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Mitsuharu Yashima, Nina Seto, Yujiro Oshita, Masataka Kakoi, [Hiroya Sakurai](https://orcid.org/0000-0003-1964-6023), [Yoshihiko Takano](https://orcid.org/0000-0002-1541-6928), Hidekazu Mukuda
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[Microscopic Evidence for Spin–Spinless Stripe Order with Reduced Ni Moments within ab Plane for Bilayer Nickelate La3Ni2O7 Probed by 139La-NQR](https://mdr.nims.go.jp/datasets/d7cacb92-edea-4fda-b72b-1e8638df10ef)
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arXiv:2503.09288v2 [cond-mat.str-el] 14 Mar 2025Microscopic evidence for spin-spinless stripe order with reduced Ni moments withinab plane for bilayer nickelate La3Ni2O7 probed by 139La-NQRMitsuharu Yashima1, Nina Seto1, Yujiro Oshita1, Masataka Kakoi1,2,Hiroya Sakurai3, Yoshihiko Takano3, and Hidekazu Mukuda11Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan2Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan and3National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0047, Japan(Dated: March 17, 2025)The intrinsic electronic properties of La3Ni2O7 have been selectively investigated by nuclearquadrupole resonance (NQR) at the La(2) site outside the NiO2 bilayers. The La(2)a site of theideal La3Ni2O7 is clearly distinguished from the La(2)b site close to the local defects. Below 150K,almost half of the intrinsic La(2)a sites are dominated by a finite internal field within the ab plane,while the other half are dominated by zero internal field. The result is fully consistent with thesingle spin-spinless stripe order of (· · · ↑ ◦ ↓ ◦ ↑ ◦ · · · ), where the reduced Ni magnetic momentsare parallel to the ab-plane. Even for the La(2)b site, the result is also explained within the samemodel by considering the inhomogeneous internal magnetic fields enhanced around the nearby de-fects such as oxygen vacancies. These findings provide unambiguous microscopic evidence for thesingle spin-spinless stripe order below 150 K at ambient pressure.1. IntroductionRemarkably high-Tc superconductivity (SC) with amaximum Tc of about 80 K was reported for bilayernickelate La3Ni2O7+δ (La327) under high pressure in2023.1–6 Since the formal valence of Ni is equivalent toNi2.5+ (d7.5), the 3dx2−y2/3z2−r2 orbitals are partially oc-cupied by 1.5 electrons. Thus, multiple degrees of free-dom of spin/charge/orbital states in d electrons are ex-pected to play some essential roles for the emergence ofSC phase under high pressure. In previous studies onLa327(δ∼ 0) at ambient pressure, the anomalies in elec-tronic states below 100 ∼ 200 K has been reported, sug-gesting the existence of spin density wave (SDW) and/orcharge density wave (CDW).2–4,7–19 As possible candi-dates, the single spin-charge (spin-spinless) stripe orderand the double spin stripe order have been proposed fromthe spectroscopies such as RIXS,11 µSR,15,16 NMR,19and RXS,17,18 although the static magnetic order has notyet been reported by neutron scattering experiment.20 Adual nature of electrons with spin and charge degreesof freedom may give rise to the complicated states as-sociated with possible defects such as oxygen vacancies(Ovacs) and stacking faults. It is highly desirable to deter-mine the intrinsic magnetic and electronic properties ofLa327 by carefully distinguishing the extrinsic effects dueto the defects. In the La327 crystal there are two crystal-lographically inequivalent La sites, one being La(1) be-tween the NiO2 planes and the other being La(2) outsidethe NiO2 bilayers. Nuclear quadrupole resonance (NQR)provides a unique opportunity to selectively probe the lo-cal electronic states at La(1) and La(2) sites, since eachNQR frequency (νQ) was deduced to be ∼ 5.6 (2.2) MHzfor the La(2) ( La(1)) site.5,13,19,21 In this Letter, we re-port the 139La(2)-NQR study on La327(δ ∼ 0), whichprovides unambiguous microscopic evidence for the singlespin-spinless stripe order for the ideal crystal site belowT ∗ ∼ 150K.2. ExperimentalPolycrystalline La327 (δ ∼ 0) was prepared by thesolid state reaction method described elsewhere.22 X-ray diffraction ensures a single phase of the orthorhom-bic structure of La327 (δ ∼ 0) with lattice parametersa = 5.3920Å, b = 5.4510Å, and c = 20.533Å.22 Theoxygen deficiency δ is determined by thermogravimet-ric analysis.22 The 139La-NQR study was performed us-ing a coarse powder of La327 (δ ∼ 0). For compari-son, it was also carried out on the oxygen-deficient poly-crystals La327 (δ∼−0.03)23 and La4Ni3O9.89 (La4310)24synthesized by the different methods. The energy lev-els of the 139La nuclear spins (I = 7/2) are split intofour levels (m = ±1/2,±3/2,±5/2,±7/2) by the nu-clear quadrupole interaction, and thus three resonancepeaks are observed for each La site in the NQR spec-trum. Here, the NQR frequency for the La(i) is definedby ν(i)Q = 3eQV(i)zz /[2I(2I − 1)h)], where V(i)zz is a princi-pal value of the electric field gradient (EFG) tensor at theLa(i) site, and Q is the electric quadrupole moment of139La. The asymmetry parameter of the EFG η(i) is de-fined as |V(i)xx − V(i)yy |/V(i)zz . The 139La(2)-NQR spectrumwas obtained at zero external field, focusing on the reso-nances at 2νQ (±5/2 ↔ ±3/2) and 3νQ (±7/2 ↔ ±5/2).The nuclear spin relaxation rate (1/T1) was measured at3νQ by the saturation recovery method25.3. ResultsIn a perfect crystal of La327 without any defects, weexpect only one resonance peak from a single La(2) sitein the NQR (3νQ) spectrum above T ∗ ∼ 150K in theparamagnetic state. However, as shown in Fig. 1(a),even in La327 (δ ∼ 0), two distinct peaks are observed,labeled La(2)a and La(2)b. The result is compared withhttp://arxiv.org/abs/2503.09288v2215.0 15.5 16.0 16.5 17.0 17.5 18.0139 La-NQR Intensity(a) La3Ni2O7+d (d ~ 0) at T = 160K La(2)aLa(2)bLa(2)4310a(b) La3Ni2O7+d (d ~ -0.03) at T = 160KFrequency (MHz)La4Ni3O10+d (d ~ -0.11) at T = 170KLa(2)4310a(c)La(2)b La(2)aFIG. 1. (Color online) (a) NQR spectra at 3νQ of La(2) aboveT ∗ in (a) La327 (δ∼ 0), compared to the results in (b) La327 (δ∼−0.03) and (c) La4310. In La327 (δ ∼ 0), two peaks, La(2)a andLa(2)b, are derived from the site of the ideal La327 and the onenear Ovac at the inner apical site, respectively. The peak at ∼15.5MHz is the intrinsic La(2) site of La4310. The La327 (δ∼0) samplein this study contains almost no stacking faults of La4310.the typical oxygen-deficient sample La327 (δ∼−0.03) inFig. 1(b) and La4310 in Fig. 1(c). The peak of La(2)ahas the largest intensity with the narrowest linewidth inboth La327 samples, and thus La(2)a is assigned to theintrinsic La(2) site in the ideal La327 crystal withoutnearby defects. As for La4310, the largest peak witha narrow linewidth at ∼ 15.5 MHz is assigned to theLa(2)4310a site of the ideal La4310 crystal without nearbydefects. We emphasize that the La327 (δ ∼ 0) samplecontains almost no stacking faults of La4310.Next we consider the origin of the La(2)b site inLa327 (δ ∼ 0). From the analysis of the 2νQ- and 3νQ-spectra, we evaluate νbQ = 5.422 MHz and ηb = 0.155for La(2)b at T = 160 K, which differ from the valuesνaQ = 5.952 MHz and ηa = 0 for La(2)a. As shown inFig. 2(a), the T dependence of the 3νQ-peak frequencyat La(2)b is quite similar to that at La(2)a above T ∗.This indicates that they both belong to the same crys-talline unit, which has almost the same T dependenceof the local EFG derived from the thermal shrinkage ofthe lattice. Furthermore, as shown in Fig. 2(b), the Tdependence of (T1T )−1 at La(2)b is exactly the same asthat at La(2)a, although these absolute values are about10 times different. In general, (T1T )−1a,b is proportionalto |Aa,bhf |2χ′′(q, ω), where Aa,bhf is a hyperfine couplingconstant at each La(2) site, and χ′′(q, ω) is a dynam-ical spin susceptibility. The identical T dependences of(T1T )−1a,b are attributed to the χ′′(q, ω) coming from NiO2bilayers in common. Thus, the difference in the absolutevalues of (T1T )−1a,b is mostly attributed to that in Aa,bhf ,which allows us to obtain the ratio |Abhf/Aahf | ∼ 3.06 from[(T1T )−1b /(T1T )−1a ]0.5. Considering these experimentalfacts, we assigned La(2)b to the La(2) site near an Ovac.FIG. 2. (Color online) T -dependences of (a) peak frequencies at3νQ and (b) (T1T )−1 for La(2)a and La(2)b of La327 (δ∼0). Theinset of (b) shows the identical T dependences of (T1T )−1 normal-ized by the values at T = 300 K for La(2)a and La(2)b.It has been reported that most of Ovacs exist at an in-ner apical site between NiO2 planes.26 The inner apicalOvac probably induces the anisotropy and inhomogene-ity of EFG at the La(2)b site, which has the finite ηb(= 0.155) and the broader linewidth than that of La(2)afor each sample. In addition, the presence of Ovac givesa local distortion to its surrounding space and induces achange in the hybridization between Ni and La(2), proba-bly leading to the modulation of Ahf at La(2) transferredfrom nearby Ni sites.Next we focus on the spin/charge ordered states belowT ∗ at La(2)a for La327 (δ ∼ 0). Figure 3(a) shows theT variations of the 2νQ- and 3νQ-spectra across T ∗. Asfor La(2)a, the 2νQ-spectrum around 11.9 MHz is largelysplit into three peaks below T ∗, where two broad peaksshift to the lower frequencies, while the other one witha narrow linewidth remains around the frequency cor-responding to zero internal field. In contrast, the 3νQ-spectrum at ∼17.8 MHz shows a slight splitting into twonarrow peaks. The 1/T1 values measured at all thesepeaks are almost the same, ruling out the possibility ofphase separation. Furthermore, it cannot be attributedto the charge anomaly primarily: considering the relationνQ ∝ Vzz , the deformation of the 3νQ-spectrum shouldbe ∼1.5 times larger than that of the 2νQ-spectrum if thecharge anomaly such as CDW is a primary cause. Thisis inconsistent with our result. Therefore, to reproducethe spectra of 2νQ and 3νQ simultaneously, the peak-shiftwas simulated as a function of the internal magnetic field(Hint) and the angle θ between Hint and Vzz . The redcurves in Fig. 3(b) show the calculated peak-frequencies3of 2νQ and 3νQ against Hint, assuming the appropriateangle θ = 88.3◦. Here, the dark (light) tone on the col-ored curve represents the large (small) intensity expectedin the spectrum. If θ were ∼ 0 or much smaller than90◦, the 3νQ spectrum would be largely split into twopeaks, one of which should be observed at a higher fre-quency side than the frequency expected for zero Hint.However, in fact, no such higher frequency peak is de-tected, indicating that θ is close to 90◦. The simulationsare compared with the experiments for 2νQ and 3νQ inFigs. 3(c) and 3(d), respectively. As shown by the pinkdashed curves, a small splitting and small shift to lowerfrequency observed for 3νQ-peaks and a large splittingand large shift for 2νQ-peaks are simultaneously repro-duced by Hint with the largest weight (≡ Hpeakint ) ∼ 0.18T and θ ∼ 88.3◦. Here, a skew normal distribution ofHint shown in Fig. 3(e) was used, which is explained indetail in the Supplement(A). We have to consider notonly the presence of above-mentioned La(2)a sites withHint 6= 0 (h±a ) but also the presence of La(2)a ones withHint = 0 (h0a), where Hint is almost canceled out, asshown by the green dashed curves in Figs. 3(c) and 3(d).The volume fraction of La(2)a with Hint = 0 [V (h0a)] isroughly comparable to that with Hint 6= 0 [V (h±a )]. Thetotal calculated spectra shown by the red solid curves inFigs. 3(c) and 3(d) are superimposed by two comparablecomponents for finite Hint (pink) and zero Hint (green)with V (h0a)/V (h±a ) ∼ 0.5. This result is consistently ex-plained by the single spin-spinless stripe order model, asdescribed later.As for La(2)b, the 3νQ spectrum at ∼16.2 MHz in Fig.3(a) exhibits a large broadening and shift below T ∗. Theblue curves in Fig. 3(b) are the peak-shift simulation at2νQ and 3νQ for La(2)b as a function of Hint under thesame θ (= 88.3◦) as that for La(2)a. To explain the verybroad spectrum from 15 to 16.5 MHz (see Fig. 3(f)), theHint must be inhomogeneously enhanced at La(2)b. Infact, the spectrum in Fig. 3(f) is well reproduced by thesimulation (blue), assuming Hpeakint ∼ 0.44 T and its skewnormal distribution shown in Fig. 3(e). It is noteworthythat the La(2)b site with Hint = 0 was not observed at∼16.2 MHz, as seen in Fig. 3(f), indicating that there arefew or no La(2)b sites with Hint = 0. In this context, itis reasonable to explain that the 2νQ-spectrum of La(2)bat ∼10.6 MHz in Fig. 3(a) is undetectably small, whichis due to a huge broadening and wide splitting by thebroad distribution of Hint = 0.2 ∼ 0.5 T, as expectedby the simulation of Fig. 3(b). These features are quitedifferent from those for La(2)a. Since Hint is generallygiven by a product of Aa,bhf and the Ni moment (MNi),the difference in Hint for La(2)a,b sites is attributed tothe variation in Ahf and/or MNi. The experimentallyobtained ratio Hpeakint (b)/Hpeakint (a) ∼ 2.44 is quite similarto |Abhf/Aahf | ∼ 3.06 obtained from the ratio of (T1T )−1.It is noteworthy that the magnitude of MNi on averagedoes not change significantly around La(2)a and La(2)b,although the local defect is present near La(2)b.FIG. 3. (Color online) (a) La(2)-NQR spectra at 2νQ (10 ∼ 12MHz) and 3νQ (15 ∼ 18 MHz) for La327 (δ ∼ 0) across T ∗. (b)Simulation of peak frequencies as a function of Hint for La(2)a(red)and La(2)b(blue). (c) 2νQ- and (d) 3νQ-spectra for La(2)a areroughly reproduced by the simulation (red line) superimposing twocomparable components from the sites with finiteHint (pink dashedline) and zero Hint (green dashed line). The intensities of twocomponents are divided by two for clarity. (e) Distributions ofHint used for the simulations in (c), (d), and (f), showing Hpeakintand full width at 1/5 maximum for La(2)a (red) and La(2)b (blue).(f) The 3νQ-spectrum of La(2)b is reproduced only by the site withfinite Hint (blue), indicating no peak of La(2)b with Hint = 0.4. DiscussionsFigure 4(a) shows the illustration of the single spin-spinless stripe model, which is consistent with our NQRresults. The MNis are antiferromagnetically aligned inthe ab-plane as (· · · ↑ ◦ ↓ ◦ ↑ ◦ · · · ) with the propaga-tion vector QSDW = (0, 1/2), as shown by the red andblue arrows in Fig. 4(a) (see also Supplement(B) for thesimplest case without any Ovacs). This spin arrangement4FIG. 4. (Color online) (a) Illustration of the single spin-spinless stripe order of MNis (red/blue arrows) antiferromagnetically alignedwithin the NiO2 layers, consistent with this study. The La(2)-O plane is also projected onto this plane. (b) Spatial distribution of Hintat La(2)a of the ideal La327, derived from the spin configuration of (a). (c) La(2)b sites around Ovacs are dominated by inhomogeneouslyenhanced Hint (see arrows of different sizes). (d) Structure of La327 with Ni moments (red/blue arrows) corresponding to the area enclosedby the orange rectangle in (a). The light green La(1) and La(2) sites indicate the nearest neighbor sites of Ovac. (e) Spatial distributionof La(2)a (dark green) and La(2)b (light green) around Ovacs (gray) located on the Ni-spin channel above T ∗, corresponding to (c) belowT ∗. The Hint at the La(2) is either parallel or antiparallel to the direction of MNi in this model, which is determined by the propertiesof Ahf composed of transferred and/or dipolar fields. For the sake of simplicity, we temporarily draw the case dominated by the dipolarfields.induces the comparable number of two La(2)a sites withHint = ±0.18 and 0 T in the ab plane, correspondingto the h±a and h0a sites on the straight Ni-spin and spin-less channels, respectively, along the a-axis in Fig. 4(b).We consider that the most possible direction of MNi isalong the a-axis: The direction of Vzz at La(2) is tiltedby about 6◦ from c- to b-axis in association with the tiltof the NiO6 octahedron, as shown in Fig. 4(d), and thusθ should naturally be close to ∼84◦ if assuming MNi ‖ b.However, the experimentally obtained θ (∼ 88.3◦) is veryclose to 90◦, suggesting that the direction of MNi avoidsthe tilting direction of the octahedra (b-axis). We alsoexclude the cases of MNi ‖ c and non-parallel to a-axiswithin the ab plane, because in such situations the h0a siteis eliminated.Next we discuss the origin of the inhomogeneously en-hanced Hint at the La(2)b site. As shown in Fig. 1, thespectral intensity for La(2)b is similar to that for La(2)ain the paramagnetic state above T ∗ for each La327 sam-ple used in this study. If there is an Ovac at an innerapical site, as shown in Fig. 4(e), the neighboring four(eight for upper and lower sites) La(2)a sites (dark green)are turned into La(2)b sites (light green). Thus, the num-ber of La(2)b would be close to that of La(2)a, assumingthat the density of Ovac at the inner apical oxygen site is∼ 1/8 and that Ovacs are separated from each other be-yond the distance of the second nearest neighbor. Sucha hypothetical La327 (δ= 1/8) crystal with inner apicalOvacs will induce the similar volume fraction for La(2)aand La(2)b, which is consistent with this study. Consid-ering this situation, as shown in Fig. 4(c), the nearestfour (eight) La(2)b sites around Ovacs are further dividedinto two magnetically different sites below T ∗, that is,the sites with strongly enhanced Hint (≡ h±±b ) and withmoderate Hint (≡ h±b ), which appear on the Ni-spin andspinless channels around Ovacs, respectively. Even at theLa(2)b site on the spinless channel, denoted as h±b , thehyperfine field from a Ni spin next to an Ovac is plausiblydifferent from that from a Ni spin without any Ovacs, re-sulting in the imperfect cancellation of Hint from the sur-5rounding Ni spins. It gives a reasonable explanation forthe experimental facts that the value of Hint at La(2)b isinhomogeneously enhanced, and no La(2)b site with Hint= 0, which are accounted for within the same model usedfor the La(2)a site.We address the feature of MNi for the intrinsic La(2)asite. The Hint was evaluated to be ∼ 0.18 T, which isone order smaller than ∼ 2 T at the La site of La2NiO4(La214) in the antiferromagnetic (AFM) order by largeM214Ni ∼ 1.7µB corresponding to a high spin state ofNi+2 (d8).27,28 Since Ahf is different from that of La214,it is difficult to estimate the exact MNi of La327 so far.However, at least the observation of the very small Hintin La327 suggests the significant reduction of MNi dueto itinerant d-electrons in metallic La327, in contrast tothe localized regime of insulating La214. According tothe previous µSR experiment,15 MNi ∼ 0.42µB is antici-pated if MNi is assumed to be within the ab plane. It isfurther supported by our experimental fact that MNi isalong the a-axis. Such a reduction of MNi suggests thatmost of spins in the d3z2−r2-orbital may be canceled byforming a spin-singlet like state, since the bonding-orbitalpart of the d3z2−r2-band derived from the NiO2 bilayerswould be almost filled in La327.29–31Therefore, it is likelythat the main amplitude of MNi originates from spins ofthe dx2−y2-band and the mixed band of d3z2−r2/x2−y2 . Ifassuming that most of MNis would be derived only fromspins in the nearly 1/4-filled dx2−y2-orbital, the maxi-mum of MNi is expected to be about 0.5µB, which isclose to the MNi discussed above.Finally, we note that the CDW order at the intrin-sic La(2)a site cannot be clearly detected from the cur-rent study in the measured T range from 100 to 300K.If the CDW order were present, it might be considerablyweaker than the SDW order in this T range. Thereforewe use the term ”spin-spinless” rather than ”spin-charge”to correctly express the current result in this paper. Ourconclusion is different from the double spin stripe anddouble charge stripe order proposed microscopically byLa(1)-NMR19 and La(2)-NQR32, respectively. In orderto deduce the magnetic structure in La327, two condi-tions must be satisfied, namely the existence of the h0asite and the direction of Hint parallel to the a-axis. Asshown in Fig. 4(d), the La(2) site is surrounded by fourfirst-nearest-neighbor Ni sites obliquely below La(2) andone second-nearest-neighbor Ni site above La(2). If thesecond-nearest-neighbor Ni site is not spinless, the can-cellation of Hint at the La(2) becomes extremely diffi-cult. Thus, the presence of the Ni-spinless channel isprobably indispensable to explain the appearance of theh0a site in the SDW order. Furthermore, a local sym-metric spin configuration of four first-nearest-neighbor Nisites around La(2) is required for the good cancellationof Hint. However, in the cases of the double spin stripeand double spin-charge stripe models, it is very difficultto obtain the innegligible amount of h0a sites due to thelow local symmetry of the spin configuration around theLa(2) site. As for the direction of Hint in these dou-ble stripe systems, it should be fairly tilted from theab-plane to the c-axis in many conditions, which is in-consistent with our NQR result. Regarding to the singlespin-spinless stripe structure, our NQR result is almostconsistent with the RIXS,11 µSR,15 and RXS17 studies.The large reduction of MNi in La327 deduced from thepresent NQR study is reasonably consistent with the un-detectably small moment suggested by the neutron scat-tering experiment20. In addition, our NQR result is ingood agreement with the spatial arrangement in whichinner apical Ovacs are located on the Ni-spin channel,not on the Ni-spinless channel (see the detail in Sup-plement(C)), indicating that the location of inner apicalOvacs may not be completely random. If inner apicalOvacs form such a pattern as the stripe, it is of interestin terms of how the pattern of Ovacs affects the SDWorder at low pressure and the superconductivity at highpressure.5. ConclusionsIn summary, the 139La(2)-NQR measurement in La327revealed the appearance of two intrinsic La(2)a sites withzero and finite Hints below T ∗ ∼ 150K, which is consis-tently explained by the single spin-spinless stripe ordermodel with the moderately reduced M327Ni ‖ a that isantiferromagnetically aligned by QSDW = (0, 1/2). Evenfor the La(2)b site close to inner apical Ovacs, these NQRresults are mostly explained within the same model byconsidering inhomogeneous Hint enhanced around Ovacs.These results provide further insight into understandingthe relationship with the high-Tc states at high pressure.AcknowledgmentsThis work was partially supported by the TakahashiIndustrial and Economic Research Foundation and JSPSKAKENHI Grant No. JP24K01333. One of the authors(M. K.) was supported by JST SPRING, Grant No. JP-MJSP2138 and by Kato Foundation for Promotion of Sci-ence, Grant No. KS-3614. Two of the authors (H. S. andY. T.) were supported by World Premier InternationalResearch Center Initiative (WPI), MEXT, Japan, GrantNo. JPMJSP2138.1 H. Sun, M. Huo, X. Hu, J. Li, Z. Liu, Y. Han, L. Tang,Z. Mao, P. Yang, B. Wang, J. Cheng, D.-X. Yao, G.-M.Zhang, and M. Wang, Nature 621, 493 (2023).62 J. Hou, P.-T. Yang, Z.-Y. Liu, J.-Y. Li, P.-F. Shan, L. Ma,G. Wang, N.-N. Wang, H.-Z. Guo, J.-P. Sun, Y. Uwatoko,M. 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This function with α = 0 isthe same as the Gaussian (normal distribution) function.As for La(2)a, the calculated 2νQ and 3νQ spectra inFigs. 3(c) and 3(d) are simultaneously reproduced withthe same parameters (ξ, σ, α) = (0.19T, 0.035T, −6),respectively. The distribution of Hint is shown by the redcurve in Fig. 3(e). The peak position of this asymmetricHint distribution (Hpeakint ) is ∼ 0.18T. As for the La(2)bsite, the calculated spectrum (blue solid line in Fig. 3(f))is reproduced by applying the parameters of the Hintdistribution (ξ, σ, α) = (0.49T, 0.22T, −6). This givesHpeakint (b) ∼ 0.44T. The distribution of Hint is shown bythe blue curve in Fig. 3(e). Both the amplitude andthe distribution width of Hint for La(2)b are much largerthan those for La(2)a.B. Single spin-spinless stripe order model : Thesimplest case for perfect crystal without any OvacsFIG. S1. (Color online) Single spin-spinless stripe order model forthe simplest case in the perfect crystal without any Ovacs. (a) Illus-tration of the single spin-spinless stripe configuration of MNis (redand blue arrows) antiferromagnetically aligned within the NiO2 lay-ers, consistent with this study. The La(2)-O plane is also projectedonto this plane. (b) Spatial distribution of Hint at the La(2)a siteof the ideal La327, derived from the spin configuration shown in(a). Almost half of the intrinsic La(2)a sites are dominated by afinite Hint within the ab plane, while the other half are dominatedby zero Hint. (c) Crystal structure of La327 including no Ovacswith MNis (red and blue arrows). As for the direction of Hint atthe La(2) site, for the sake of simplicity, we temporarily draw thecase where the dipolar fields are predominant.8FIG. S2. (Color online) (a) Illustration of the single spin-spinless stripe order of MNis (red/blue arrows) antiferromagnetically alignedwithin the NiO2 layers, consistent with this study. The La(2)-O plane is also projected onto this plane. (b) Spatial distribution of Hint atLa(2)a of the ideal La327, derived from the spin configuration of (a). (c) La(2)b sites around Ovacs are dominated by the enhanced Hint(see arrows of different sizes). (d) Structure of La327 with Ni moments (red/blue arrows) corresponding to the area enclosed by the orangerectangle in (a). The light green La(1) and La(2) sites indicate the nearest neighbor sites of Ovac. (e) Spatial distribution of La(2)a (darkgreen) and La(2)b (light green) around Ovacs (gray) on the Ni-spinless channel above T ∗, corresponding to (c) below T ∗. The Hint at theLa(2) is either parallel or antiparallel to the direction of MNi in this model, which is determined by the properties of the Ahf composedof transferred and/or dipolar fields. We temporarily draw the case dominated by the dipolar fields for simplicity.C. Influence of relative positional differencesbetween the inner apical Ovac site andNi-spin/spinless channelsHere we comment on the reason why we adopt the sce-nario that the inner apical Ovac site is located on theNi-spin channel in Fig. 4. In order to obtain such aconclusion, we also consider the another possibility thatinner apical Ovacs are located on the Ni-spinless chan-nels. It is possible that an Ovac can randomly come intoany inner apical oxygen sites. Figure S2(e) shows thecase where all inner apical Ovacs are on the Ni-spinlesschannels. In this case, Hint is canceled on the Ni-spinlesschannel even at the La(2)b site. This is not consistentwith the present NQR result, where there are few or noLa(2)b sites with Hint = 0. Therefore, most of inner api-cal Ovacs are likely located on the Ni-spin channel. Theseresults suggest that Ovacs may also form a stripe patternlike the Ni-spin/spinless channels. Ni spins are inducedon the channel with higher oxygen deficiency, correspond-ing to the Ni-spin channel. On the other hand, no Nispins are induced in the channel with almost no oxygendeficiency, corresponding to the Ni-spinless channel. Itis of interest in terms of how the possible spatial patternof Ovacs affects the SDW order at low pressure and thesuperconductivity at high pressure.