Planar CuO_2 hole density estimation in multilayered high-T_c cuprates

TL;DR

This study establishes a reliable method using Cu-NMR Knight shift measurements at room temperature to determine the hole density in CuO_2 planes of multilayered high-T_c cuprates, enabling separate estimates for different layers.

Contribution

The paper demonstrates that the Cu-NMR Knight shift at 300 K reliably measures hole density in multilayered cuprates, including compounds with more than three CuO_2 planes, and distinguishes between layers.

Findings

K_s(300 K) increases monotonically with hole density p.

The K_s(300 K)-p relationship is valid across various multilayered cuprates.

Hole densities can be separately estimated for each CuO_2 plane.

Abstract

We report that planar CuO_2 hole densities in high-T_c cuprates are consistently determined by the Cu-NMR Knight shift. In single- and bi-layered cuprates, it is demonstrated that the spin part of the Knight shift K_s(300 K) at room temperature monotonically increases with the hole density $p$ from underdoped to overdoped regions, suggesting that the relationship of K_s(300 K) vs. p is a reliable measure to determine p. The validity of this K_s(300 K)-p relationship is confirmed by the investigation of the p-dependencies of hyperfine magnetic fields and of spin susceptibility for single- and bi-layered cuprates with tetragonal symmetry. Moreover, the analyses are compared with the NMR data on three-layered Ba_2Ca_2Cu_3O_6(F,O)_2, HgBa_2Ca_2Cu_3O_{8+delta}, and five-layered HgBa_2Ca_4Cu_5O_{12+delta}, which suggests the general applicability of the K_s(300 K)-p relationship to multilayered compounds with more than three CuO_2 planes. We remark that the measurement of K_s(300 K) enables us to separately estimate p for each CuO_2 plane in multilayered compounds, where doped hole carriers are inequivalent between outer CuO_2 planes and inner CuO_2 planes.