Mechanism of metallization and superconductivity suppression in YBa$_2($Cu$_{0.97}$Zn$_{0.03})_3$O$_{6.92}$ revealed by $^{67}$Zn NQR

We measure the nuclear quadrupole resonance (NQR) signal on the Zn site in nearly optimally doped YBa$_2$Cu$_3$O$_{6.92}$, when Cu is substituted by 3\% of isotopically pure $^{67}$Zn. We observe that Zn creates large insulating islands, confirming two earlier conjectures: that doping provokes an orbital transition in the CuO$_2$ plane, which is locally reversed by Zn substitution, and that the islands are antiferromagnetic. Also, we find that the Zn impurity locally induces a breaking of the D$_4$ symmetry. Cluster and DFT calculations show that the D$_4$ symmetry breaking is due to the same partial lifting of degeneracy of the nearest-neighbor oxygen sites as in the LTT transition in La$_{2-x}$Ba$_x$CuO$_4$, similarly well-known to strongly suppress superconductivity. These results show that in-plane oxygen $2p^5$ orbital configurations are principally involved in the metallicity and superconductivity of all high-T$_c$ cuprates, and provide a qualitative symmetry-based constraint on the SC mechanism.

High-temperature superconductivity (SC) in the cuprate perovskites is still unexplained. There are two effects which lower the SC temperature T c so abruptly that they may be interfering with the SC mechanism itself. One is the low-temperature orthorombic-to-tetragonal (LTO/LTT) transition in La 7/8 Ba 1/8 CuO 4 (LBCO) [1], the other is Zn substitution of the in-plane coppers. While the first is limited to the La cuprates, the Zn effect is present in all of them. NMR has found [2] that the Curie response appearing in underdoped YBa 2 Cu 3 O 7−δ (YBCO) upon Zn substitution is due to the nearestneighbor (nn) Cu sites, showing them to be electronically different than the bulk in-plane coppers, which carry no local spin in the SC compositions [3]. ARPES has established [4] that the Zn doping introduces no carriers into the planes, while STM has shown large screening oscillations around the Zn site, dubbed "desert islands" [5].
Upon its discovery, the Zn effect was argued [6] to provide a major insight into the SC orbital environment. A SC-enabling orbital transition from Cu 2+ /O 2− to Cu + /O − was conjectured [7] around 6% hole doping, which Zn was supposed to revert locally. This idea implied an oxygen-dominated SC metal. Using X-ray absorption spectroscopy, the Cu + /O − configuration was directly observed to appear in the SC compositions [8]. Including the oxygens, explicitly via the Emery model [9], or implicitly via a second-neighbor (t ) parameter [10] in the t-J model [11], was later found [12] to be necessary to interpret ARPES and neutron-scattering data, significantly, also in electron-doped cuprates [13]. Once the Sr hole in La 2−x Sr x CuO 4 was shown to remain localized [14], the above orbital transition [7,15] de facto became the default doping scenario in the cuprates, without direct experimental corroboration. Its local reversal by Zn implied a characteristic signature, a Coulomb "domino effect" of charge redistribution around the Zn site, because the charge mismatch between the O 2− configurations near Zn and O − in the bulk was not expected to be stabilized across a single Cu site [6,7].
We provide direct evidence of the conjectured orbital transition and charge redistribution by measuring the nuclear quadrupole resonance (NQR) signal on the Zn site itself. We find that Zn creates a large insulating cluster, extending at least as far as the nn coppers, even in nearly optimally doped YBCO, and that it breaks the D4 symmetry of the planar unit cell in the same way as the LTT transition in LBCO.
Optimally doped YBCO powders were prepared with nominally 3% substitution of Cu by isotopically pure 67 Zn, leading to about 4% Cu substitution in the planes, because Zn preferentially substitutes the in-plane Cu upon annealing [16]. Zn doping lowers the SC T c to 57 K with a sharp Meissner effect [17]. Zn and Cu NQR experiments were performed with a standard spin-echo sequence, using a Tecmag Apollo NMR/NQR spectrometer and a flowing gas cryostat for sample temperature variation. Due to the the small amounts of Zn and relatively low frequencies of 67 Zn NQR in YBCO, the signal was averaged many times (up to 2·10 6 for the "forbidden" NQR line, see below), while care was taken to minimize temperature drift during long acquisitions. In spin-lattice relaxation measurements we employed a saturation recovery sequence (with spin echo detection).
In pure NQR, the nuclear spin Hamiltonian reads [18] where Q is the quadrupole moment of the 67 Zn nucleus, V zz the out-of-plane principal component of the electric field gradient (EFG) tensor, η = |(V xx − V yy ) /V zz |, and I = 5/2 for 67 Zn. When the EFG tensor is axially symmetric (η = 0), this Hamiltonian gives rise to two NQR lines, corresponding to the transitions 1/2→3/2 and 3/2→5/2 with frequencies ν 3/2→5/2 = 2ν 1/2→3/2 . The measured spectrum clearly breaks axial symmetry: the two strong lines are unequally spaced, and the"forbidden" line corresponding to 1/2→5/2 can be de- All three possible transitions for spin-5/2 NQR were detected, including the"forbidden" transition 1/2→5/2, showing that the local EFG at the zinc site is not axially symmetric. For clarity, the 3/2→5/2 and 1/2→5/2 lines have been scaled by a factor of 2 and 10, respectively. tected ( Fig. 1). Detection of all three lines in the correct frequency and intensity ratios proves that the signal is really due to 67 Zn, as there are no other spin-5/2 nuclei in the system. The detected lines come from in-plane Zn nuclei, because the chain sites should have completely different symmetry (η ≈ 1), smaller EFG components, and much lower intensity, given that Zn mostly substitutes planar coppers. Indeed, in Zn NMR at 11 T we found both a central line, with intensity similar to the NQR lines in Fig. 1, and a much weaker and broadened line, consistent with a chain signal. An NQR search down to 9 MHz yielded no results, but if the Zn and Cu EFG's at the chain sites are comparable, the chain signal should be around 6 MHz, remaining unobserved.
The resonance lines barely move with temperature, indicating that the asymmetry is a property of the ground state. Thus all components of the EFG tensor at the zinc site are determined from the 67 Zn NQR spectrum alone. Using the known value of Q, we obtain (V zz , V xx , V yy ) = (−50.4, 31.5, 18.9) · 10 21 V/m 2 , yielding η = 0.25. These values are in stark contrast to those at the in-plane Cu sites; aside from the significant asymmetry, the magnitude of V zz is about five times larger than the corresponding Cu site value [19]. Obviously the charge environments of the Zn and bulk plane Cu sites are very different. Previous cluster calculations [20,21] found that the net charge at the Zn site was indeed larger than on a bulk copper site, without considering lattice distortions.
In Fig. 2 we show the temperature dependence of the 67 Zn spin-lattice relaxation, with two discernible processes at lower, and a single exponential relaxation at higher temperatures (inset). The data are irreconcilable with a metallic environment, either the usual (Korringa) 1/(T 1 T ) ∼ const., or the "nearly AF" temperature dependence 1/(T 1 T ) ∼ a + b/(T + T AF ) [22][23][24]. Although . Thick full lines are Arrhenius fits for the primary and secondary relaxation. The thin dashed line is a proposed two-phonon process correction for the secondary relaxation [17]. The slow copper relaxation process (full diamonds) is seen to follow the slow Zn relaxation. The upper inset shows two characteristic 67 Zn relaxation curves -at 250 K (full symbols) and 77 K (empty symbols) -demonstrating the existence of two processes at lower temperatures. The lines are fits to Eq. (3). The lower inset shows spin-lattice relaxation measurements of copper NQR at 31.5 MHz, which also contain a slow process at low temperatures. The large, quickly decaying contribution is of bulk copper. Lines are a guide to the eye.
the data allow a stretched-exponential fit, which would indicate local disorder, as in CDW systems [25,26], we can rule that out: even a small amount of disorder broadens the NQR line significantly. (E.g. in our sample 3% of Zn broadens the bulk-Cu NQR line by a factor of ∼ 5.) However, the relative width of the Zn lines in Fig. 1 is barely larger than the width of the Cu NQR line in the unsubstituted material, implying that the local environments of the in-plane Zn impurities are uniform, as corroborated by the Meissner effect, indicating good-quality samples. Conversely, if some Zn atoms did have different environments, their NQR lines would be strongly shifted and thus undetectable in the present measurement.
We conclude that the peculiar relaxation is an intrinsic property of every single Zn site, and quantify it by a simple two-component model. The Zn moments are insulated from the planar metal, and relax quickly by some local mechanism with a rate 1/τ 0 . They feed exclusively the nn Cu moments, which relax slowly to the environment with a rate 1/τ 1 . The magnetizations M and m of the Zn and nn Cu moments evolve according to (2) Solving the coupled system gives the 67 Zn magnetization, Such a double-exponential relaxation fits the experimental curves well, up to T ≈ 200 K, where τ 1 becomes too small to be resolved. The fits yield smaller overall leastsquare deviations than stretched-exponential fits at low temperatures. Both the"internal" fast relaxation time τ 0 and the"external" slow relaxation time τ 1 are plotted in Fig. 2, with clearly very different magnitude and temperature behaviour. The strong temperature dependence of the slow component τ 1 is well described by an Arrhenius curve of the form 1/τ 1 ∼ e −∆/kT with a gap of ∆ ∼ 0.1 eV, consistently with a superexchange interaction between the nn Cu local moments, confirming the conjecture [2] that there is a local AF cluster around the Zn site, which we argue below is insulating. We prove directly that the second-stage m(t) refers to Cu nn spins, by detecting a slow relaxation process in copper NQR. The nn Cu and bulk Cu signals overlap in pure NQR [17]. Nevertheless, a long tail due to nn Cu was detected in the NQR relaxation curves (Fig. 2, lower inset). As shown in Fig. 2, the values τ 1 (T ), extracted from this independent measurement, fall on the same curve as τ 1 (T ), showing that the same relaxation of nn Cu is being measured in two ways. Conversely, the temperature dependence of the Cu relaxation observed far from impurities and in pure YBCO [27] cannot be fitted to our τ 1 , hence the second-stage amplitude m(t) cannot refer to the bulk (metallic) Cu spins. (A somewhat similar model was proposed for nn Cu in Zn-Y248 [28].) The unambiguous identification of m(t) and the large difference between the relaxation rates of the Zn and nn Cu moments constrain our interpretation by excluding several simple alternatives. The second process has to be the slower one, or the two stages would not be resolved. The first reservoir has to feed the second exclusively, otherwise the specific algebraic relationships valid in the limit τ 0 τ 1 , would change and spoil the rescaling of the raw data, required for the extracted nn Cu τ 1 (T ) curve to coincide with the directly measured τ 1 (T ) curve in Fig. 2. Finally, the intermediate states, by which Zn moments relax to the nn Cu moments, do not thermalize, or otherwise a third magnetization reservoir would be necessary in Eq. (2) to describe the data. We can identify these intermediate states microscopically from three observed properties: the Zn relaxation is fast, it is gapped with a small gap of ∼ 20 meV (Fig. 2), and the Zn NQR line has broken D4 symmetry. The first property indicates electronic states, the second that they are localized. The third is a property of the planar ZnO 4 cluster, as we now show by two independent calculations.
We have performed a cluster DFT calculation of molecular states in plaquettes containing four Cu atoms, a central Zn impurity, and their oxygen pyramids [17,[29][30][31]. We obtain a lattice distortion with broken tetragonal symmetry, with low-lying excited states appearing with the distortion. The D4 symmetry is lost by breaking the degeneracy between the two oxygens in the planar unit cell (Fig. 3). The same symmetry breaking appears in the LTT tilt [1,32]. The excited states are ≈ 100 meV above the ground state, which is an overestimate, taking into account the crudeness of the calculation.
We also performed periodic DFT calculations [33][34][35] with supercells consisting (for simplicity) of 3 × 3 and 5 × 5 La 2 CuO 4 unit cells, with the central Cu replaced by Zn. We intentionally employ the tendency of DFT calculations to spurious metallicity, so as to model the disruption by Zn under circumstances least favorable to it. Remarkably, Zn breaks the electronic D4 symmetry in this ordered lattice even if the atoms are held fixed in their ideal-lattice positions, as shown in Fig. 4a. (In STM measurements [5] the symmetry is broken even further, with the Zn atom preferentially approaching one of the oxygens, which may be a surface effect.) Breaking the degeneracy of the two oxygens in the unit cell splits the vH singularity [32]. For realistic 4% Zn doping the excitation scale from E f drops to about 20 meV (Fig. 4b), which is an underestimate, because of the artificial periodicity and lack of atomic relaxation in the model system.
Qualitatively, the electronic D4 symmetry breaking in the periodic calculation is consistent with the deforma- tion in the small-cluster calculation. The energy scale of the local cluster is bracketed between 20 and 100 meV by these two limits. Without discussing the coupling mechanism, we conclude that the Zn moments relax to nn Cu moments via electronic states of the planar ZnO 4 cluster.
The present measurement has important repercussions for the composition of the SC metal in the cuprates. The gapped NQR relaxation of the Zn and nn Cu sites, and the large EFG's at the Zn site, are incompatible with a metallic environment. However, an insulating environment indicates that the in-plane oxygen atoms in the SC materials are in a different orbital configuration than in the parent materials [6]. One can express the proposal of Ref. [7] as a chemical reaction in the solid state, whose balance is tuned by doping. As mentioned above, the right-hand-side (rhs) configuration was observed very early [8] to appear concomitantly with SC. We observe the insulating islands precisely where the O 2p 5 (O − ) configuration of the SC metal cannot appear, because Zn is already in the 3d 10 (Zn 2+ ) configuration next to the parent 2p 6 (O 2− ). Because the parent 3d 9 (Cu 2+ ) configuration is converted to 3d 10 (Cu + ) in the SC compositions, the on-site repulsion U d , due to the large ionization energy of the 3d 8 (Cu 3+ ) configuration, is not relevant to the normal state of the SC metal at low energy. Indeed, a careful dynamical treatment of U d in the limit of significant Cu-O covalency, but starting from the 3d 10 vacuum, shows that the direct effects of U d are observed in ARPES away from the Fermi energy [36]. As described so far, the observed local reversal of the reaction (5) to the left-hand-side would reduce the SC fraction, but not necessarily the SC T c . However, we have uncovered an unsuspected effect of the Zn impurities on the SC metal itself. The Coulomb domino effect around Zn sites breaks D4 symmetry by lifting the degeneracy of the oxygens in the planes, in the same manner as the LTT tilt in LBCO [1,32]. This symmetrybreaking explains why Zn doping helps stabilize the LTT phase [37]. In Fig. 4a, it progresses to the next-nn O sites beyond the nn Cu sites (consistently with the fact that the nn Cu sites are not metallic either), involving at least the next-nn Cu sites on their other side. This observation elevates the O x -O y site-energy splitting to a universal antagonist of SC in the cuprates. Its microscopic effect on the SC is obscured in the LTT tilt, because the split vH singularity shifts electrons away from the FS [32]. Any lowering of the density of states at the FS should lower T c , whatever the SC mechanism. We find, however, that scattering on the oxygen-splitting phonon is negatively affecting the SC electrons microscopically in all cuprates, given that all are subject to the Zn effect.
The requirement that the two oxygens in the unit cell be degenerate is a qualitative constraint on the SC mechanism. It means that the oxygens need to appear in symmetry-determined, rather than parameterdetermined, superpositions, because only the former ones are singularly perturbed by even a small O x -O y splitting. One such oxygen singlet superposition was previously found [38] to destabilize the Zhang-Rice singlet [11], provided the Cu-O covalency is effectively reduced, which it is if 3d 10 is the relevant vacuum [36], as inferred here.
To conclude, we have measured the NQR signal in Znsubstituted optimally doped YBCO on the Zn sites themselves for the first time. We find that Zn creates large insulating islands, reverting the optimally doped material locally to the closed O 2p 6 orbitals characteristic of the parent compound, in which the Cu 3d 9 orbitals are open. Conversely, the SC metal is based to zeroth order on open O 2p 5 orbitals and closed Cu 3d 10 orbitals, far from the effects of the large Cu on-site repulsion U d . Zn impurities break the degeneracy of the two oxygen orbitals within a unit cell, which is strongly detrimental to SC in all cuprates, and points to the direct involvement of O x -O y degenerate superpositions in the SC mechanism.
Conversations with S. Barišić Samples. Fine (micron-sized) powder samples of nearly optimally doped YBCO were prepared for the NQR experiments by a standard solid state synthesis with repeated annealing. High-purity precursor materials were used (Y 2 O 3 , CuO and BaO, 99.99% from Sigma-Aldrich), and the zinc was introduced by substituting 3% molar of CuO with ZnO (89.6% 67 Zn enriched, from Eurisotop). Samples were characterized by powder X-ray, iodometry (to determine the amount of oxygen) and Meissner shielding measurements, to confirm their phase purity and homogeneity. While the small width of the 67 Zn NQR lines (shown in the main paper) is the most sensitive indication of the microscopic homogeneity of the samples, we show in addition the Meissner shielding measurement displaying a sharp superconducting transition (Fig. 5). Relatively large amounts of powder were used for Zn NQR due to the small concentration of zinc in the sample and low NQR frequencies -typical experimental quantities were ∼ 500 mg.
Copper NMR and NQR. In order to measure nn copper relaxation in NQR, Cu NMR spectra were recorded in a magnetic field to identify the nn signal and separate it from other further-neighbour contributions. The field-sweep spectrum is shown in Fig. 6. Different contributions were separated using an exact diagonalization of the NMR Hamiltonian with quadrupolar interactions, exploiting the fact that the nn Cu site has different sym-  metry from bulk and further-neighbour sites. The NMR lineshape could be consistently fitted with a superposition of three contributions: bulk, next-nearest (and other further) neighbours -represented by a broadened symmetrical line -and a nearest-neighbour line with broken rotational symmetry. The parameters extracted from the fit show that the pure NQR lines of nn and bulk copper overlap, while they are partially resolved in the NMR spectrum, causing a necessarily large contribution of bulk copper to the NQR relaxation measurement. The pure NQR measurements leading to the relaxation curves shown in the main paper were performed at a frequency of 31.5 MHz, where both bulk and nn contributions appear.
Zn relaxation model. The two-step relaxation model in Eq. (2) of the main paper is a coupled linear system easily solved for the two magnetizations, yielding the solution of the form given in Eq. (3) in the paper, with relaxation rates and constants The constants A ± are wholly given in terms of the two relaxation times τ 0 and τ 1 , without introducing additional fitting parameters. The fit has the same number of parameters as a stretched exponential. In the limit of short τ 1 τ 0 , the secondary relaxation process cannot be observed (α + → 1/τ 1 while A + → 0), as intuitively expected, because the magnetization reservoir m is emptied much faster than it can be refilled. In the actually realized limit of long τ 1 τ 0 , A ± → 1/2, in agreement with the experimental relaxation curves shown in Fig. 2 of the main paper. This agreement eliminates a three-step process. We note that the 'raw' spin-lattice relaxation times for Zn and Cu were corrected with the usual phase space factors (3 for spin 3/2 and 10 for spin 5/2 NQR) in obtaining Fig. 2 in the main paper.
As an additional detail, the τ 1 data points in Fig. 2 of the main paper seem to deviate from the Arrhenius curve at lowest temperatures and longest relaxation times. Although we have only one τ 1 and one τ 1 point there, the tendency of both to the same deviation brings us to tentatively propose a correction at the lowest temperatures, shown by a dashed line in the figure. It was modelled by the dominant two-phonon Raman process [18], with the characteristic temperature dependence 1/T 1 ∼ T 2 (which might actually be faster due to the relevant temperatures being close to the Debye temperature). It is not unrealistic that the transition matrix elements are small enough to lead to relaxation times of the order of 0.1 second [18]. However, the small number of data points, at the edge of the measurable range, precludes a positive identification.
Cluster DFT calculations. As the primary purpose of the cluster calculation was to explore the electronic neighbourhood of the Zn substituent and its effects on the lattice semi-quantitatively, the investigated cluster was relatively small (Fig. 7). In addition to the atoms shown, point charges were placed on the positions of the nearest Ba and Y ions. For all calculations we used the hybrid functional B3LYP and the rather simple polarized Ahlrichs basis set [29]. The RI approximation was used throughout [30]. The employed spin multiplicity of 5 corresponded to the copper atoms being quite strongly polarized, as in previous calculations [21]. In atomic relaxation calculations the furthermost in-plane and all apical oxygen atoms, and all point charges were held fixed, with other atoms free to move. Such a procedure yielded relatively large lattice deformations, which would probably be smaller in a more realistic cluster. However, the gross symmetry features of the deformation are robust with respect to calculation parameters. Due to the computational cost of high-precision calculations, we did not undertake a quantitative comparison with the observed NQR parameters, but this should in principle be possible. We checked that the weak orthorhombicity inherent in YBCO does not change the nature of the lattice deformation brought upon by Zn substitution, compared to a perfectly tetragonal initial setting. Supercell DFT calculations. For the ground state electronic structure calculation we used plane-wave selfconsistent field DFT code (PWscf), within the Quantum Espresso (QE) package [33], and Perdew-Burke-Ernzerhof (PBE) parametrization of the generalized gradient approximation (GGA) for the exchange-correlation potential [34]. The ground-state electronic density was calculated using a 5 × 5 × 1 Monkhorst-Pack special K-point mesh, with 6 special points in the irreducible Brillouin zone. In the PWscf code we used projectoraugmented-wave-based pseudopotentials for La, Cu and O atoms, and we found the energy spectrum to be convergent with a 75 Ry plane-wave cutoff. For the in-plane (1×1) unit cell parameter we used a = 7.15696 a.u. which is the experimental lattice constant commonly used in the literature. For the unit supercell in the perpendicular direction (separation between periodically repeated La 2 CuO 4 planes) we take L = 3.5a = 25.11 a.u.. The local density of states (LDOS) ρ(E, r) = n,k |ψ n,k (r)| 2 δ(E−E n,k ), which simulates the STM image, is calculated from the Kohn-Sham (KS) wave functions ψ n,k and energies E n,k obtained in the ground state calculation. The spectral function distribution for the k points along the high symmetry Γ-Σ-Y directions of the original (1×1) Brillouin zone was calculated using a recently proposed method for supercell band structure unfolding [35].