Nuclear Quadrupole Resonance Frequency in Multilayered Cuprates

Abstract

The 63 Cu nuclear quadrupole resonance (NQR) frequency Q in the multilayered cuprates is calculated in the cluster model by the exact diagonalization method. The charge imbalance between the outer CuO 2 plane (OP) with apical oxygen O A and the inner plane (IP) without O A in three-layered Tl 2 Ba 2 Ca 2 Cu 3 O 10 is estimated by comparing our results with the experimental Q . In Tl-based cuprates with more than three layers, we predict a large enhancement of the splitting of Q between OP and IP by taking into account the reduction in bond length between Cu and O A and the resulting increase in charge transfer energy. Our results show that the NQR frequency is a useful quantity for estimating the charge imbalance in the multilayered cuprates. Many studies have been aimed at a high superconducting transition temperature, T c . Regarding high-T c cuprates, maximum T c depends on materials, e.g., T c $ 40 K for the La family and T c $ 90 K for the Y family, even if carrier densities are optimized. In particular, among hole-doped cuprates, such material dependence closely correlates with an energy difference between in-plane and apical oxygens, Á" A .1) Actually, a spatial variation in pairing gap due to a modulation of the apical oxygen O A is observed by scanning tunneling microscopy.2,3) In addition, it is known that the disorder around the apical site is much more harmful on T c than other randomness. 4)On the other hand, the T c of multilayered cuprates correlates with the number of CuO 2 planes in a unit cell, n, and shows a maximum at n ¼ 3.5,6) One of the reasons why T c is suppressed for n > 3 is charge imbalance, [7][8][9][10][11][12] i.e., the hole concentration in pyramidally coordinated outer planes (OPs) is different from that in square-coordinated inner planes (IPs). 5,[7][8][9][10][11][12][13][14] A nuclear magnetic resonance (NMR) study has revealed that the hole concentration in OP, OP , is larger than that in IP, IP .8) The magnitude of charge imbalance, Á ¼ OP À IP , increases with n and becomes 0.10 at most for n ¼ 3.8) Such charge imbalance induces some interesting phases, e.g., two kinds of superconducting gap 7) and the coexistence of superconducting and antiferromagnetic states. [9][10][11][12]15,16) To estimate the local charge density, the nuclear quadrupole resonance (NQR) frequency Q is a useful quantity, 17,18) since Q is determined by a local charge distribution in the ground state. In the NQR measurement for three-layered Tl 2 Ba 2 Ca 2 Cu 3 O 10 (Tl2223), 18) charge imbalance has been observed as two separated peaks with an approximately 6.6 MHz difference. Here, we note that the Knight shift K c is also proportional to a local charge density on a measured site. However, one needs to examine not only the ground state but also the excited states and the neighboring spinspin interactions, since K c is proportional to the susceptibility and the transferred hyperfine couplings. 19) In addition, one needs to measure not only the 63 Cu site but also the 17 O site to estimate the hole densi...

Bulk and surface nanoscale hole density inhomogeneity in HgBa2CuO4+δand BiChen1, Khaliullin2, Sushkov3 2011Phys. Rev. B

“…The Cu NQR frequency in cuprates is therefore very sensitive to the doping level and is directly proportional to the local hole concentration. The contribution of the 3d hole to the field gradient is significantly compensated by contributions of holes located at nearby oxygens 8,9 therefore the slope of the NQR frequency versus doping varies among different cuprate families.…”