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Tomoki Deguchi, Takeshi Hara, [Yuta Ishii](https://orcid.org/0000-0002-8957-5833), Hao-Bo Li, Azusa N. Hattori, Hidekazu Tanaka, Hajime Sagayama, Yusuke Wakabayashi
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[Long-period ordering induced by hydrogen doping in films on (001) substrates](https://mdr.nims.go.jp/datasets/c64ea808-0c24-4cf0-81c4-d8bee18c5cbf)
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Long-period ordering induced by hydrogen doping in ${\rm NdNiO}_3$ films on ${\rm SrTiO}_3$ (001) substratesPHYSICAL REVIEW B 113, 174113 (2026)Long-period ordering induced by hydrogen doping in NdNiO3 films on SrTiO3 (001) substratesTomoki Deguchi ,1,* Takeshi Hara ,1 Yuta Ishii,2 Hao-Bo Li ,3 Azusa N. Hattori ,3 Hidekazu Tanaka ,3Hajime Sagayama,4,† and Yusuke Wakabayashi 1,‡1Department of Physics, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan2Center for Basic Research on Materials (CBRM), National Institute for Materials Science (NIMS),1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan3SANKEN (Institute of Scientific and Industrial Research), The University of Osaka, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan4Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan(Received 21 November 2025; revised 6 March 2026; accepted 31 March 2026; published 18 May 2026)Hydrogen doping offers a versatile method to dynamically control the doping level of metal oxides over a widerange, yet it introduces strong lattice modulation whose structural details have been poorly investigated. Here, weelucidate the hydrogen-induced structural modulation in NdNiO3 thin films using synchrotron x-ray diffraction.While the strain relaxed pristine film exhibits a bulklike√2 × √2 × 2 structure, the hydrogen-induced insulatingphase adopts a 1 × 1 × 2 structure with some incommensurate modulation. Our results provide the first directexperimental evidence for hydrogen-induced formation of a superstructure in rare-earth nickelates.DOI: 10.1103/gd7h-6967I. INTRODUCTIONCarrier doping is a fundamental strategy to control theelectronic properties of transition metal oxides. In perovskiteoxides, A-site substitution has been widely employed to tunethe 3d electron number and associated physical propertiessuch as magnetism and transport. While this approach pro-vides precise control of the nominal doping level over a widerange, it fixes the carrier concentration during synthesis. Re-versible external control has been pursued through variousapproaches, including electric field gating via electric doublelayers [1–4] and chemical insertion of mobile ionic species[5–7]. Among chemical insertion methods, hydrogen insertioninto transition metal oxides has emerged as a powerful routeto induce large changes in electronic properties [8–11].Rare-earth nickelates RNiO3 provide a prototypical plat-form for studying correlation-driven metal-insulator transi-tions (MIT) [12]. These compounds exhibit a systematicevolution of the MIT temperature with rare-earth ionic radius,reflecting the interplay between bandwidth, electron corre-lation, and structural distortions [12]. The low-temperatureinsulating phase is accompanied by charge disproportionationand antiferromagnetic ordering [13–15], while the high-temperature metallic phase shows paramagnetic behavior.*Contact author: deguchi.tomoki.q6@dc.tohoku.ac.jp†Present address: Nagoya University Synchrotron Radiation Re-search Center (NUSR), Nagoya University, Nagoya 464-8603, Japan.‡Contact author: wakabayashi@tohoku.ac.jpPublished by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.Hydrogen insertion into RNiO3 thin films induces a MITwith resistivity changes exceeding six orders of magni-tude [5,11,16,17]. This process is reversible upon annealing,enabling potential applications in resistive switching andmemristive devices [18–21]. Experimentally, hydrogen istypically introduced by exposing RNiO3 films patternedwith platinum catalysts to H2 gas at elevated temperatures[5,22–27]. Hydrogen dissociates on the platinum surface anddiffuses into the film over length scales of tens of micrometerswithin minutes.Despite extensive investigations [5,6,16,22–25,27–32], themicroscopic mechanism underlying the hydrogen-inducedMIT remains incompletely understood. Key open questionsinclude: which crystallographic sites does hydrogen occupy[6,30], what is the hydrogen stoichiometry in the insulat-ing phase [23,25], and how does hydrogen insertion modifythe crystal structure and electronic configuration. Addressingthese questions requires direct structural characterization ofhydrogenated RNiO3 at the atomic scale.Recent density functional theory (DFT) calculations [30]have provided theoretical insight into possible hydrogen con-figurations in Hx-RNiO3, where x denotes the hydrogenconcentration. Systematic studies for R = Sm, assuming a2√2 × √2 × 2 supercell, evaluated the energetic stability ofvarious hydrogen arrangements after full structural optimiza-tion. Configurations with x = 1 and x = 0.5 were found toexhibit significantly lower total energies compared to otherstoichiometries. Notably, the calculation for x = 0.5 configu-ration exhibits a layered arrangement of Ni valences, distinctfrom the checkerboard pattern [13–15,33,34] observed in thelow-temperature insulating phase of bulk RNiO3. However,experimental verification of these predicted structures hasbeen lacking. Even whether hydrogen incorporation induceslong-range structural ordering or forms a disordered solidsolution remains an open question.2469-9950/2026/113(17)/174113(7) 174113-1 Published by the American Physical Societyhttps://orcid.org/0009-0004-3058-9415https://orcid.org/0009-0001-4907-7506https://orcid.org/0000-0002-0277-0848https://orcid.org/0000-0002-5770-6026https://orcid.org/0000-0002-3368-8708https://orcid.org/0000-0003-3107-0338https://ror.org/01dq60k83https://ror.org/026v1ze26https://ror.org/035t8zc32https://ror.org/01g5y5k24https://crossmark.crossref.org/dialog/?doi=10.1103/gd7h-6967&domain=pdf&date_stamp=2026-05-18https://doi.org/10.1103/gd7h-6967https://creativecommons.org/licenses/by/4.0/TOMOKI DEGUCHI et al. PHYSICAL REVIEW B 113, 174113 (2026)Here we address this issue through synchrotron x-raydiffraction studies of epitaxial NdNiO3 thin films grown onSrTiO3 (001) substrates. We compare the diffraction patternsof pristine and hydrogenated films. Our measurements revealthat hydrogen insertion drives the formation of a distinct crys-tallographic phase, absent in the pristine films, characterizedby the wave vector 12 c∗pc with incommensurate modulation,where the subscript pc denotes pseudocubic notation, whilethe alternating tilting of NiO6 octahedra is substantially re-duced. These results provide direct experimental evidence forthe formation of layered structure in Hx-RNiO3 and establish astructural framework for understanding the hydrogen-inducedmetal-insulator transition.II. EXPERIMENTEpitaxial NdNiO3 thin films were grown on10×10×0.5 mm3 SrTiO3(100) substrates (Crystalbase Co.)using a pulsed laser deposition system with a handmadeceramic target under optimized growth conditions of 660 ◦Cand oxygen pressure of 30 Pa. The laser energy (ArF, λ =193 nm) was kept at 1.9 J/cm2 with a repetition rate of6 Hz. After deposition, the samples were cooled to roomtemperature with growth pressure in 30 minutes.The surface of the NdNiO3 films was covered with a Ptmesh catalyst to dissociate H2 into atomic hydrogen. The Ptmesh had a pitch of 5 µm, similar to that used in Ref. [24]. Asample was split into two pieces. One piece was hydrogenatedby annealing in Ar(96%)-H2(4%) at 300 ◦C for 20 minutes(hereafter referred to as H-NNO), while the other piece waskept as a pristine reference (hereafter referred to as PR-NNO).The lattice parameters of bulk NdNiO3 in the Pbnm settingare ao = 5.389 Å, bo = 5.382 Å, and co = 7.610 Å [35], cor-responding to a pseudocubic lattice parameter apc = 3.807 Å.Throughout this paper, we use the pseudocubic notation forindexing.Synchrotron x-ray diffraction experiments were performedat a photon energy of 16 keV at beamlines BL-4C and BL-8Bof the Photon Factory, KEK, Japan. At BL-8B, reciprocalspace maps were obtained using the oscillation photographmethod with a 2D detector (PILATUS3 S 1M) in air atroom temperature. At BL-4C, Bragg reflection intensitieswere measured by the ω-scan method in vacuum at roomtemperature.III. RESULTS AND ANALYSISFirst, we examined the structure of the PR-NNO film.Figures 1(a) and 1(b) show the reciprocal space maps ofPR-NNO on the (hk1) and (hk 32 ) planes, respectively. Thein-plane lattice parameters are fully relaxed from those ofthe substrate. Although the centers of the substrate Braggreflections are slightly offset from the l = 1 plane, tails ofthe strong substrate reflections are visible as sharp features inpanel (a) [for example, those at (3,3) and (1,3) are prominent].In addition to the film Bragg reflections at integer h, k, and lpositions, many weak Bragg reflections appear at half-integerpositions. The peak positions are consistent with the Pbnmunit cell of NdNiO3 assuming all six possible multidomainvariants (co oriented along the apc, bpc, or cpc directions, eachTABLE I. Structural parameters of the PR-NNO film. The latticeparameters are apc = bpc = 3.813 Å, and cpc = 3.812 Å. The corre-sponding parameters for the bulk structure [35] are also provided forcomparison.Par. PR-NNO Bulkx(Nd) 0.4836(5) 0.4799(6)y(Nd) 0.5131(6) 0.5142(6)x(O1) 0.226(5) 0.2190(7)y(O1) 0.218(6) 0.2111(7)x(O2) 0.500(7) 0.5004(4)y(O2) 0.287(5) 0.2846(4)z(O2) 0.285(10) 0.2878(4)U (Nd)(Å2) 0.0275(9) 0.0077(4)U (Ni)(Å2) 0.02 0.00646(13)U (O1)(Å2) 0.035(10) 0.0096(6)U (O2)(Å2) U (O1) 0.0111(5)with either right- or left-handed coordination). Due to themultidomain structure and relaxed lattice parameters, the filmBragg reflections are broader than those of the substrate. Thepseudocubic lattice parameters of PR-NNO are apc = bpc =3.813 Å and cpc = 3.812 Å. Diffuse streaks extending fromthe strong film Bragg reflections (positions where h + k + l iseven) are attributable to dislocations parallel to the apc or bpcaxes [36]. This feature was observed only in some samples,suggesting that these diffuse streaks are not essential to themain functionality of NdNiO3 films.Given this information, we measured film Bragg reflectionintensities using a large four-circle diffractometer to collectprecise intensities under controlled illumination conditions[37]. Assuming the space group of PR-NNO is the same asthat of the bulk, Pbnm, structural parameters were derived byBayesian analysis [38,39]. The total number of Bragg reflec-tions used for the refinement was 114, and the total numberof structural parameters was 11. To reduce the number ofstructural parameters, we employed isotropic atomic displace-ment parameters U and used a common U for the two oxygensites.Figure 2 shows the observed Bragg intensities (Iobs) plottedagainst the calculated intensities (Icalc). The number of reflec-tions with very strong intensities is limited due to overlapbetween intense substrate Bragg reflections and film reflec-tions. This reduction in the number of accessible reflectionslimits information on the Ni site, which contributes Braggintensity only at integer h, k, and l positions in the pseu-docubic indexing. For this reason, we fixed U (Ni) at 0.02 Å2.The Bayesian analysis yielded the structural parameters sum-marized in Table I, with an R value (R =∑ |√Iobs−√Icalc|∑ √Iobs) of0.106. The bulk values reported in Ref. [35] are also listedfor comparison. The obtained atomic positions for PR-NNOare close to those of bulk NdNiO3.Figures 1(c) and 1(d) show the reciprocal space maps ofH-NNO. Clear changes in the intensity distribution causedby hydrogen doping indicate a substantial structural differ-ence between the two samples. Several notable features areobserved: an overall increase in background intensity (i.e.,monotonic diffuse scattering), additional broad streaks around174113-2LONG-PERIOD ORDERING INDUCED BY HYDROGEN … PHYSICAL REVIEW B 113, 174113 (2026)FIG. 1. Reciprocal space maps of (a) PR-NNO hk1, (b) PR-NNO hk 32 , (c) H-NNO hk1, and (d) H-NNO hk 32 , together with line profilesalong (e) the h11, (f) the h 1232 , and (g) the h1 32 lines. The intensity is shown on a logarithmic scale in all panels. The insets in (c) and (d) displaythe maps after removing hydrogen from H-NNO.integer h, k, and l positions along diagonal directions, andsignificant changes in the intensities of weak Bragg reflec-tions at half-integer positions. The increased diffuse scatteringsuggests enhanced structural disorder. The additional diagonalstreaks indicate that hydrogen doping induces an incommen-surate transverse-mode lattice modulation characterized bythe wave vector of (x,−x, 0) (see the Appendix for details).At x � 0.37, these modulations manifest as superlattice peaks.The streaks extending toward the Bragg reflections are similarto the scatterings reported for Pr0.5Ca0.5MnO3 [40], whichwere regarded as a signature of short-range correlation amongpoint defects. Changes in half-integer reflection intensitiesreveal changes in the long-range ordered structure. Sincequantitative structure analysis of systems with incommen-surate modulations is inherently difficult, we examine thestructure of H-NNO qualitatively based on the diffractionintensity distribution. The insets in Figs. 1(c) and 1(d) showthe reciprocal space maps after removing the hydrogen fromH-NNO. It is clear that incommensurate peaks have disap-peared while the intensity distribution of ( 12 , 0, 0) and (0, 0, 12 )reflections has modified. This implies that the structuralchange by hydrogen doping is reversible, except for a domainrepopulation.Line profiles along the yellow horizontal lines inFigs. 1(a)–1(d) are presented in Figs. 1(e)–1(g). Panel (e)shows the profiles on the (h11) line. The intensities of strongpeaks at h = 1 and 2 for the two samples are nearly thesame. In general, strong Bragg intensities are dominated byoverall structural features and are insensitive to the detailsof structural modulation; therefore, this similarity indicates174113-3TOMOKI DEGUCHI et al. PHYSICAL REVIEW B 113, 174113 (2026)FIG. 2. Observed intensity Iobs vs calculated intensity Icalc basedon the resulting structure model of the PR-NNO film.that the illumination conditions for the two measurementswere similar. In the high-h region (h = 3 and 4), the intensityfor H-NNO is weaker than that for PR-NNO, possibly dueto larger atomic displacement parameters (U ’s) in H-NNO.Importantly, H-NNO shows negligible intensity at positionscharacterized by the wave vector ( 12 , 0, 0). This reductionindicates suppression of the PR-NNO structural modulationcharacterized by (001)o, which involves A-site displacements,in domains with co ‖ apc.Profiles along the (h 1232 ) line shown in panel (g) exhibitsubstantial reduction in the intensities of peaks characterizedby the wave vector ( 12 , 12 , 12 ) in H-NNO. The intensity of thesereflections is a measure of NiO6 octahedral tilting [37,41,42];see Appendix B for details. Therefore, H-NNO exhibits re-duced alternating octahedral tilting compared to PR-NNO,and can be regarded as 1 × 1 × 2 structure.Profiles along the (h1 32 ) line shown in panel (f) exhibit apronounced increase in the intensities of peaks characterizedby the wave vector (0, 0, 12 ) in H-NNO. This indicates thathydrogenation induces a distinct twofold periodic order alongthe out-of-plane direction. The contrast in intensity with peaksat ( 12 , 0, 0) exhibits the orientational alignment of the H-NNOlattice.IV. DISCUSSIONOur structural investigation reveals that hydrogen dopinginto NdNiO3 films induces substantial structural modulationbeyond simple lattice expansion. This finding has importantimplications for computational studies: calculations of elec-tronic and protonic behavior in highly doped states mustinclude detailed structural relaxation. Calculations withoutsuch relaxation, which have been performed in some previousstudies, are justified only for lightly doped regimes.While the structure of PR-NNO is essentially identical tothat of bulk NdNiO3, Fig. 3(a), hydrogen doping producestwo key structural changes: suppressed NiO6 octahedral tiltingand the emergence of an incommensurate lattice modulation.Figures 3(b) and 3(c) show transverse-mode and longitudinal-mode modulation forming a 1 × 1 × 2 superstructure. Thelongitudinal-mode modulation involves a layered arrangementof NiO6 octahedra having alternating volumes, suggestinglayered valence ordering.Recent scanning transmission electron microscopy(STEM) studies [29] reported that fully strained Hx-NdNiO3grown on LaAlO3 exhibits enhanced NiO6 tilting, whichappears to contradict our x-ray observations. However, severaldifferences exist between the two studies. First, our samplesare strain-relaxed NdNiO3 films grown on SrTiO3, whereasthe STEM study examined strained films on LaAlO3. Second,diffraction and STEM probe different aspects of structure:x-ray diffraction is sensitive to long-range order, whileSTEM images projected atomic positions and can detect localstructures even when long-range order is absent. Therefore,our observation of weak ( 12 , 12 , 12 ) reflections does not excludethe presence of finite octahedral tilting with substantialspatial disorder as described in Appendix B. QuantitativeFIG. 3. (a) Structure of PR-NNO. Schematic illustrations of possible H-NNO structure with (b) longitudinal and (c) transverse displace-ments. All structures are viewed along the bpc axis.174113-4LONG-PERIOD ORDERING INDUCED BY HYDROGEN … PHYSICAL REVIEW B 113, 174113 (2026)high-resolution structure analysis on homogeneous H-NNOsamples is needed to fully resolve this discrepancy.We now compare our findings with recent DFT calcu-lations on Hx-SmNiO3 [30]. The calculations predict thatx = 0.5 exhibits alternating Ni2+ and Ni3+ layers, consistentwith our observed twofold periodicity. This correspondencesuggests a hydrogen concentration near x = 0.5 in H-NNO,although our experiment does not provide direct quantifica-tion. However, the calculations predict substantial octahedraltilting, contradicting our observation of suppressed tilting.This discrepancy highlights the need for computational workon H-NNO that explicitly assumes the 1 × 1 × 2 structurewith minimal tilting to clarify the hydrogen configuration andits effect on electronic states.V. CONCLUDING REMARKSWe have examined the crystal structure of the hydrogen-induced insulating phase of NdNiO3 using synchrotron x-raydiffraction. While the pristine film exhibits essentially thebulklike√2 × √2 × 2 structure, hydrogen doping drives atransition to a qualitatively different structural state: alternat-ing octahedral tilting is suppressed, and a long-period orderwith 1 × 1 × 2 periodicity along cpc emerges alongside anincommensurate modulation with wave vector (x,−x, 0), x �0.37. These observations point to a hydrogen-induced layeredordering of NiO6 octahedra, distinct from the checkerboardcharge order of pristine RNiO3.Whether the commensurate 1 × 1 × 2 order and the in-commensurate modulation coexist within the same region orsegregate spatially due to variations in hydrogen concentrationremains an open question.ACKNOWLEDGMENTSThis work was performed under the Cooperative ResearchProgram of NJRC Mater. & Dev. (MEXT) and supported bya Grant-in-Aid for Scientific Research from the Japan Soci-ety for the Promotion of Science (JSPS KAKENHI, GrantsNo. JP22H02024 and No. JP23K23292). The synchrotronradiation experiments at the Photon Factory were carried outwith the approval of the Photon Factory Program AdvisoryCommittee (Proposals No. 2022G016, No. 2023G527, andNo. 2024G005).DATA AVAILABILITYThe data that support the findings of this article are notpublicly available upon publication because it is not techni-cally feasible and/or the cost of preparing, depositing, andhosting the data would be prohibitive within the terms of thisresearch project. The data are available from the authors uponreasonable request.APPENDIX A: SCATTERING FROM TRANSVERSE-MODELATTICE MODULATIONThe scattering amplitude for a given scattering vector Q,F (Q), caused by a positional modulation un = u sin(q · Rn),where Rn, un, u, and q denote the average position of the nthatom, displacement of the nth atom, the amplitude of the struc-tural modulation, and the modulation vector, respectively, canbe written asF (Q) =∑nfn exp[iQ · (Rn + un)]�∑nfn exp(iQ · Rn)+ iQ · u∑nfn exp(iQ · Rn) sin(q · Rn), (A1)where fn denotes the atomic scattering factor of the nth atom.The first term produces the Bragg reflections, and the secondterm produces the superlattice reflections at G ± q, where Gdenotes the reciprocal lattice vector. The superlattice reflec-tion term is proportional to Q · u.Figure 1(c) shows the region of Q = (h, k, 1) with h, k >0, indicating that the component of u along the (1,1,0)direction is primarily observed. Each Bragg reflection isaccompanied by incommensurate satellite reflections char-acterized by the wave vector q = (x,−x, 0) with x � 0.37.Therefore, the observed incommensurate lattice modulationis predominantly of transverse character.APPENDIX B: STRUCTURE FACTORS FOR ( 121212 ) REFLECTIONSBragg peaks characterized by the wave vector ( 12 , 12 , 12 ) in pseudocubic notation correspond to h + k : odd and l : odd inPbnm notation. Calculated intensities for (hkl ) : even-odd-odd reflections and odd-even-odd reflections as a function of structureparameters are presented.(i) h = even, k = odd, l = odd:Iortho(hkl ) = |(−1)l+12 4 fNd sin (2πhxNd) cos (2πkyNd) e− 12 Q2U (Nd)+ (−1)k+ l+12 4 fO sin (2πhxO1) cos (2πkyO1) e− 12 Q2U (O1)− (−1)h+k+12 8 fO sin (2πhxO2) sin (2πkyO2) sin (2π lzO2) e− 12 Q2U (O2)|2, (B1)where Xα (X : x, y, or z, α : Nd, O1, or O2) denote the displacement of α from their Pm3̄m positions in the X directions, and Qis the scattering vector.174113-5TOMOKI DEGUCHI et al. PHYSICAL REVIEW B 113, 174113 (2026)(ii) h = odd, k = even, l = odd:Iortho(hkl ) = |(−1)l+12 4 fNd sin (2πhxNd) cos (2πkyNd) e− 12 Q2U (Nd)+ (−1)k+ l+12 4 fO sin (2πhxO1) cos (2πkyO1) e− 12 Q2U (O1)− (−1)h+k+12 8 fO cos (2πhxO2) cos (2πkyO2) sin (2π lzO2) e− 12 Q2U (O2)|2. (B2)Based on the values of x(Nd) and y(Nd) in Table I, |xNd| � 12 |[0.5 − x(Nd) sin 45◦] + [0.5 − y(Nd) cos 45◦]| = 0.0012 forPR sample, thus the fNd term can be neglected. In order to reduce the intensities of all these reflections, either (i) xO1 and zO2are small or (ii) U (O) is large. If we assume that the average oxygen sites in H-NNO are the same as those in PR-NNO, U (O)has to be larger than 0.4 Å2, which is ten times larger than PR-NNO and 100 times larger than bulk NNO. Such a large U valueis physically unreasonable in well-ordered crystal lattice. Therefore, the observed reduction in ( 121212 ) reflection intensity showsthe suppression of alternating octahedral tilting.[1] H. Shimotani, H. Asanuma, A. 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