Local structure of Sr₂CuO_3.3, a 95 K cuprate superconductor without CuO₂ planes

Significance

CuO₂ planes are a universal component of cuprate superconductors. Sr₂CuO_3+δ that has a T_c of 95 K despite its overdoping has been reported to have vacancies in these planes. Extended X-ray absorption fine structure measurements not only provide definitive proof but furthermore show that in magnetically oriented samples not only are there also apical O vacancies but that the -Cu-O- chains normal to the orienting field are complete while the O sites of the chains parallel with this field are only half filled. These unique characteristics of a material with such a high transition temperature demonstrate that there are still substantial gaps in our knowledge of exotic superconductivity, including such fundamental aspects as the types of structures that support it.

Abstract

The local structure of the highly “overdoped” 95 K superconductor Sr₂CuO_3.3 determined by Cu K X-ray absorption fine structure (XAFS) at 62 K in magnetically oriented samples shows that 1) the magnetization is perpendicular to the c axis; 2) at these levels of precision the Cu sublattice is tetragonal in agreement with the crystal structure; the O sublattice has 3) continuous -Cu-O- chains that orient perpendicular to an applied magnetic field; 4) approximately half-filled -Cu-O- chains that orient parallel to this field; 5) a substantial number of apical O vacancies; 6) O ions at some apical positions with expanded Cu-O distances; and 7) interstitial positions that imply highly displaced Sr ions. These results contradict the universally accepted features of cuprates that require intact CuO₂ planes, magnetization along the c axis, and a termination of the superconductivity when the excess charge on the CuO₂ Cu ions exceeds 0.27. These radical differences in charge and structure demonstrate that this compound constitutes a separate class of Cu-O–based superconductors in which the superconductivity originates in a different, more complicated structural unit than CuO₂ planes while retaining exceptionally high transition temperatures.

Although 135 K has remained the highest transition temperature in cuprates since 6 y after their initial discovery (1, 2), given that an accurate theory remains lacking, still higher transition temperatures cannot be ruled out. Here we report X-ray absorption fine structure (XAFS) experiments on Sr₂CuO_3.3 (SCO) prepared by high-pressure oxygen (HPO) methods that show that this compound lacks the CuO₂ planes found in all other cuprates while retaining a T_c of 95 K. The HPO cuprates (3–5) give a second, T_c vs. Cu-charge phase diagram whose superconducting region differs radically from the “dome” (6) common to the “conventional” materials that are doped by reaction with O₂. Instead of the superconductivity terminating with the formation of a Fermi liquid when the excess charge on the Cu atoms in the CuO₂ planes reaches ∼0.27 per Cu, T_c plateaus or even continues to increase, opening a new region of superconductivity on the high Cu-charge side of the phase diagram. In addition, these HPO cuprates are tetragonal, their heat capacities demonstrate coexisting Fermi liquid and superconducting electrons (7, 8), and they do not adhere to the empirical correlation between T_c and the Cu-apical O (Oap) (9–11) or apical cation (12) distance. Ba₂CuO_3.2 (8, 13, 14), a structural analog of SCO, exhibits an oblate Cu geometry with its Cu-Oap distance of less than 1.9 Å, presumably inverting the ordering of the d_x²_-y² and d_z² states (8). SCO and related compounds were first prepared shortly after the initial discovery of cuprates (15). Jin and coworkers subsequently found multiple phases (16–18), but recent improvements in the synthesis now produce single-phase SCO with T_c = 95 K (SI Appendix, Fig. S1) (17, 18)

Between La₂CuO_4+δ and Sr₂CuO_3+δ (SCO) the structure changes radically. La₂CuO_4+δ exhibits the common cuprate geometry (19) with fully ordered CuO₂ planes with 3.78-Å Cu-Cu distances with O midway between, fully occupied Cu-Oap sites at 2.41 Å, and Cu-La at 3.24 Å. The structure of the other parent, Sr₂CuO₃ (20), is notable for its highly orthorhombic symmetry with -Cu-O- chains with a 3.91-Å Cu-Cu distance in the a direction and 3.48-Å Cu-Cu distances in the b direction that lacks bridging O. The disparate nature of the connections between the Cu sites along the crystallographic axes results in Sr₂CuO₃ being a “nearly ideal … [one-dimensional] … Heisenberg antiferromagnet” (21). The Oap sites are all occupied with the same 1.95 Cu-Oap distances as in the chains. This gives c-oriented SrCuO₂ planes with 3.22-Å Cu-Sr distances. Increasing the O stoichiometry by only ∼10% in HPO SCO results in its transformation to a tetragonal space group with a Cu-Cu distance of 3.8 Å that is typical of cuprates. However, its bulk stoichiometry with a fractional number of O atoms differs from the formula of its unit cell that is constrained to integers, and the absence of superlattice peaks demonstrates that these excess O atoms are distributed aperiodically (or dynamically). This disorder within the constraints of the tetragonal symmetry that presumably does not apply to the O sites causes ambiguities in the crystallographic determination of its structure that include the possibility of vacancies in the CuO₂ planes (22, 23).

XAFS is arguably the most incisive experimental method for probing these behaviors in mixed valence, transition metal, correlated materials. It complements the crystallographic analysis of SCO because 1) it does not depend on long-range order or translational symmetry and therefore reveals aperiodic local lattice distortions; 2) its element selectivity separates and isolates many of the atom pairs to give a better basis for detailed analysis than X-ray or neutron pair distribution function analysis; and 3) its intrinsic time and energy scale that correspond to collective dynamical phenomena in correlated materials make it sensitive to the dynamical and instantaneous aspects of the structure, S(q, ω) or S(q, t = 0) (24–28). The differences between the extended XAFS (EXAFS) (29, 30) and complementary diffraction and neutron scattering measurements (24, 31) were therefore key in originally identifying and characterizing the Cu-Oap double-well potential (32), its assignment to a tunneling polaron (25, 27, 33), and its coupling to the superconductivity in other cuprates (28, 34, 35). Tunneling polarons differ from the common small polarons that exhibit thermally activated hopping between neighboring sites in a crystal, exchanging the normal crystal structure adopted by the atoms at the second site with the distorted polaron structure and excess charge that had been at the first. A tunneling polaron is the oscillatory interchange between two distinct arrangements of a given set of atoms that contain the excess charge, with the two structures denoted by the charges and positions/local geometries of the constituent atoms. The tunneling polaron remains in the same location within a crystal, where it could be pinned because of stationary defects or special aspects of the atoms of its location. In addition, in contrast to the original, elementary, three-atom model of a Cu atom bracketed by two Oap, it may involve a large number of atoms and the two structures will be nondegenerate (36, 37).

A procedure that was key in these studies was the enhancement of the sensitivity of EXAFS to the different components of the structure (38) by orienting the samples in a magnetic field to align them along a unique crystallographic axis. The spectra therefore measure the projections of the neighbor atoms on the axis parallel to the orienting magnetic field and the plane perpendicular to it, rendering the problem one of cylindrical symmetry. The EXAFS will therefore help elucidate the characteristics of a crystallographically modulated structure (18), the widths of the distributions and whether they are continuous or consist of discrete, separated distances. The diffraction peaks of these samples were measured with the incident and diffracted X-rays in the plane normal to the axis along which the XAFS was measured (SI Appendix, Fig. S2). The (001) reflections of a YBa₂Cu₃O₇ and the two SCO samples were analyzed by the method of March and Dollase (39). The corresponding angular probability functions of the c crystallographic axis (Fig. 1) show that the E||H sample and E⊥H samples are oriented, although to a somewhat lesser degree than for YBa₂Cu₃O₇. The alignment of its c axis normal to YBa₂Cu₃O₇ E||H is evident. The induced magnetization in SCO is therefore orthogonal to the c axis, unlike all other cuprates where the c axis orients strongly along the field direction. SCO maintains at least some of the magnetic anisotropy from the CuO₂ chains in undoped Sr₂CuO₃ (40) despite its tetragonal space group. This confirms the prior suggestion that the crystal structure is incomplete, augmented by showing that the properties of SCO are coupled to these extracrystallographic factors. The unique direction parallel to the magnetization will be labeled “a,” the orthogonal direction in the Cu planes “b.”

Fig. 1.

March and Dollase probability factors (39) for sample orientation in magnetic field. The result for the YBa₂Cu₃O₇||H sample that was prepared in the same mold as the SCO||H sample is included for reference to show the 90° rotation of the (001) axis (c axis) of the two compounds.

The capabilities and limitations of EXAFS in elucidating structure and dynamics in correlated materials are described in SI Appendix. The original EXAFS spectrum, χ(k), is best presented as its Fourier transform, χ(R), because the modulus peaks that originate in the constituent waves of the original χ(k) correspond to the contributions of the neighbor atom shells arranged from short to long absorber–neighbor distances to give an approximate representation of the partial pair distribution. Inspection of the Fourier transforms of the Cu K EXAFS of the two orientations (Fig. 2) show the same Sr and Cu contributions at, respectively, R = 2.9 and 3.5 Å. The contribution of the Cu neighbors in both the a and bc-oriented spectra differs from all other cuprates where it occurs only in E||ab spectra, corroborating this unique orientation found in the diffraction. Curve-fitting analysis finds 3.79 Å Cu-Cu distances. An identical Cu-Cu distance for both orientations demonstrates that the tetragonal symmetry found crystallographically is intrinsic and not the result of small, orthorhombic domains averaging to tetragonal. The amplitudes of the Cu signals that are ∼40% of the amount displayed by other cuprates (29, 41) are also consistent with a division of the Cu contribution between the two orientations. The Cu-Sr pair is best fit with the principal and a smaller shell separated by an amount just above the resolution limit, 3.22/3.35-Å Cu-Sr distances for E||H and 3.24/3.38 Å for E⊥H. These are equal within the uncertainty for the two orientations. This result is indicative of an overall anharmonic distribution. The Cu-Cu and principal Cu-Sr distances are within 0.01–0.02 Å of the crystallographic values.

Fig. 2.

EXAFS [Fourier transform or χ(R) representation] of SCO (A) along the same direction as the magnetic field and (B) perpendicular to the magnetic field. The main figures show the data and fit in real space, the Upper Right Insets the data and fits in the original (before Fourier transformation) momentum (k)/energy domain, and the Lower Right Insets show the Fourier transform moduli of the data, fits, and differences in their upper halves and the contributions of the individual neighbor shells, inverted for clarity, in their lower halves. The vertical green lines trace the position of the spectral features for, from low to high, the O neighbor at 1.92 Å, the O neighbor at 2.6 Å, the Sr neighbors, and the Cu neighbors with a bridging O ion between them. The relative numbers of atoms are reflected by the peak amplitudes, reduced by 1/R².

If the O sublattice is tetragonal then all of the Cu-O distances in the E||H spectrum from the aa plane must be found in the E⊥H spectrum, with any additional ones belonging to the c component. Deviation of the O positions from the tetragonal symmetry of the Cu-Sr sublattice is evident in the comparison of the locations of the peaks of the two spectra (Fig. 2). Unlike the tetragonal arrangement of the Cu and Sr atoms, the O sublattice is therefore orthorhombic with distinct a and b axes but insufficiently ordered to give a clear signature in the diffraction pattern dominated by the Cu and Sr. The E||H spectrum measures the a components of the Cu pair distribution. The O region of the spectrum for E||H is dominated by a single peak (Fig. 2A) (29, 42). Complete curve fits, however, require three O neighbors at 1.92, 2.09, and 2.31 Å, with a fourth low-amplitude shell at 2.64 Å giving a small improvement in the fit (Fig. 2 A, Inset and SI Appendix, Fig. S3). The 1.92-Å Cu-O distance is close to half of the 3.79-Å Cu-Cu distance. The E⊥H spectrum displays three distinct peaks in the O neighbor region. The lower position of the first one demonstrates a shorter Cu-O distance than in the a direction, just as the other peaks at higher R signify longer ones. This complicated spectrum is fit by four O neighbors at 1.83, 2.00, 2.27, and 2.61 Å (Fig. 2 B, Inset). An additional small feature in both spectra at R ∼ 2.5 Å is fit by Sr and/or O at ∼2.8–2.9 Å. The 1.83- and 2.00-Å distances with their equivalent amplitudes could be the two parts of an off-center O in a b-oriented -Cu-O- chain and/or two Cu-Oap distances of a distorted square Cu site with O vacancies in the ab plane. The differences between 1.83, 1.92, 2.00, and 2.09 Å are significantly larger than the normal EXAFS error ±0.02 Å, confirming the separate a and b Cu-O distributions and division of the spectra into a and the combined bc component. Since the Cu-Cu wave in χ(k) in both spectra is defined by the amplitudes and phases of the Cu-O-Cu moiety with the bridging O, a corresponding fraction of the 1.83- and 2.00-Å Cu-O pairs in the bc-oriented spectrum must be the bridging O of the Cu-O-Cu pairs along the b axis. Remaining O neighbors may be Oap, including the O at the longer distances if Sr displacements allow expansion of the Cu–Oap bond.

Insofar as the most significant finding of this study is the location of the O ions and vacancies in the aa-oriented Cu planes a thorough analysis was performed that provides a graphic presentation of the relevant results. As explained previously, the 0.11-Å resolution derived from the upper limit of the spectra ensures that the individual Cu-O waves in χ(k) in the E||a spectrum are easily separable. Rather than rely solely on curve-fit results, the location of the O vacancies is addressed by directly comparing the isolated Cu-O-Cu and Cu-O EXAFS waves against appropriate standards, in this case the same waves from, respectively, the E||bc-oriented spectra and the E||a spectra from YBa₂Cu_2.75Mo_0.25O_7.54 that we have shown has fully ordered CuO₂ planes and CuO₃-type chains. This comparison not only gives the relative numbers of Cu-O-Cu pairs and bridging O in the E||H||a spectrum by direct comparison of their magnitudes but also tests the extent to which their originating structures are identical via the similarity of their phases and amplitude envelopes. The Cu-O-Cu waves in χ(k) from the two orientations (Fig. 3A) are almost identical, verifying this assignment and the presumption that uncorrelated thermal motion makes the contributions of any unbridged Cu-Cu pairs negligible. Deriving the relative numbers of Cu atoms requires correcting the spectral amplitudes by the polarization geometry factors of 3 for the E||H||a spectrum and 3/2 for the E⊥H||bc (43). The essentially identical amplitudes therefore demonstrate that the numbers of Cu-O-Cu neighbors and therefore bridging O in the a direction are only close to half that for b. The a-oriented, partial -Cu-O- chains and presumably the mixed Cu(II, III) valence resulting from the added charge from the excess O account for the conversion of the rectangular arrangement of the Cu and Sr atoms of Sr₂CuO₃ to their square geometry in SCO, even while the O atoms separate into different arrangements along the a and b directions so that their sublattice has orthorhombic symmetry (40). This same parameter is obtained independently by comparing the Cu-O wave from the E||H||a spectrum with the one from YSr₂Cu_2.75Mo_0.25O_7.54 (Fig. 3B) with its known structure (6). The amplitude ratio is 0.6–0.7. After the same factor of 2 polarization correction, the corrected amplitude of 0.35 times the average 3–1/3 O/Cu neighbors in YSr₂Cu_2.75Mo_0.25O_7.54 gives ∼1.1 O atoms in the a direction for SCO. The numbers of O and Cu neighbors therefore show that the b⊥H -Cu-O- chains are essentially intact from Sr₂CuO₃ and the a||H -Cu-O- chains are around half filled (Fig. 4A). This half filling corresponds to the Cu(II):(III) ratio.

Fig. 3.

EXAFS waves and amplitudes for direct comparison of relative atom numbers. (A) The Cu-Cu EXAFS from the two orientations of SCO. (B) The nearest-neighbor Cu-O waves and amplitudes from the a orientation of SCO and the ab orientation of YSr₂Cu_2.75Mo_0.25O_7.54 and the ratio of the amplitudes ×5. The Cu-O-Cu and Cu-O EXAFS from the spectra were separated by subtracting all of the other components (Fig. 2) from the fits followed by Fourier back-transformation over the width of the spectral feature from the Cu. These are the original waves; converting to relative numbers of atoms from the amplitude ratios requires the polarization correction described in the text.

Fig. 4.

Conceptual depictions of O vacancies in Sr₂CuO_3.3. The a-oriented -Cu-O- chain occupancy distribution (occupancy vs. r, where r is defined as location on a trajectory through the Cu plane) for: (A) a random, homogeneous distribution caused by no cooperation between the O atoms; (B) a moderate tendency for clustering resulting in an inhomogeneous distribution; (C) a strong tendency for clustering causing nanophase separation and a heterogeneous structure composed of domains below the diffraction limit in size consisting of either CuO₂ planes or -Cu-O- chains. (D) The corresponding structure of A. (E) The corresponding structure of C.

Since ordering of the O vacancies in the b-oriented -Cu-O- chains would be observed in the diffraction, these are likely located aperiodically. However, within the constraints of an aperiodic distribution it is still possible that the O atoms in these -Cu-O- chains cluster. At one extreme there is no cooperativity between them, these O atoms are located randomly, and their overall distribution is homogeneous on a scale sufficiently large to overcome small deviations (Fig. 4A). This random distribution results in Cu ions with two, three, and four O neighbors within the aa Cu plane whose Cu-O distances would be close to half of the 3.79-Å distance between the pairs of Cu atoms that they bridge as in La₂CuO₄ (Fig. 4D). At the other extreme these O atoms may cluster into domains with the ordered CuO₂ plane structure (Fig. 4 C and E) whose only restriction is that their size must be below the diffraction limit, which becomes larger if these domains are aperiodically distributed in the material. This distribution results in a heterogeneous, nanophase separated structure. Intermediate distributions that would be inhomogeneous (Fig. 4B) are not antithetical to any of these considerations. However, which of these possibilities actually occurs does have consequences. If these O atoms are fully clustered then it is easily understood that the superconductivity resides in the CuO₂ domains, enabled by the short pair-correlation lengths, and would be very similar to conventional cuprates except it would percolate between the domains instead of flowing unobstructed. In contrast, in the homogeneous distribution, the superconductivity would be quenched at either the vacancy or occupied sites and therefore filamentary. For YSr₂Cu_2.75Mo_0.25O_7.54, the Mo served as a probe for its own organization (6), but there is no comparable probe for the O atoms within SCO. However, our unpublished EXAFS spectra over a range of temperatures are more consistent with the random, homogeneous type of structure.

The remaining issue for the structure is local, the disposition of the O neighbors with Cu-O distances greater than 2 Å and the possibility of Sr at ∼2.8 Å. Assigning formal charges or valence, the Cu with four O neighbors therefore already has the preferred Cu²⁺ square planar geometry if Oap are missing or at longer distances that may be tilted from the c axis. Similarly, if the Oap are at their Sr₂CuO₃ positions then the Cu ions with two a-chain O vacancies will have the same Cu(II) assignment with the axial positions on the a chain vacant. This scenario implies that the Cu ions with three O neighbors from the plane would be Cu(III), which accommodates a wider range of geometries that would include their Oap neighbors. Consistent with the added charge, each adventitious O therefore results in ∼2 Cu(III) and a similar number of O in a-oriented -Cu-O- chains, with the second O coming from a displacement of an Oap into the bridging position in the chain. The varying Cu geometries will give the range of Cu-Oap distances, with disorder reducing the EXAFS amplitudes. Further insight is gained by tracking the evolution of the structure from Sr₂CuO₃ to T-La₂CuO₄ at the Sr site. The Sr in Sr₂CuO₃ has seven O nearest neighbors with Sr-O distances in a narrow range around 2.5 Å (Fig. 5A), whereas La₂CuO₄ has eight La-O from 2.6 to 2.8 Å and a ninth very short one to the apical O at 2.36 Å (Fig. 5B). Sr₂CuO₃ is presumably stable because of its high local symmetry and uniform Cu(II). In SCO this symmetry is destroyed by the half-filled b-oriented Cu-O- chains, apical O vacancies, and the mixed Cu valence. The noninteger bulk stoichiometry will also result in unit cells with different compositions and structures whose distribution lacks translational symmetry. The removal of the apical O opens an extremely large space for the Sr (Fig. 5C). Displacements of the Sr in combination with the Cu(II, III) mixture would cause collective displacements and highly unusual Sr and Cu geometries. One such possibility, a rotation of a CuO₂ moiety, is depicted (Fig. 5C). The longer Cu-O pairs could thus be Cu-Oap expanded because of the displaced Sr. The very short ∼2.8-Å Cu-Sr distance that gives the best fits of the Cu EXAFS at some temperatures would thus be somewhat analogous to the 2.7-Å Cu-Cu distances in the alkali metal MCuO₂ compounds, here caused by bent, double-O bridges.

Fig. 5.

Conceptual depictions of possible displacements in Sr₂CuO_3.3. (A) Sr₂CuO₃ with the Cu-O chains at the bottom, (B) the T structure of La₂CuO₄ with the CuO₂ planes derived from the Cu-O chains by the insertion of O bridges between the Cu pairs on the b axis of Sr₂CuO₃ at the bottom, and (C) Sr₂CuO_3.3 with the Cu atoms in the ab planes at the bottom and Oap and one of the bridging O atoms removed. The structure in C with Sr is produced from B with La by removing the central apical and a b-oriented Cu-O- chain O atoms and displacing the central Sr atom and two of its O neighbors in the directions of the arrows in B, with expanded Sr–O bonds magenta and pink, expanded Cu–O bonds turquoise. The Oap vacancy in SCO creates a large volume for the Sr atom that the chain O vacancy renders asymmetric. The O excess results in comparable amounts of Cu(II) and (III). The displacement of the Sr atom accompanied by a rotation of the O-Cu-O moiety around the b axis is a possible mechanism for giving the longer Cu-O distances found by the EXAFS. These motions would be facilitated by cooperative action of the atoms in neighboring unit cell in which the inverse motions are synchronized so that this extended set of atoms oscillate between this structure and its mirror image coherently as a tunneling polaron.

The question of the whether the O vacancies are located in the apical positions or in highly disrupted CuO₂ planes is therefore moot; they are located in both positions. The vacancies will result in substantial displacements of the O ions to give Cu and Sr geometries compatible with the Cu(II, III) combination. Collective and cooperative effects could be expected to result in preferred configurations of sets of atoms, but these would be positioned aperiodically throughout the crystal. Solving the structure in the tetragonal space group would give the average position of their projections onto the axes through the nearest Cu. In contrast, EXAFS gives a more complete depiction of this system because of its sensitivity to local order. The unpaired electron density along the a-oriented Cu-O chains resides in a different orbital than in other cuprates, and the a-b anisotropy rotates the magnetization. Superconductivity in the disrupted CuO_1.5 planes has been described: either percolation of the short coherence length superconductivity that resides in domains with the conventional CuO₂ structure, or filamentary superconductivity through continuous Cu-O networks. If ordered, two-dimensional structures with Cu and O atoms are required there is an alternative: planes in the c direction with Sr that still have a square sublattice of Cu but with a type of Cu-Sr-O unit that will have different Cu energy levels and occupations. These unique attributes of the composition, structure, magnetism, and other properties of SCO demonstrate the existence of a class of exotic superconductors. This class of materials would have the second-highest transition temperature after conventional cuprates. Under certain conditions, superconductivity can occur just as effectively via more structurally complex alternatives to the ubiquitous CuO₂ planes.

Materials and Methods

Single-phase SCO with T_c = 95 K (SI Appendix, Fig. S1) and 19% superconducting volume fraction was prepared by annealing Sr₂CuO₃ and KClO₄ in amounts giving a nominal composition of Sr₂CuO_3.3 at around 7 GPa and 1,050 °C for 30 min (17, 18). The XAFS samples were prepared by having a mixture of the Sr₂CuO_3.3 in epoxy set in the bore of a 16-T magnet. X-ray diffraction analysis of these samples showed only the Sr₂CuO_3.3 pattern (SI Appendix, Fig. S2). XAFS was measured in the continuous transmission mode on beamline 2–2 at the Stanford Synchrotron Radiation Lightsource. XAFS spectra were analyzed by standard methods (44) with curve fits using amplitudes and phases calculated by the feff9 code (45). A more detailed description is found in SI Appendix. Original data are available from S.D.C. on request (st3v3n.c0nrads0n@icloud.com).