Charge density variation in YBa2Cu3O6+y

Planar Cu and O NMR and the Pseudogap of Cuprate Superconductors

Recently, an analysis of all available planar oxygen shift and relaxation data for the cuprate high-temperature superconductors showed that the data can be understood with a simple spin susceptibility from a metallic density of states common to all cuprates. It carries a doping dependent but temperature independent pseudogap at the Fermi surface, which causes the deviations from normal metallic behavior, also in the specific heat. Here, a more coherent, unbiased assessment of all data, including planar Cu, is presented and consequences are discussed, since the planar Cu data were collected and analyzed prior to the O data. The main finding is that the planar Cu shifts for one direction of the external magnetic field largely follow from the same states and pseudogap. This explains the shift suppression stated more recently, which leads to the failure of the Korringa relation in contrast to an enhancement of the relaxation due to antiferromagnetic spin fluctuations originally proposed. However, there is still the need for a second spin component that appears to be associated with the Cu 3d(x2−y2) hole to explain the complex Cu shift anisotropy and family dependence. Furthermore, it is argued that the planar Cu relaxation which was reported recently to be rather ubiquitous for the cuprates, must be related to this universal density of states and the second spin component, while not being affected by the simple pseudogap. Thus, while this universal metallic density of states with a pseudogap is also found in the planar Cu data, there is still need for a more elaborate scenario that eludes planar O.

Temperature-Independent Cuprate Pseudogap from Planar Oxygen NMR

Planar oxygen nuclear magnetic resonance (NMR) relaxation and shift data from all cuprate superconductors available in the literature are analyzed. They reveal a temperature-independent pseudogap at the Fermi surface, which increases with decreasing doping in family-specific ways, i.e., for some materials, the pseudogap is substantial at optimal doping while for others it is nearly closed at optimal doping. The states above the pseudogap, or in its absence are similar for all cuprates and doping levels, and Fermi liquid-like. If the pseudogap is assumed exponential it can be as large as about 1500 K for the most underdoped systems, relating it to the exchange coupling. The pseudogap can vary substantially throughout a material, being the cause of cuprate inhomogeneity in terms of charge and spin, so consequences for the NMR analyses are discussed. This pseudogap appears to be in agreement with the specific heat data measured for the YBaCuO family of materials, long ago. Nuclear relaxation and shift show deviations from this scenario near Tc, possibly due to other in-gap states.

Tc and Other Cuprate Properties in Relation to Planar Charges as Measured by NMR

Nuclear magnetic resonance (NMR) in cuprate research is a prominent bulk local probe of magnetic properties. NMR also, as was shown over the last years, actually provides a quantitative measure of local charges in the CuO 2 plane. This has led to fundamental insights, e.g., that the maximum T c is determined by the sharing of the parent planar hole between Cu and O. Using bonding orbital hole contents on planar Cu and O measured by NMR, instead of the total doping x, the thus defined two-dimensional cuprate phase diagram reveals significant differences between the various cuprate materials. Even more importantly, the reflected differences in material chemistry appear to set a number of electronic properties as we discuss here, for undoped, underdoped and optimally doped cuprates. These relations should advise attempts at a theoretical understanding of cuprate physics as well as inspire material chemists towards new high- T c materials. Probing planar charges, NMR is also sensitive to charge variations or ordering phenomena in the CuO 2 plane. Thereby, local charge order on planar O in optimally doped YBCO could recently be proven. Charge density variations seen by NMR in both planar bonding orbitals with amplitudes between 1% to 5% appear to be omnipresent in the doped CuO 2 plane, i.e., not limited to underdoped cuprates and low temperatures.

Bulk Charge Ordering in the CuO2 Plane of the Cuprate Superconductor YBa2Cu3O6.9 by High-Pressure NMR

Cuprate superconductors still hold many open questions, and recently, the role of symmetry breaking electronic charge ordering resurfaced in underdoped cuprates as a phenomenon that competes with superconductivity. Here, unambiguous nuclear magnetic resonance (NMR) proof is presented for the existence of local charge ordering in nearly optimally doped YBa2Cu3O6.9, even up to room temperature. Increasing pressure and decreasing temperature leads to the highest degree of order in the sense that the two oxygen atoms of the unit cell of the CuO2 plane develop a charge difference of about 0.02 holes, and order throughout the whole crystal. At ambient conditions, a slightly smaller charge difference and a decreased order is found. Evidence from literature data suggests that this charge ordering is ubiquitous to the CuO2 plane of all cuprates. Thus, the role of charge ordering in the cuprates must be reassessed.

Perspective on the phase diagram of cuprate high-temperature superconductors

Universal scaling laws can guide the understanding of new phenomena, and for cuprate high-temperature superconductivity the influential Uemura relation showed, early on, that the maximum critical temperature of superconductivity correlates with the density of the superfluid measured at low temperatures. Here we show that the charge content of the bonding orbitals of copper and oxygen in the ubiquitous CuO2 plane, measured with nuclear magnetic resonance, reproduces this scaling. The charge transfer of the nominal copper hole to planar oxygen sets the maximum critical temperature. A three-dimensional phase diagram in terms of the charge content at copper as well as oxygen is introduced, which has the different cuprate families sorted with respect to their maximum critical temperature. We suggest that the critical temperature could be raised substantially if one were able to synthesize materials that lead to an increased planar oxygen hole content at the expense of that of planar copper.