Pressure effect on iron-based superconductor LaFeAsO1−xHx: Peculiar response of 1111-type structure

A systematic study of the crystal structure of a layered iron oxypnictide LaFeAsO1−xHx as a function of pressure was performed using synchrotron X-ray diffraction. This compound exhibits a unique phase diagram of two superconducting phases and two parent phases. We established that the As–Fe–As angle of the FeAs4 tetrahedron widens on the application of pressure due to the interspace between the layers being nearly infilled by the large La and As atoms. Such rarely observed behaviour in iron pnictides implies that the FeAs4 coordination deviates from the regular tetrahedron in the present systems. This breaks a widely accepted structural guide that the superconductivity favours the regular tetrahedron, albeit the superconducting transition temperature (Tc) increases from 18 K at ambient pressure to 52 K at 6 GPa for x = 0.2. In the phase diagram, the second parent phase at x ~ 0.5 is suppressed by pressure as low as ~1.5 GPa in contrast to the first parent phase at x ~ 0, which is robust against pressure. We suggest that certain spin-fluctuation from the second parent phase is strongly related to high-Tc under pressure.

Iron pnictides are a new family of high-temperature superconductors, whose charge carriers located primarily in the two-dimensional iron plane play an active role in its superconductivity [1][2][3][4] . The supporting pnictide (Pn) atoms strongly perturb the 3d multi-orbital bands of Fe atoms through hybridization between Fe-3d and Pn-p electrons [2][3][4] . As a consequence, chemical substitution along with carrier-doping/chemical-pressure, or application of pressure on the crystal can drastically modify electronic properties, such as the superconducting transition temperature (T c ) of these materials [2][3][4][5] . Based on studies on chemical substitution in iron pnictides, an empirical guideline has been established that T c is maximised when the geometry of the FePn 4 unit approaches a regular tetrahedron 6 . The application of pressure is a direct and clean way to modify the local geometry of FePn 4 without the degradation of the crystal in comparison to the chemical substitution; hence, the detailed crystal structure under pressure warrants further investigation.
One of the fascinating materials in iron pnictides is LaFeAsO 1−x H x , which has a ZrCuSiAs-type structure with alternating stacks of conducting FeAs 4 moieties and insulating (O, H)La 4 layers (Fig. 1a) 7,8 . LaFeAsO 1−x H x exhibits a unique phase diagram on hydrogen anion substitution i.e. electron doping: two superconducting domes with T c,max = 26 K at x ~ 0.08 (SC1) and T c,max = 37 K at x ~ 0.35 (SC2), and two parent phases at x ~ 0 (PP1) and x ~ 0.5 (PP2) [9][10][11][12] . The SC2 and PP2 are rarely observed among high-T c materials because they usually become normal metal in the heavily electron-doped region 11 . The resistivity behaviour changes from Fermi-liquid to non-Fermi liquid types with doping the electron, implying the electronic correlation developed in the higher x region 7 . Takahashi et al. have recently demonstrated that the application of pressure on LaFeAsO 0.72 H 0.18 induced a notable enhancement of the T c from 18 K at ambient pressure to 52 K at 6 GPa 13 . Interestingly, the maximum T c of LaFeAsO 0.72 H 0.18 under pressure was similar to that of Sm1111 (55 K), the highest known T c among iron-based superconductors 14 .
Here, we examine the crystal structure of LaFeAsO 1−x H x , (x = 0.0, 0.2, and 0.51), under pressure to analyse the relation between the FeAs 4 geometry and the T c . The results reveal that the FeAs 4 unit deviates from regular tetrahedron on the application of pressure. This is an unexpected finding that breaks the hitherto believed guideline of approaching a regular FePn 4 tetrahedron with an increase in T c . Furthermore, we demonstrate that the peculiar PP2 is rapidly suppressed by pressure, while the conventional PP1 is robust against pressure 15-17 . We suggest that strong spin-fluctuations, originating from an orbital-selective Mott state in the PP2, is a key for enhancing the T c under pressure. The pressure responses of the FeAs 4 modification, the parent phases, and their correlation are previously unexplained peculiarities in 1111-type iron pnictides. The atomic positions are displayed in Fig. S1b (Supplementary Information). In Fig. 2a-c the Fe-As bond length (d Fe−As ), As-Fe-As bond angle (α As-Fe-As ), and As height from the Fe plane (h As ) are plotted as a function of pressure, where the parameters are described in the inset of Fig. 2a (detailed experimental data in Supplementary Information, Table S1). On the application of pressure, d Fe-As and h As decrease, while α As-Fe-As increases i.e. opens up for all the compositions. The degree of pressure response of α As-Fe-As is calculated to be + 0.049, + 0.18, and + 0.24°/GPa for x = 0, 0.20, and 0.51, respectively. In contrast, that of α As-Fe-As in BaFe 2 As 2 and LiFe 2 As 2 has been estimated at − 0.48 and − 0.29°/GPa, respectively, implying that their α As-Fe-As bond-angles reduction with pressure 21,22 .

Results and Discussion
Pressure works primarily to infill the interspace between the FeAs 4 conduction layer and the (O, H)La 4 insulating layer. Figure 2d displays the La-As distances (d La-As ). Based on previous reports 23, 24 , the sum of the radii of La and As ions was found to be 3.25 Å, which provides an estimate of the interspace distance. d La-As and α As-Fe-As change from 3.308(2) Å and 111.9(1)° at ambient pressure to 3.211(1) Å and 113.2(1)° at 7.7 GPa for x = 0.20, respectively (Fig. 2e). As d La-As for x = 0.20 is close to the interspace filling limit, the pressure response of α As-Fe-As results in a greater shift at higher x. Though the hard sphere perspective is simple, it can yield important findings with regard to superconductivity, but it has not been defined in explicit detail previously in the La1111 system 17,25 . Furthermore, as h As can be calculated as: h As = d Fe-As cos(α As-Fe-As /2), it also responds to pressure and decreases significantly in the higher x region. On the other hand, in 122-type iron arsenides with a ThCr 2 Si 2 structure, the drastic reduction of the As-As distance between the FeAs 4 layers generally causes a structural collapse with the formation of an (As-As) 4− molecule 19,21 , which possibly drives the reduction of α As-Fe-As . This distinguishable response of 1111 and 122 compounds to pressure is attributed to the absence of an intervening blocking layer between two FeAs 4 layers in the latter class of iron arsenides. Figure 3 exhibits the contour plots of T c against α As-Fe-As and d Fe-As under pressure, where the values of T c in the whole map are interpolated from ref. 13. Since the thermal effect is small when compared to the pressure, it is valid to discuss the relation between the T c and the structural parameters at room temperature. Pressure triggers h As As-Fe-As   the merge of the two SC domes at ambient pressure into a single SC dome along with an increase of T c to 52 K at 6 GPa for x = 0.2. After the merge, the ridge line of T c runs along the line for x = 0.20 as the pressure is increased.
In iron-based superconductors, the relation between the maximum T c and structural parameters of FeAs 4 has been proposed as follows: the highest T c is achieved when α As-Fe-As approaches 109.5° as in a regular tetrahedron of FeAs 4 or when h As ~ 1.38 Å 6,26 . Theoretical argument has been advanced that antiferromagnetic spin-or orbital-fluctuation is maximised as FeAs 4 adopts a nearly regular tetrahedron geometry, leading to an optimum T c [27][28][29] . The former is strongly related to the number and topology of Fermi surfaces, while the latter is due to the electron-phonon interaction. In agreement with the above rule, SmFeAsO 0.78 H 0.22 , which has the highest T c of 55 K in iron pnictides, exhibits nearly ideal values of α As-Fe-As (109.3°) and h As (1.386 Å) at ambient pressure 30 . Moreover, the α As-Fe-As for BaFe 2 As 2 and LiFeAs act toward and away from the regular tetrahedron of FeAs 4 along with increasing and decreasing the T c , respectively 21,22 . However, our present results reveal that while α As-Fe-As and h As of LaFeAsO 0.8 H 0.2 deviate from the optimum values with pressure (Fig. 3), there is a significant increase in T c . Thus, this work highlights the inconsistencies in the guides for increasing the T c . The electronic state calculations illustrate that the Fermi surface topologies of LaFeAsO 0.8 H 0.2 are unaltered on the application of pressure ( Supplementary Information, Fig. S2). Additionally, the band width of Fe-3d widens with pressure because of the shortening of d Fe-As , resulting in a decrease of the spin-fluctuation that should cause T c to decrease as well 27 . Thus, the properties examined so far fail to account for the increase of T c under pressure.
In order to find the reason behind the enhancement of T c , we next examined the parent phase under pressure. Both parent phases indicated tetragonal to orthorhombic (T-O) structural transitions (T S ), and subsequently an antiferromagnetic ordering (T N ). Figure 4a shows the temperature dependence of the full width at half maximum (FWHM) of the 220 reflection for x = 0.51, which is a good indicator of the T-O structural transition 11 . The transitions of T S2 are indicated by arrows and are estimated from the power law fitting. At 0.5 and 0.9 GPa, there is moderate broadening of the FWHM in the high-temperature region as extensive fluctuations occur in the vicinity of the structural transition. At 1.5 GPa, the FWHM exhibits slight broadening at low-temperature, not due to the structural transition but on account of the precursory phenomenon near the phase boundary. No broadening was observed at 3.  low-pressure. Conversely, the PP1 could be seen up to 20 GPa (T N1 ) and 30 GPa (T S1 ) and was robust against pressure 15-17 . In Fig. 4b, we summarise the entire phase diagram of LaFeAsO 1−x H x at ambient pressure and 6 GPa.
The distinct responses to pressure for both parent phases are unexpected and presumably arise due to their different origins. Since the origin of PP1 is interpreted as a spin density wave with Fermi surface nesting 31,32 , its robust behaviour of PP1 against pressure is consistent with insensitive change of the Fermi surface 15, 16,33 . In contrast, the origin of PP2 is seemingly less relevant to the Fermi surface topology. Iimura et al. performed an electronic state calculation based on the molecular orbital concept for LaFeAsO 1−x H x 34 . In the low x region, the bonding and antibonding states of the Fe-3d and As-4p orbitals give a large gap. This gap decreases rapidly with an increase in h As , namely a decrease in the hybridization of Fe and As orbitals, making the non-bonding Fe-3d xy orbital the half-filled state. The resulting state implies that the orbital selective Mott state on Fe-3d xy is realised in the higher x region, i.e. in PP2, for LaFeAsO 1−x H x 35 . Contrary to electron doping with increasing x, the pressure induces the rapid decrease of h As as shown in Fig. 2c. Therefore, in contrast to PP1, PP2 can be easily broken by pressure.
Generally in high-T c superconductors, the nature of the parent phase influences the superconducting state; that is, fluctuations derived from the parent phase may drive the pairing of the superconducting electrons. Thus, the origins of SC1 and SC2 adhering to PP1 and PP2, respectively, can be considered as fluctuations from PP1 and PP2 11 . The former is the itinerant type spin-fluctuation 32 , and the latter is another type spin-fluctuation with a strongly localised character of the orbital selective Mott phase. Since PP2 disappears easily with pressure, the fluctuation from PP2 should also be sensitive to pressure. Thus, we suggest that the significant enhancement of T c under pressure is mainly due to the favourable change of the latter fluctuation. The relation between the present results and the other mechanism of orbital-or charge-fluctuations remains unclear [36][37][38][39] . To identify the above suggestion, the further investigation on the spin/structural dynamics is required in this system.

Conclusion
We established that the FeAs 4 tetrahedron in LaFeAsO 1−x H x deviates from the regular one with applied pressure, which is inconsistent with the conventional believed structural guides for increasing the T c . We found that the PP2 at x ~ 0.5 is lost under low-pressure, contrary to the sluggish pressure reaction of PP1 at x ~ 0. Pressure presumably suppresses the itinerant spin-fluctuation driving the superconductivity from PP1, but enhances another spin-fluctuation with the localised character from PP2 in 1111-type iron pnictides. These pressure responses of the FeAs 4 modification and the parent phases are previously unexplained peculiarities in 1111-type. In future, we plan to further increase the T c by combining the effects of the regular tetrahedron geometry of FeAs 4 and the strong fluctuation state from PP2 under pressure in 1111 systems.

Methods
LaFeAsO 1−x H x powder samples were prepared by a high-pressure solid-state reaction as reported in literature 7 . The hydrogen content in these systems was determined by thermal desorption spectroscopy. Synchrotron X-ray diffraction (sXRD) was performed at room temperature for pressures up to ~8 GPa at NE1A of PF-AR, KEK. Pressure was applied using a diamond anvil cell (DAC) with 600 μ m culet diamond anvils and a gasket with a 300 μ m hole. The DAC, in which the anvils are supported by the 45° tapered slit window without a backing plate, has the advantage of reducing the background scatter and simplifying the absorption correction of diamond ( Supplementary Information, Fig. S3a). A very fine powder results in a perfect Debye ring of reflections on the two-dimensional image ( Supplementary Information, Fig. S3b). The measured wavelength of λ = 0.4217 Å and the wide open angle of the DAC can approach a d-spacing of < 0.7 Å, which enables accurate determination of atomic positions. The two-dimensional images collected using a RIGAKU R-AXIS on the curved imaging plate were integrated to yield 2θ-intensity data. Crystal structures were refined by the Rietveld method indexed to the space group of P4/nmm, and the reliable factors in the refinements were R wp = 3.9-6.6% ( Supplementary Information, Fig. S3c) 40 . Moreover, we traced the PP2 on the application of pressure by means of sXRD down to 8 K at BL-8B of PF, KEK, measured at λ = 0.8267 Å. A 4:1 methanol-ethanol mixture was used as a pressure transmitting medium in all the experiments.