a new mechanism of superconductivity as the origin of the significant enhancement of Tc in SC2 relative to SC1, because the ground-state properties in the parent compounds generally persist unabated, even in the superconducting state. Future band structure calculations taking into account the orthorhombic crystal and magnetic structures would confirm and clarify this new ordered state.