Striped Interstitial Oxygen Order in Oxides

• Striped interstitial oxygen order is the self-organization of excess oxygen into quasi-1D patterns, creating nanoscale domains with distinct oxygen occupancy.
• It is characterized by specific crystallographic modulations and reciprocal-space satellite signatures that reveal variations in lattice symmetry and electronic structure.
• The ordered oxygen stripes influence superconductivity and magnetism differently across oxides, highlighting the role of host lattice properties in determining material behavior.

Searching arXiv for the cited papers on striped/interstitial oxygen order in cuprates and nickelates. Striped interstitial oxygen order denotes the self-organization of excess oxygen into quasi-one-dimensional motifs—stripes, wires, or nanoscale puddles—with well-defined reciprocal-space satellites and material-specific consequences for lattice symmetry, carrier density, magnetism, and superconductivity. In the literature considered here, the phenomenon appears in several distinct forms: nanoscale Ortho-II puddles in YBa$_2$Cu$_3$O$_{6.33}$, stage-1 interstitial-O phases in La$_2$PrNi$_2$O$_{7+\delta}$, self-organized O$_i$ wires in HgBa$_2$CuO$_{4+\delta}$, and ordered interstitial stripes in La$_2$NiO$_3$0 (Campi et al., 2012, Dong et al., 5 Aug 2025, Jarlborg et al., 2017, Jarlborg et al., 2015). Across these systems, the same structural label conceals markedly different microscopic realizations: some stripes are associated with half-filled chain order, some with spacer-layer interstitials, some with neutral ozone-like complexes, and their coupling to superconductivity is not universal (Bucher, 2020).

1. Structural motifs and crystallographic realizations

The crystallographic content of striped oxygen order depends strongly on the host lattice. In YBa$_3$1Cu$_3$2O$_3$3, the relevant motif is the Ortho-II superstructure, observed as satellite peaks at $_3$4 in reciprocal-lattice units. This corresponds to a two-unit-cell repeat along the crystallographic $_3$5 axis, with modulation wavelength $_3$6 Å, and in the basal Cu(1) layer the O interstitials populate every second Cu(1)-chain, leaving the chains in between empty (Campi et al., 2012).

In high-pressure-oxygen-annealed La$_3$7PrNi$_3$8O$_3$9, two stage-1 interstitial-O ordered phases appear. The period-$_{6.33}$0 phase has stripe spacing $_{6.33}$1 Å and wavevector $_{6.33}$2; the period-$_{6.33}$3 phase has stripe spacing $_{6.33}$4 Å and wavevector $_{6.33}$5. Each interstitial oxygen sits at fractional coordinates $_{6.33}$6 or $_{6.33}$7 in the RP unit cell, directly above planar O, and the stripes run parallel to the $_{6.33}$8-axis with no long-range ordering along $_{6.33}$9 (Dong et al., 5 Aug 2025).

In HgBa$_2$0CuO$_2$1, Jarlborg and Bianconi modeled O$_2$2 ordering in the Hg spacer plane using a $_2$3 in-plane supercell. Two interstitial oxygens occupy former empty-sphere positions at $_2$4 and $_2$5, generating one-dimensional wires running along $_2$6, separated by $_2$7 along $_2$8, for $_2$9 (Jarlborg et al., 2017).

In La$_2$0NiO$_2$1, the ordered interstitials form stripes along $_2$2. For $_2$3, the stripe modulation vector is $_2$4; for $_2$5, $_2$6. In the $_2$7 supercell, one interstitial stripe appears per repeat distance $_2$8 Å (Jarlborg et al., 2015).

System	Oxygen-order motif	Characteristic periodicity
YBa$_2$9Cu$_{7+\delta}$0O$_{7+\delta}$1	Ortho-II chain fragments / striped puddles	$_{7+\delta}$2, $_{7+\delta}$3
La$_{7+\delta}$4PrNi$_{7+\delta}$5O$_{7+\delta}$6	Stage-1 interstitial-O stripes	$_{7+\delta}$7 Å or $_{7+\delta}$8 Å
HgBa$_{7+\delta}$9CuO$_i$0	O$_i$1 wires in Hg plane	wires along $_i$2, separation $_i$3
La$_i$4NiO$_i$5	Ordered O$_i$6 stripes	$_i$7 or $_i$8

These realizations already indicate that “striped interstitial oxygen order” is not a single structure type. It is instead a family of oxygen-ordering phenomena sharing quasi-1D spatial organization but differing in site occupancy, modulation axis, and dimensionality of coherence.

2. Real-space organization, nanoscale heterogeneity, and domain statistics

Campi et al. showed that in YBa$_i$9Cu$_2$0O$_2$1 the Ortho-II order does not form a homogeneous superstructure. Rather, it appears as nanoscale striped puddles with local oxygen concentration $_2$2, embedded in an oxygen-depleted matrix with $_2$3 (Campi et al., 2012). The domain size was extracted from the full-width at half-maximum of the Ortho-II satellite through the Scherrer-type relation $_2$4, giving puddle diameters in the range $_2$5–$_2$6 nm, equivalently $_2$7–$_2$8 nm in some scans. Along the $_2$9 direction the mean size is about $_{4+\delta}$0 nm with $_{4+\delta}$1 nm, while along $_{4+\delta}$2 the distribution is broader and more skewed. The skewness parameters are $_{4+\delta}$3 and $_{4+\delta}$4, indicating long high-size tails in $_{4+\delta}$5.

The corresponding $_{4+\delta}$6XRD maps, acquired over a $_{4+\delta}$7 area with $_{4+\delta}$8 step, reveal a granular network of Ortho-II patches immersed in an O-poor background (Campi et al., 2012). This establishes a mesoscale hierarchy: atomic oxygen ordering produces nanometer-scale ordered regions, and those regions themselves form a heterogeneous micrometer-scale network.

A different form of heterogeneity is present in La$_{4+\delta}$9PrNi$_2$0O$_2$1, where period-$_2$2 and period-$_2$3 domains coexist. The stripes run parallel to the $_2$4-axis, but there is no long-range ordering along $_2$5, so the ordered state is intrinsically quasi-1D rather than a fully coherent 2D superlattice (Dong et al., 5 Aug 2025). In HgBa$_2$6CuO$_2$7, the calculations likewise imply strong spatial segregation: the new 1D electronic states are confined near the oxygen interstitial wires, with only a small spread onto nearby sites, while beyond the second Hg-O$_2$8 layer the electronic character reverts to that of the undoped bulk (Jarlborg et al., 2017).

This body of work suggests that striped oxygen order is best understood as a form of nanoscale or mesoscale self-organization rather than simple long-range compositional modulation. Ordered oxygen-rich regions and oxygen-poor regions are often co-present, and the electronic properties can be sharply different in the two environments.

3. Reciprocal-space signatures and experimental characterization

The experimental fingerprint of striped oxygen order is the appearance of satellite reflections or transformed-image satellites at wavevectors set by the oxygen modulation. In YBa$_2$9Cu$_3$00O$_3$01, scanning micro X-ray diffraction in reflection mode used a $_3$02 keV undulator beam at ESRF ID13, a Si(111) monochromator, tapered-capillary focus to $_3$03, a CCD area detector, $_3$04 raster steps, and a probing depth of about $_3$05. At each pixel the Ortho-II satellite was fit to extract integrated intensity, peak position with constant $_3$06, and FWHM along $_3$07 and $_3$08 (Campi et al., 2012).

The thermal evolution of the same superstructure was followed in transmission-mode XRD with a $_3$09 keV beam, $_3$10 spot, sample thickness $_3$11, at the Elettra XRD1 beamline using a Mar-CCD detector at $_3$12 mm and a motorized K-diffractometer. The Ortho-II satellites vanish at $_3$13 K. Upon heating, peak intensity collapses rapidly while the FWHM broadens, and both quantities exhibit hysteresis on cooling at $_3$14 K/min (Campi et al., 2012).

In La$_3$15PrNi$_3$16O$_3$17, multislice electron ptychography acquired along $_3$18 resolves individual O columns. High-pressure-oxygen-annealed samples show dark-contrast extra columns at interstitial sites. Fourier transforms of the ptychographic images display satellite spots at $_3$19, aligned in the high-pressure-oxygen-annealed state and shifted relative to the misaligned satellites of the as-grown 327 phase, providing direct evidence for the new modulation wavevectors $_3$20 and $_3$21 (Dong et al., 5 Aug 2025).

Electron energy-loss spectroscopy supplies the complementary electronic signature. In the as-grown nickelate, the oxygen K-edge prepeak occurs at $_3$22 eV with normalized intensity $_3$23. After high-pressure oxygen annealing, the prepeak is enhanced to $_3$24 and redshifted by about $_3$25 eV, $_3$26. Because the O K-edge transition obeys $_3$27 for O $_3$28 O $_3$29, these changes signal increased O $_3$30-Ni $_3$31 ligand-hole density (Dong et al., 5 Aug 2025).

Taken together, $_3$32XRD, transmission XRD, ptychography, EELS, and supercell electronic-structure calculations provide a consistent methodology for connecting oxygen occupancy, modulation wavevector, local domain structure, and electronic response.

4. Electronic structure, hole count, and magnetic response

In La$_3$33PrNi$_3$34O$_3$35, each interstitial oxygen contributes nominally two holes. Quantitative phase-contrast analysis gives $_3$36 in the period-$_3$37 domains and $_3$38 in the period-$_3$39 domains, so that $_3$40 holes/Ni, yielding $_3$41 and $_3$42. This shifts the Fermi level deeper into the $_3$43-$_3$44 hybridized band and empties the flat bonding $_3$45 band; in the simplified density-of-states expression $_3$46, the spectral weight at $_3$47 arising from the $_3$48 band is strongly reduced in the high-pressure-oxygen-annealed state relative to the as-grown state (Dong et al., 5 Aug 2025).

In HgBa$_3$49CuO$_3$50, the O$_3$51 wires produce a distinct electronic reconstruction. Relative to $_3$52, the chemical potential shifts downward by about $_3$53 eV at $_3$54, shrinking the original large quasi-2D Cu-O Fermi surface and bringing a second band of predominantly O$_3$55-Hg character just below $_3$56. A minimal model is

$_3$57

with $_3$58 and $_3$59 eV. As $_3$60 crosses $_3$61, a new small quasi-1D Fermi-surface pocket appears, corresponding to a Lifshitz transition. The total density of states at $_3$62 rises from $_3$63 eV$_3$64/cell for $_3$65 to $_3$66 eV$_3$67/cell in the striped $_3$68 case, with an O$_3$69 $_3$70-DOS of $_3$71 eV$_3$72 per atom near the stripe (Jarlborg et al., 2017).

In La$_3$73NiO$_3$74, ordered O$_3$75 stripes generate a contrasting redistribution of local density of states and magnetism. For La$_3$76Ni$_3$77O$_3$78, the two Ni nearest the O$_3$79 have $_3$80–$_3$81, whereas those far away have $_3$82–$_3$83. The magnetic moments show that ferromagnetism is suppressed at the stripes and enhanced in the Ni planes between stripes: nearest Ni have $_3$84, next-nearest Ni show $_3$85 to $_3$86, and distant Ni reach $_3$87–$_3$88 (Jarlborg et al., 2015).

A separate line of argument, developed for oxygen-enriched cuprates, treats the stripe-forming objects as neutral ozone-like complexes rather than charged lattice-site defects. In that model, the rows of O$_3$89 complexes have nearly constant incommensurability $_3$90 r.l.u., corresponding to $_3$91, and because the O$_3$92 molecule-ion is spin-singlet with $_3$93, the charge modulation carries no accompanying magnetization stripes, $_3$94 (Bucher, 2020). This is distinct from the Sr-doped 214 case, where $_3$95.

The general lesson is that oxygen stripes may either create new quasi-1D metallic states, redistribute spectral weight among existing bands, or quench local magnetic moments, depending on the electronic structure of the host lattice and the crystallographic site occupied by oxygen.

5. Relation to superconductivity: enhancement, suppression, and granularity

The coupling between striped oxygen order and superconductivity is material dependent rather than universal. In YBa$_3$96Cu$_3$97O$_3$98, superconductivity with $_3$99 K occurs in a network of nanoscale oxygen-ordered patches interspersed with oxygen-depleted regions. Inside the Ortho-II puddles the local oxygen stoichiometry reaches $_{6.33}$00, while the matrix remains strongly oxygen depleted. The granular topology sets the scale for Josephson coupling between puddles, limits coherence-length overlap, and helps explain why $_{6.33}$01 is only $_{6.33}$02 K despite locally optimal chain loading (Campi et al., 2012).

In La$_{6.33}$03PrNi$_{6.33}$04O$_{6.33}$05, the effect is the opposite. High-pressure oxygen annealing induces striped interstitial oxygen order, introduces quasi-1D lattice potentials and excess hole carriers into $_{6.33}$06-$_{6.33}$07 hybridized orbitals, and ultimately suppresses superconductivity. The paper emphasizes that this behavior starkly contrasts with cuprate superconductors, where similar interstitial oxygen ordering enhances superconductivity instead (Dong et al., 5 Aug 2025). A plausible implication is that the sign and strength of the coupling between oxygen order and pairing depend on which bands are being doped and on whether the lattice modulation improves or degrades the relevant metal-oxygen overlap.

For oxygen-enriched cuprates more broadly, the stripe picture of (Bucher, 2020) links the absence of magnetization stripes to higher maximal transition temperatures. In that treatment, oxygen-enriched HgBa$_{6.33}$08CuO$_{6.33}$09 reaches $_{6.33}$10 K, whereas La$_{6.33}$11Sr$_{6.33}$12CuO$_{6.33}$13 peaks at about $_{6.33}$14 K and La$_{6.33}$15Nd$_{6.33}$16Sr$_{6.33}$17CuO$_{6.33}$18 at about $_{6.33}$19 K. The same work interprets the cusp-like fall of stripe-peak intensity below $_{6.33}$20 in oxygen-enriched “123” cuprates as a weakening of the axial binding of O$_{6.33}$21 trains by fluctuating spin-singlet Cooper pairs (Bucher, 2020).

These results caution against treating oxygen order as either uniformly beneficial or uniformly detrimental. In cuprates, oxygen-rich stripe networks can coexist with or assist superconductivity; in the bilayer nickelate considered here, striped interstitial oxygen order competes with it.

6. Thermal evolution, symmetry breaking, and comparative interpretation

The most explicit thermal phase evolution in this group of studies is the Ortho-II order-disorder transition in YBa$_{6.33}$22Cu$_{6.33}$23O$_{6.33}$24. At room temperature the average sizes in the two in-plane orientations coincide, but above the order-disorder transition at $_{6.33}$25 K the equivalence of horizontal and vertical chain puddles is spontaneously broken: in the $_{6.33}$26–$_{6.33}$27 K window, puddles aligned along one axis grow slightly larger than their orthogonal counterparts. Weak, short-lived Ortho-II-like correlations persist above $_{6.33}$28 K up to about $_{6.33}$29 K, and the emergent anisotropy is interpreted as spontaneous symmetry breaking in the critical fluctuation zone (Campi et al., 2012).

In La$_{6.33}$30PrNi$_{6.33}$31O$_{6.33}$32, the ordered interstitials create a quasi-1D lattice potential along $_{6.33}$33,

$_{6.33}$34

with $_{6.33}$35 in period-$_{6.33}$36 domains and $_{6.33}$37 more prominent in period-$_{6.33}$38 domains (Dong et al., 5 Aug 2025). The same study states that the stripes lock in an orthorhombic octahedral tilt that reduces Ni-O-Ni overlap. This provides a concrete structural mechanism for why the same formal operation—adding interstitial oxygen and allowing it to self-organize—can stabilize superconductivity in one oxide family and suppress it in another.

A recurrent misconception is that all oxygen stripes should have similar magnetic fingerprints. The comparative record does not support that view. In the ozone-complex picture for oxygen-enriched cuprates, the stripe-forming units are neutral and spin-singlet, so $_{6.33}$39 even when charge-order satellites are present (Bucher, 2020). In HgBa$_{6.33}$40CuO$_{6.33}$41, spin-polarized calculations similarly place the magnetic response in the oxygen-poor domains free of O$_{6.33}$42 wires and find it to be essentially insensitive to the density of O$_{6.33}$43 wires (Jarlborg et al., 2017). In La$_{6.33}$44NiO$_{6.33}$45, by contrast, the oxygen-rich stripes locally quench ferromagnetism while more distant Ni sites show enhanced ferromagnetic moments (Jarlborg et al., 2015).

The comparative significance of striped interstitial oxygen order therefore lies in its non-universality. It is a structurally recurrent motif across layered oxides, but its electronic meaning is host-specific: a nanoscale percolative chain network in underdoped YBa$_{6.33}$46Cu$_{6.33}$47O$_{6.33}$48, a competing interstitial-stripe phase in La$_{6.33}$49PrNi$_{6.33}$50O$_{6.33}$51, a Lifshitz-tuned wire state in HgBa$_{6.33}$52CuO$_{6.33}$53, and a magnetism-suppressing stripe order in La$_{6.33}$54NiO$_{6.33}$55. This suggests that the key invariant is the self-organization of oxygen defects into quasi-1D textures, whereas the resulting superconducting and magnetic phenomenology is controlled by the underlying band structure, lattice topology, and local oxygen site chemistry.